%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWW473_3 : TPTP v8.2.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n028.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 07:23:57 EDT 2024

% Result   : Theorem 6.46s 1.43s
% Output   : Refutation 6.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      : 3232
% Syntax   : Number of formulae    : 8570 (2106 unt; 752 typ;   0 def)
%            Number of atoms       : 20492 (3904 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives : 19765 (7091   ~;6972   |;2162   &)
%                                         (1780 <=>;1754  =>;   0  <=;   6 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :   11 (   2 avg)
%            Number of types       :  140 ( 139 usr)
%            Number of type conns  :  939 ( 511   >; 428   *;   0   +;   0  <<)
%            Number of predicates  : 1455 (1453 usr;1424 prp; 0-4 aty)
%            Number of functors    :  583 ( 583 usr; 102 con; 0-4 aty)
%            Number of variables   : 14492 (13685   !; 807   ?;14492   :)

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

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

tff(type_def_7,type,
    pname: $tType ).

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

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

tff(type_def_10,type,
    nat: $tType ).

tff(type_def_11,type,
    option_com: $tType ).

tff(type_def_12,type,
    fun_a_a: $tType ).

tff(type_def_13,type,
    fun_a_pname: $tType ).

tff(type_def_14,type,
    fun_a_bool: $tType ).

tff(type_def_15,type,
    fun_a_int: $tType ).

tff(type_def_16,type,
    fun_a_nat: $tType ).

tff(type_def_17,type,
    fun_a_fun_a_a: $tType ).

tff(type_def_18,type,
    fun_a_fun_a_bool: $tType ).

tff(type_def_19,type,
    fun_a_fun_pname_bool: $tType ).

tff(type_def_20,type,
    fun_a_fun_bool_bool: $tType ).

tff(type_def_21,type,
    fun_a_fun_int_bool: $tType ).

tff(type_def_22,type,
    fun_a_fun_nat_bool: $tType ).

tff(type_def_23,type,
    fun_a_1255737515l_bool: $tType ).

tff(type_def_24,type,
    fun_a_1752562919a_bool: $tType ).

tff(type_def_25,type,
    fun_pname_a: $tType ).

tff(type_def_26,type,
    fun_pname_pname: $tType ).

tff(type_def_27,type,
    fun_pname_bool: $tType ).

tff(type_def_28,type,
    fun_pname_int: $tType ).

tff(type_def_29,type,
    fun_pname_nat: $tType ).

tff(type_def_30,type,
    fun_pname_fun_a_bool: $tType ).

tff(type_def_31,type,
    fun_pn1208287926_pname: $tType ).

tff(type_def_32,type,
    fun_pn800050071e_bool: $tType ).

tff(type_def_33,type,
    fun_pn250273176l_bool: $tType ).

tff(type_def_34,type,
    fun_pn665169337t_bool: $tType ).

tff(type_def_35,type,
    fun_pn406123357t_bool: $tType ).

tff(type_def_36,type,
    fun_pn422929397l_bool: $tType ).

tff(type_def_37,type,
    fun_pn479984722e_bool: $tType ).

tff(type_def_38,type,
    fun_bool_bool: $tType ).

tff(type_def_39,type,
    fun_bo1549164019l_bool: $tType ).

tff(type_def_40,type,
    fun_int_a: $tType ).

tff(type_def_41,type,
    fun_int_pname: $tType ).

tff(type_def_42,type,
    fun_int_bool: $tType ).

tff(type_def_43,type,
    fun_int_int: $tType ).

tff(type_def_44,type,
    fun_int_fun_a_bool: $tType ).

tff(type_def_45,type,
    fun_in2065004473e_bool: $tType ).

tff(type_def_46,type,
    fun_in531499254l_bool: $tType ).

tff(type_def_47,type,
    fun_int_fun_int_bool: $tType ).

tff(type_def_48,type,
    fun_int_fun_int_int: $tType ).

tff(type_def_49,type,
    fun_int_fun_nat_bool: $tType ).

tff(type_def_50,type,
    fun_in1106722302l_bool: $tType ).

tff(type_def_51,type,
    fun_in711834963l_bool: $tType ).

tff(type_def_52,type,
    fun_in938817141l_bool: $tType ).

tff(type_def_53,type,
    fun_in719570932t_bool: $tType ).

tff(type_def_54,type,
    fun_in791894553l_bool: $tType ).

tff(type_def_55,type,
    fun_nat_a: $tType ).

tff(type_def_56,type,
    fun_nat_pname: $tType ).

tff(type_def_57,type,
    fun_nat_bool: $tType ).

tff(type_def_58,type,
    fun_nat_int: $tType ).

tff(type_def_59,type,
    fun_nat_nat: $tType ).

tff(type_def_60,type,
    fun_nat_fun_a_bool: $tType ).

tff(type_def_61,type,
    fun_na936072029e_bool: $tType ).

tff(type_def_62,type,
    fun_na1469252690l_bool: $tType ).

tff(type_def_63,type,
    fun_nat_fun_int_bool: $tType ).

tff(type_def_64,type,
    fun_nat_fun_nat_bool: $tType ).

tff(type_def_65,type,
    fun_nat_fun_nat_nat: $tType ).

tff(type_def_66,type,
    fun_na1632405922l_bool: $tType ).

tff(type_def_67,type,
    fun_na2122364079l_bool: $tType ).

tff(type_def_68,type,
    fun_na1583160273l_bool: $tType ).

tff(type_def_69,type,
    fun_na1436237685l_bool: $tType ).

tff(type_def_70,type,
    fun_na35521688t_bool: $tType ).

tff(type_def_71,type,
    fun_fun_a_bool_a: $tType ).

tff(type_def_72,type,
    fun_fun_a_bool_pname: $tType ).

tff(type_def_73,type,
    fun_fun_a_bool_bool: $tType ).

tff(type_def_74,type,
    fun_fun_a_bool_int: $tType ).

tff(type_def_75,type,
    fun_fun_a_bool_nat: $tType ).

tff(type_def_76,type,
    fun_fu1731003005a_bool: $tType ).

tff(type_def_77,type,
    fun_fu868269973a_bool: $tType ).

tff(type_def_78,type,
    fun_fu554186387l_bool: $tType ).

tff(type_def_79,type,
    fun_fu859530750t_bool: $tType ).

tff(type_def_80,type,
    fun_fu600484770t_bool: $tType ).

tff(type_def_81,type,
    fun_fu1471507361l_bool: $tType ).

tff(type_def_82,type,
    fun_fu1663643505a_bool: $tType ).

tff(type_def_83,type,
    fun_fu386216885l_bool: $tType ).

tff(type_def_84,type,
    fun_fu1434634199l_bool: $tType ).

tff(type_def_85,type,
    fun_fun_pname_bool_a: $tType ).

tff(type_def_86,type,
    fun_fu1499449723_pname: $tType ).

tff(type_def_87,type,
    fun_fu1430349052l_bool: $tType ).

tff(type_def_88,type,
    fun_fu1830380701ol_int: $tType ).

tff(type_def_89,type,
    fun_fu1668467777ol_nat: $tType ).

tff(type_def_90,type,
    fun_fu410713561e_bool: $tType ).

tff(type_def_91,type,
    fun_fu31783638l_bool: $tType ).

tff(type_def_92,type,
    fun_fu1159356667t_bool: $tType ).

tff(type_def_93,type,
    fun_fu900310687t_bool: $tType ).

tff(type_def_94,type,
    fun_fu802393907l_bool: $tType ).

tff(type_def_95,type,
    fun_fu2101097872e_bool: $tType ).

tff(type_def_96,type,
    fun_fu931343505l_bool: $tType ).

tff(type_def_97,type,
    fun_fu1232732404l_bool: $tType ).

tff(type_def_98,type,
    fun_fun_int_bool_a: $tType ).

tff(type_def_99,type,
    fun_fu953875929_pname: $tType ).

tff(type_def_100,type,
    fun_fu819804446l_bool: $tType ).

tff(type_def_101,type,
    fun_fun_int_bool_int: $tType ).

tff(type_def_102,type,
    fun_fun_int_bool_nat: $tType ).

tff(type_def_103,type,
    fun_fu989146164l_bool: $tType ).

tff(type_def_104,type,
    fun_fu554825757t_bool: $tType ).

tff(type_def_105,type,
    fun_fu380257692t_bool: $tType ).

tff(type_def_106,type,
    fun_fu295779777t_bool: $tType ).

tff(type_def_107,type,
    fun_fu1151772339l_bool: $tType ).

tff(type_def_108,type,
    fun_fu1075512626t_bool: $tType ).

tff(type_def_109,type,
    fun_fu1637550549l_bool: $tType ).

tff(type_def_110,type,
    fun_fu587680722l_bool: $tType ).

tff(type_def_111,type,
    fun_fun_nat_bool_a: $tType ).

tff(type_def_112,type,
    fun_fu665170229_pname: $tType ).

tff(type_def_113,type,
    fun_fu425979586l_bool: $tType ).

tff(type_def_114,type,
    fun_fun_nat_bool_int: $tType ).

tff(type_def_115,type,
    fun_fun_nat_bool_nat: $tType ).

tff(type_def_116,type,
    fun_fu1016514960l_bool: $tType ).

tff(type_def_117,type,
    fun_fu1080509377t_bool: $tType ).

tff(type_def_118,type,
    fun_fu821463397t_bool: $tType ).

tff(type_def_119,type,
    fun_fu429110920t_bool: $tType ).

tff(type_def_120,type,
    fun_fu1217155507l_bool: $tType ).

tff(type_def_121,type,
    fun_fu915923926t_bool: $tType ).

tff(type_def_122,type,
    fun_fu1436348701l_bool: $tType ).

tff(type_def_123,type,
    fun_fu1516990510l_bool: $tType ).

tff(type_def_124,type,
    fun_fu885608257l_bool: $tType ).

tff(type_def_125,type,
    fun_fu2020802748ol_nat: $tType ).

tff(type_def_126,type,
    fun_fu911136611l_bool: $tType ).

tff(type_def_127,type,
    fun_fu418465139l_bool: $tType ).

tff(type_def_128,type,
    fun_fu399576434l_bool: $tType ).

tff(type_def_129,type,
    fun_fu1730389579ol_nat: $tType ).

tff(type_def_130,type,
    fun_fu2087345469l_bool: $tType ).

tff(type_def_131,type,
    fun_fu1911931399l_bool: $tType ).

tff(type_def_132,type,
    fun_fu1540142484l_bool: $tType ).

tff(type_def_133,type,
    fun_fu236049833ol_nat: $tType ).

tff(type_def_134,type,
    fun_fu1070826941l_bool: $tType ).

tff(type_def_135,type,
    fun_fu209342027l_bool: $tType ).

tff(type_def_136,type,
    fun_fu814369080l_bool: $tType ).

tff(type_def_137,type,
    fun_fu411113733ol_nat: $tType ).

tff(type_def_138,type,
    fun_fu616551101l_bool: $tType ).

tff(type_def_139,type,
    fun_fu140186515l_bool: $tType ).

tff(type_def_140,type,
    fun_fu255076663l_bool: $tType ).

tff(type_def_141,type,
    fun_fu1438281908l_bool: $tType ).

tff(type_def_142,type,
    fun_fu717296342l_bool: $tType ).

tff(type_def_143,type,
    fun_fu61768826l_bool: $tType ).

tff(func_def_0,type,
    cOMBB_1897541054_pname: ( fun_a_fun_a_bool * fun_pname_a ) > fun_pname_fun_a_bool ).

tff(func_def_1,type,
    cOMBB_375279840ol_int: ( fun_a_fun_a_bool * fun_int_a ) > fun_int_fun_a_bool ).

tff(func_def_2,type,
    cOMBB_bool_bool_a: ( fun_bool_bool * fun_a_bool ) > fun_a_bool ).

tff(func_def_3,type,
    cOMBB_647938656_pname: ( fun_bool_bool * fun_pname_bool ) > fun_pname_bool ).

tff(func_def_4,type,
    cOMBB_bool_bool_int: ( fun_bool_bool * fun_int_bool ) > fun_int_bool ).

tff(func_def_5,type,
    cOMBB_bool_bool_nat: ( fun_bool_bool * fun_nat_bool ) > fun_nat_bool ).

tff(func_def_6,type,
    cOMBB_1972296269bool_a: ( fun_bo1549164019l_bool * fun_a_bool ) > fun_a_fun_bool_bool ).

tff(func_def_7,type,
    cOMBB_675860798_pname: ( fun_bo1549164019l_bool * fun_pname_bool ) > fun_pn250273176l_bool ).

tff(func_def_8,type,
    cOMBB_1652995168ol_int: ( fun_bo1549164019l_bool * fun_int_bool ) > fun_in531499254l_bool ).

tff(func_def_9,type,
    cOMBB_1015721476ol_nat: ( fun_bo1549164019l_bool * fun_nat_bool ) > fun_na1469252690l_bool ).

tff(func_def_10,type,
    cOMBB_338059395a_bool: ( fun_bo1549164019l_bool * fun_fun_a_bool_bool ) > fun_fu554186387l_bool ).

tff(func_def_11,type,
    cOMBB_2095475776e_bool: ( fun_bo1549164019l_bool * fun_fu1430349052l_bool ) > fun_fu31783638l_bool ).

tff(func_def_12,type,
    cOMBB_1974511970t_bool: ( fun_bo1549164019l_bool * fun_fu819804446l_bool ) > fun_fu989146164l_bool ).

tff(func_def_13,type,
    cOMBB_444170502t_bool: ( fun_bo1549164019l_bool * fun_fu425979586l_bool ) > fun_fu1016514960l_bool ).

tff(func_def_14,type,
    cOMBB_int_bool_nat: ( fun_int_bool * fun_nat_int ) > fun_nat_bool ).

tff(func_def_15,type,
    cOMBB_1628441366ol_nat: ( fun_int_fun_int_bool * fun_nat_int ) > fun_nat_fun_int_bool ).

tff(func_def_16,type,
    cOMBB_800536526ol_nat: ( fun_nat_fun_nat_bool * fun_nat_nat ) > fun_nat_fun_nat_bool ).

tff(func_def_17,type,
    cOMBB_1146692694ol_nat: ( fun_na1436237685l_bool * fun_nat_nat ) > fun_na1436237685l_bool ).

tff(func_def_18,type,
    cOMBB_1273333599bool_a: ( fun_fun_a_bool_bool * fun_a_fun_a_bool ) > fun_a_bool ).

tff(func_def_19,type,
    cOMBB_313729068ol_int: ( fun_fu1471507361l_bool * fun_int_fun_a_bool ) > fun_in1106722302l_bool ).

tff(func_def_20,type,
    cOMBB_1823939024ol_nat: ( fun_fu1471507361l_bool * fun_nat_fun_a_bool ) > fun_na1632405922l_bool ).

tff(func_def_21,type,
    cOMBB_607112096ol_int: ( fun_fu802393907l_bool * fun_in2065004473e_bool ) > fun_in711834963l_bool ).

tff(func_def_22,type,
    cOMBB_2117322052ol_nat: ( fun_fu802393907l_bool * fun_na936072029e_bool ) > fun_na2122364079l_bool ).

tff(func_def_23,type,
    cOMBB_1418110531ol_int: ( fun_fu819804446l_bool * fun_int_fun_int_bool ) > fun_int_bool ).

tff(func_def_24,type,
    cOMBB_1761098400ol_int: ( fun_fu1151772339l_bool * fun_int_fun_int_bool ) > fun_in938817141l_bool ).

tff(func_def_25,type,
    cOMBB_1123824708ol_nat: ( fun_fu1151772339l_bool * fun_nat_fun_int_bool ) > fun_na1583160273l_bool ).

tff(func_def_26,type,
    cOMBB_955900739ol_nat: ( fun_fu425979586l_bool * fun_nat_fun_nat_bool ) > fun_nat_bool ).

tff(func_def_27,type,
    cOMBB_516767136ol_int: ( fun_fu1217155507l_bool * fun_int_fun_nat_bool ) > fun_in791894553l_bool ).

tff(func_def_28,type,
    cOMBB_2026977092ol_nat: ( fun_fu1217155507l_bool * fun_nat_fun_nat_bool ) > fun_na1436237685l_bool ).

tff(func_def_29,type,
    cOMBC_a_a_bool: fun_a_fun_a_bool > fun_a_fun_a_bool ).

tff(func_def_30,type,
    cOMBC_1355376034l_bool: fun_a_1255737515l_bool > fun_fu1731003005a_bool ).

tff(func_def_31,type,
    cOMBC_394484100a_bool: fun_a_1752562919a_bool > fun_fu868269973a_bool ).

tff(func_def_32,type,
    cOMBC_pname_a_bool: fun_pname_fun_a_bool > fun_a_fun_pname_bool ).

tff(func_def_33,type,
    cOMBC_1149511130e_bool: fun_pn800050071e_bool > fun_pn800050071e_bool ).

tff(func_def_34,type,
    cOMBC_1058051404l_bool: fun_pn422929397l_bool > fun_fu410713561e_bool ).

tff(func_def_35,type,
    cOMBC_int_a_bool: fun_int_fun_a_bool > fun_a_fun_int_bool ).

tff(func_def_36,type,
    cOMBC_int_int_bool: fun_int_fun_int_bool > fun_int_fun_int_bool ).

tff(func_def_37,type,
    cOMBC_1753430397l_bool: fun_in1106722302l_bool > fun_fu859530750t_bool ).

tff(func_def_38,type,
    cOMBC_316919022l_bool: fun_in711834963l_bool > fun_fu1159356667t_bool ).

tff(func_def_39,type,
    cOMBC_94739984l_bool: fun_in938817141l_bool > fun_fu554825757t_bool ).

tff(func_def_40,type,
    cOMBC_1683390479t_bool: fun_in719570932t_bool > fun_fu380257692t_bool ).

tff(func_def_41,type,
    cOMBC_1848398772l_bool: fun_in791894553l_bool > fun_fu1080509377t_bool ).

tff(func_def_42,type,
    cOMBC_nat_int_bool: fun_nat_fun_int_bool > fun_int_fun_nat_bool ).

tff(func_def_43,type,
    cOMBC_nat_nat_bool: fun_nat_fun_nat_bool > fun_nat_fun_nat_bool ).

tff(func_def_44,type,
    cOMBC_1928494297l_bool: fun_na1632405922l_bool > fun_fu600484770t_bool ).

tff(func_def_45,type,
    cOMBC_386238098l_bool: fun_na2122364079l_bool > fun_fu900310687t_bool ).

tff(func_def_46,type,
    cOMBC_620423604l_bool: fun_na1583160273l_bool > fun_fu295779777t_bool ).

tff(func_def_47,type,
    cOMBC_226598744l_bool: fun_na1436237685l_bool > fun_fu821463397t_bool ).

tff(func_def_48,type,
    cOMBC_178881787t_bool: fun_na35521688t_bool > fun_fu429110920t_bool ).

tff(func_def_49,type,
    cOMBC_1732670874l_bool: fun_fu1471507361l_bool > fun_fu1471507361l_bool ).

tff(func_def_50,type,
    cOMBC_1284144636l_bool: fun_fu802393907l_bool > fun_fu802393907l_bool ).

tff(func_def_51,type,
    cOMBC_605892544l_bool: fun_fu1151772339l_bool > fun_fu1151772339l_bool ).

tff(func_def_52,type,
    cOMBC_1693257480l_bool: fun_fu1217155507l_bool > fun_fu1217155507l_bool ).

tff(func_def_53,type,
    cOMBC_331553030l_bool: fun_fu418465139l_bool > fun_fu418465139l_bool ).

tff(func_def_54,type,
    cOMBC_7971162l_bool: fun_fu1911931399l_bool > fun_fu1911931399l_bool ).

tff(func_def_55,type,
    cOMBC_348868698l_bool: fun_fu209342027l_bool > fun_fu209342027l_bool ).

tff(func_def_56,type,
    cOMBC_595898202l_bool: fun_fu140186515l_bool > fun_fu140186515l_bool ).

tff(func_def_57,type,
    cOMBI_nat: fun_nat_nat ).

tff(func_def_58,type,
    cOMBK_a_pname: x_a > fun_pname_a ).

tff(func_def_59,type,
    cOMBK_bool_a: bool > fun_a_bool ).

tff(func_def_60,type,
    cOMBK_bool_int: bool > fun_int_bool ).

tff(func_def_61,type,
    cOMBK_bool_nat: bool > fun_nat_bool ).

tff(func_def_62,type,
    cOMBK_int_nat: int > fun_nat_int ).

tff(func_def_63,type,
    cOMBS_a_bool_bool: ( fun_a_fun_bool_bool * fun_a_bool ) > fun_a_bool ).

tff(func_def_64,type,
    cOMBS_568398431l_bool: ( fun_pn250273176l_bool * fun_pname_bool ) > fun_pname_bool ).

tff(func_def_65,type,
    cOMBS_int_bool_bool: ( fun_in531499254l_bool * fun_int_bool ) > fun_int_bool ).

tff(func_def_66,type,
    cOMBS_nat_bool_bool: ( fun_na1469252690l_bool * fun_nat_bool ) > fun_nat_bool ).

tff(func_def_67,type,
    cOMBS_1035972772l_bool: ( fun_fu554186387l_bool * fun_fun_a_bool_bool ) > fun_fun_a_bool_bool ).

tff(func_def_68,type,
    cOMBS_350070575l_bool: ( fun_fu31783638l_bool * fun_fu1430349052l_bool ) > fun_fu1430349052l_bool ).

tff(func_def_69,type,
    cOMBS_1912792529l_bool: ( fun_fu989146164l_bool * fun_fu819804446l_bool ) > fun_fu819804446l_bool ).

tff(func_def_70,type,
    cOMBS_1187019125l_bool: ( fun_fu1016514960l_bool * fun_fu425979586l_bool ) > fun_fu425979586l_bool ).

tff(func_def_71,type,
    body: pname > option_com ).

tff(func_def_72,type,
    finite_card_a: fun_fun_a_bool_nat ).

tff(func_def_73,type,
    finite_card_pname: fun_fu1668467777ol_nat ).

tff(func_def_74,type,
    finite_card_int: fun_fun_int_bool_nat ).

tff(func_def_75,type,
    finite_card_nat: fun_fun_nat_bool_nat ).

tff(func_def_76,type,
    finite1306199131a_bool: fun_fu2020802748ol_nat ).

tff(func_def_77,type,
    finite1340463720e_bool: fun_fu1730389579ol_nat ).

tff(func_def_78,type,
    finite1876863882t_bool: fun_fu236049833ol_nat ).

tff(func_def_79,type,
    finite346522414t_bool: fun_fu411113733ol_nat ).

tff(func_def_80,type,
    finite_finite_a: fun_fun_a_bool_bool ).

tff(func_def_81,type,
    finite_finite_pname: fun_fu1430349052l_bool ).

tff(func_def_82,type,
    finite_finite_int: fun_fu819804446l_bool ).

tff(func_def_83,type,
    finite_finite_nat: fun_fu425979586l_bool ).

tff(func_def_84,type,
    finite347923420a_bool: fun_fu885608257l_bool ).

tff(func_def_85,type,
    finite595471783e_bool: fun_fu399576434l_bool ).

tff(func_def_86,type,
    finite1395289673t_bool: fun_fu1540142484l_bool ).

tff(func_def_87,type,
    finite2012431853t_bool: fun_fu814369080l_bool ).

tff(func_def_88,type,
    finite1381704300l_bool: fun_fu255076663l_bool ).

tff(func_def_89,type,
    finite786885583l_bool: fun_fu1438281908l_bool ).

tff(func_def_90,type,
    finite2095298929l_bool: fun_fu717296342l_bool ).

tff(func_def_91,type,
    finite1701474069l_bool: fun_fu61768826l_bool ).

tff(func_def_92,type,
    finite_folding_one_a: ( fun_a_fun_a_a * fun_fun_a_bool_a ) > bool ).

tff(func_def_93,type,
    finite1282449217_pname: ( fun_pn1208287926_pname * fun_fu1499449723_pname ) > bool ).

tff(func_def_94,type,
    finite1626084323ne_int: ( fun_int_fun_int_int * fun_fun_int_bool_int ) > bool ).

tff(func_def_95,type,
    finite988810631ne_nat: ( fun_nat_fun_nat_nat * fun_fun_nat_bool_nat ) > bool ).

tff(func_def_96,type,
    finite1819937229idem_a: ( fun_a_fun_a_a * fun_fun_a_bool_a ) > bool ).

tff(func_def_97,type,
    finite89670078_pname: ( fun_pn1208287926_pname * fun_fu1499449723_pname ) > bool ).

tff(func_def_98,type,
    finite1432773856em_int: ( fun_int_fun_int_int * fun_fun_int_bool_int ) > bool ).

tff(func_def_99,type,
    finite795500164em_nat: ( fun_nat_fun_nat_nat * fun_fun_nat_bool_nat ) > bool ).

tff(func_def_100,type,
    abs_abs_int: int > int ).

tff(func_def_101,type,
    minus_minus_int: fun_int_fun_int_int ).

tff(func_def_102,type,
    minus_minus_nat: fun_nat_fun_nat_nat ).

tff(func_def_103,type,
    minus_1762468890a_bool: fun_fu1663643505a_bool ).

tff(func_def_104,type,
    minus_1015773161e_bool: fun_fu2101097872e_bool ).

tff(func_def_105,type,
    minus_1449998731t_bool: fun_fu1075512626t_bool ).

tff(func_def_106,type,
    minus_2067140911t_bool: fun_fu915923926t_bool ).

tff(func_def_107,type,
    one_one_int: int ).

tff(func_def_108,type,
    one_one_nat: nat ).

tff(func_def_109,type,
    plus_plus_int: fun_int_fun_int_int ).

tff(func_def_110,type,
    plus_plus_nat: fun_nat_fun_nat_nat ).

tff(func_def_111,type,
    times_times_int: fun_int_fun_int_int ).

tff(func_def_112,type,
    times_times_nat: fun_nat_fun_nat_nat ).

tff(func_def_113,type,
    zero_zero_int: int ).

tff(func_def_114,type,
    zero_zero_nat: nat ).

tff(func_def_115,type,
    the_a: fun_fun_a_bool_a ).

tff(func_def_116,type,
    the_int: fun_fun_int_bool_int ).

tff(func_def_117,type,
    the_nat: fun_fun_nat_bool_nat ).

tff(func_def_118,type,
    if_nat: bool > fun_nat_fun_nat_nat ).

tff(func_def_119,type,
    bit1: int > int ).

tff(func_def_120,type,
    pls: int ).

tff(func_def_121,type,
    number_number_of_int: int > int ).

tff(func_def_122,type,
    number_number_of_nat: int > nat ).

tff(func_def_123,type,
    succ: int > int ).

tff(func_def_124,type,
    suc: fun_nat_nat ).

tff(func_def_125,type,
    nat_case_bool: ( bool * fun_nat_bool ) > fun_nat_bool ).

tff(func_def_126,type,
    nat_case_nat: ( nat * fun_nat_nat ) > fun_nat_nat ).

tff(func_def_127,type,
    semiri1621563631at_int: fun_nat_int ).

tff(func_def_128,type,
    nat_neg: fun_int_bool ).

tff(func_def_129,type,
    nat_tsub: fun_int_fun_int_int ).

tff(func_def_130,type,
    the_com: option_com > com ).

tff(func_def_131,type,
    bot_bot_bool: bool ).

tff(func_def_132,type,
    bot_bot_nat: nat ).

tff(func_def_133,type,
    bot_bot_fun_a_bool: fun_a_bool ).

tff(func_def_134,type,
    bot_bo844097828e_bool: fun_pname_bool ).

tff(func_def_135,type,
    bot_bot_fun_int_bool: fun_int_bool ).

tff(func_def_136,type,
    bot_bot_fun_nat_bool: fun_nat_bool ).

tff(func_def_137,type,
    ord_less_int: fun_int_fun_int_bool ).

tff(func_def_138,type,
    ord_less_nat: fun_nat_fun_nat_bool ).

tff(func_def_139,type,
    ord_le1912455174t_bool: fun_fu1151772339l_bool ).

tff(func_def_140,type,
    ord_le382113706t_bool: fun_fu1217155507l_bool ).

tff(func_def_141,type,
    ord_less_eq_bool: fun_bo1549164019l_bool ).

tff(func_def_142,type,
    ord_less_eq_int: fun_int_fun_int_bool ).

tff(func_def_143,type,
    ord_less_eq_nat: fun_nat_fun_nat_bool ).

tff(func_def_144,type,
    ord_le1311769555a_bool: fun_fu1471507361l_bool ).

tff(func_def_145,type,
    ord_le313189616e_bool: fun_fu802393907l_bool ).

tff(func_def_146,type,
    ord_le951220754t_bool: fun_fu1151772339l_bool ).

tff(func_def_147,type,
    ord_le1568362934t_bool: fun_fu1217155507l_bool ).

tff(func_def_148,type,
    ord_le1375614389l_bool: fun_fu418465139l_bool ).

tff(func_def_149,type,
    ord_le675606854l_bool: fun_fu1911931399l_bool ).

tff(func_def_150,type,
    ord_le1848167016l_bool: fun_fu209342027l_bool ).

tff(func_def_151,type,
    ord_le1454342156l_bool: fun_fu140186515l_bool ).

tff(func_def_152,type,
    collect_a: fun_a_bool > fun_a_bool ).

tff(func_def_153,type,
    collect_pname: fun_pname_bool > fun_pname_bool ).

tff(func_def_154,type,
    collect_int: fun_int_bool > fun_int_bool ).

tff(func_def_155,type,
    collect_nat: fun_nat_bool > fun_nat_bool ).

tff(func_def_156,type,
    collect_fun_a_bool: fun_fun_a_bool_bool > fun_fun_a_bool_bool ).

tff(func_def_157,type,
    collec1974731493e_bool: fun_fu1430349052l_bool > fun_fu1430349052l_bool ).

tff(func_def_158,type,
    collect_fun_int_bool: fun_fu819804446l_bool > fun_fu819804446l_bool ).

tff(func_def_159,type,
    collect_fun_nat_bool: fun_fu425979586l_bool > fun_fu425979586l_bool ).

tff(func_def_160,type,
    collec707592106l_bool: fun_fu885608257l_bool > fun_fu885608257l_bool ).

tff(func_def_161,type,
    collec1613912337l_bool: fun_fu399576434l_bool > fun_fu399576434l_bool ).

tff(func_def_162,type,
    collec1409689523l_bool: fun_fu1540142484l_bool > fun_fu1540142484l_bool ).

tff(func_def_163,type,
    collec1015864663l_bool: fun_fu814369080l_bool > fun_fu814369080l_bool ).

tff(func_def_164,type,
    image_a_a: ( fun_a_a * fun_a_bool ) > fun_a_bool ).

tff(func_def_165,type,
    image_a_pname: ( fun_a_pname * fun_a_bool ) > fun_pname_bool ).

tff(func_def_166,type,
    image_a_int: ( fun_a_int * fun_a_bool ) > fun_int_bool ).

tff(func_def_167,type,
    image_a_nat: ( fun_a_nat * fun_a_bool ) > fun_nat_bool ).

tff(func_def_168,type,
    image_a_fun_a_bool: ( fun_a_fun_a_bool * fun_a_bool ) > fun_fun_a_bool_bool ).

tff(func_def_169,type,
    image_819518260e_bool: ( fun_a_fun_pname_bool * fun_a_bool ) > fun_fu1430349052l_bool ).

tff(func_def_170,type,
    image_a_fun_int_bool: ( fun_a_fun_int_bool * fun_a_bool ) > fun_fu819804446l_bool ).

tff(func_def_171,type,
    image_a_fun_nat_bool: ( fun_a_fun_nat_bool * fun_a_bool ) > fun_fu425979586l_bool ).

tff(func_def_172,type,
    image_pname_a: ( fun_pname_a * fun_pname_bool ) > fun_a_bool ).

tff(func_def_173,type,
    image_pname_pname: ( fun_pname_pname * fun_pname_bool ) > fun_pname_bool ).

tff(func_def_174,type,
    image_pname_int: ( fun_pname_int * fun_pname_bool ) > fun_int_bool ).

tff(func_def_175,type,
    image_pname_nat: ( fun_pname_nat * fun_pname_bool ) > fun_nat_bool ).

tff(func_def_176,type,
    image_112932426a_bool: ( fun_pname_fun_a_bool * fun_pname_bool ) > fun_fun_a_bool_bool ).

tff(func_def_177,type,
    image_47868345e_bool: ( fun_pn800050071e_bool * fun_pname_bool ) > fun_fu1430349052l_bool ).

tff(func_def_178,type,
    image_1512837979t_bool: ( fun_pn665169337t_bool * fun_pname_bool ) > fun_fu819804446l_bool ).

tff(func_def_179,type,
    image_2129980159t_bool: ( fun_pn406123357t_bool * fun_pname_bool ) > fun_fu425979586l_bool ).

tff(func_def_180,type,
    image_int_a: ( fun_int_a * fun_int_bool ) > fun_a_bool ).

tff(func_def_181,type,
    image_int_pname: ( fun_int_pname * fun_int_bool ) > fun_pname_bool ).

tff(func_def_182,type,
    image_int_fun_a_bool: ( fun_int_fun_a_bool * fun_int_bool ) > fun_fun_a_bool_bool ).

tff(func_def_183,type,
    image_637364955e_bool: ( fun_in2065004473e_bool * fun_int_bool ) > fun_fu1430349052l_bool ).

tff(func_def_184,type,
    image_275383677t_bool: ( fun_int_fun_int_bool * fun_int_bool ) > fun_fu819804446l_bool ).

tff(func_def_185,type,
    image_892525857t_bool: ( fun_int_fun_nat_bool * fun_int_bool ) > fun_fu425979586l_bool ).

tff(func_def_186,type,
    image_nat_a: ( fun_nat_a * fun_nat_bool ) > fun_a_bool ).

tff(func_def_187,type,
    image_nat_pname: ( fun_nat_pname * fun_nat_bool ) > fun_pname_bool ).

tff(func_def_188,type,
    image_nat_int: ( fun_nat_int * fun_nat_bool ) > fun_int_bool ).

tff(func_def_189,type,
    image_nat_fun_a_bool: ( fun_nat_fun_a_bool * fun_nat_bool ) > fun_fun_a_bool_bool ).

tff(func_def_190,type,
    image_1655916159e_bool: ( fun_na936072029e_bool * fun_nat_bool ) > fun_fu1430349052l_bool ).

tff(func_def_191,type,
    image_1556378401t_bool: ( fun_nat_fun_int_bool * fun_nat_bool ) > fun_fu819804446l_bool ).

tff(func_def_192,type,
    image_26036933t_bool: ( fun_nat_fun_nat_bool * fun_nat_bool ) > fun_fu425979586l_bool ).

tff(func_def_193,type,
    image_fun_a_bool_a: ( fun_fun_a_bool_a * fun_fun_a_bool_bool ) > fun_a_bool ).

tff(func_def_194,type,
    image_1854862208_pname: ( fun_fun_a_bool_pname * fun_fun_a_bool_bool ) > fun_pname_bool ).

tff(func_def_195,type,
    image_fun_a_bool_int: ( fun_fun_a_bool_int * fun_fun_a_bool_bool ) > fun_int_bool ).

tff(func_def_196,type,
    image_fun_a_bool_nat: ( fun_fun_a_bool_nat * fun_fun_a_bool_bool ) > fun_nat_bool ).

tff(func_def_197,type,
    image_876012084bool_a: ( fun_fun_pname_bool_a * fun_fu1430349052l_bool ) > fun_a_bool ).

tff(func_def_198,type,
    image_1283814551_pname: ( fun_fu1499449723_pname * fun_fu1430349052l_bool ) > fun_pname_bool ).

tff(func_def_199,type,
    image_41399353ol_int: ( fun_fu1830380701ol_int * fun_fu1430349052l_bool ) > fun_int_bool ).

tff(func_def_200,type,
    image_1551609309ol_nat: ( fun_fu1668467777ol_nat * fun_fu1430349052l_bool ) > fun_nat_bool ).

tff(func_def_201,type,
    image_fun_int_bool_a: ( fun_fun_int_bool_a * fun_fu819804446l_bool ) > fun_a_bool ).

tff(func_def_202,type,
    image_62782965_pname: ( fun_fu953875929_pname * fun_fu819804446l_bool ) > fun_pname_bool ).

tff(func_def_203,type,
    image_2069007511ol_int: ( fun_fun_int_bool_int * fun_fu819804446l_bool ) > fun_int_bool ).

tff(func_def_204,type,
    image_1431733819ol_nat: ( fun_fun_int_bool_nat * fun_fu819804446l_bool ) > fun_nat_bool ).

tff(func_def_205,type,
    image_fun_nat_bool_a: ( fun_fun_nat_bool_a * fun_fu425979586l_bool ) > fun_a_bool ).

tff(func_def_206,type,
    image_1921560913_pname: ( fun_fu665170229_pname * fun_fu425979586l_bool ) > fun_pname_bool ).

tff(func_def_207,type,
    image_1133522419ol_int: ( fun_fun_nat_bool_int * fun_fu425979586l_bool ) > fun_int_bool ).

tff(func_def_208,type,
    image_496248727ol_nat: ( fun_fun_nat_bool_nat * fun_fu425979586l_bool ) > fun_nat_bool ).

tff(func_def_209,type,
    insert_a: fun_a_1752562919a_bool ).

tff(func_def_210,type,
    insert_pname: fun_pn479984722e_bool ).

tff(func_def_211,type,
    insert_int: fun_in719570932t_bool ).

tff(func_def_212,type,
    insert_nat: fun_na35521688t_bool ).

tff(func_def_213,type,
    insert_fun_a_bool: fun_fu1434634199l_bool ).

tff(func_def_214,type,
    insert1325755072e_bool: fun_fu1232732404l_bool ).

tff(func_def_215,type,
    insert_fun_int_bool: fun_fu587680722l_bool ).

tff(func_def_216,type,
    insert_fun_nat_bool: fun_fu1516990510l_bool ).

tff(func_def_217,type,
    the_elem_a: fun_fun_a_bool_a ).

tff(func_def_218,type,
    the_elem_int: fun_fun_int_bool_int ).

tff(func_def_219,type,
    the_elem_nat: fun_fun_nat_bool_nat ).

tff(func_def_220,type,
    fFalse: bool ).

tff(func_def_221,type,
    fNot: fun_bool_bool ).

tff(func_def_222,type,
    fTrue: bool ).

tff(func_def_223,type,
    fconj: fun_bo1549164019l_bool ).

tff(func_def_224,type,
    fdisj: fun_bo1549164019l_bool ).

tff(func_def_225,type,
    fequal_a: fun_a_fun_a_bool ).

tff(func_def_226,type,
    fequal_pname: fun_pn800050071e_bool ).

tff(func_def_227,type,
    fequal_int: fun_int_fun_int_bool ).

tff(func_def_228,type,
    fequal_nat: fun_nat_fun_nat_bool ).

tff(func_def_229,type,
    fequal_fun_a_bool: fun_fu1471507361l_bool ).

tff(func_def_230,type,
    fequal533582459e_bool: fun_fu802393907l_bool ).

tff(func_def_231,type,
    fequal_fun_int_bool: fun_fu1151772339l_bool ).

tff(func_def_232,type,
    fequal_fun_nat_bool: fun_fu1217155507l_bool ).

tff(func_def_233,type,
    fimplies: fun_bo1549164019l_bool ).

tff(func_def_234,type,
    hAPP_a_a: ( fun_a_a * x_a ) > x_a ).

tff(func_def_235,type,
    hAPP_a_bool: ( fun_a_bool * x_a ) > bool ).

tff(func_def_236,type,
    hAPP_a_fun_a_a: ( fun_a_fun_a_a * x_a ) > fun_a_a ).

tff(func_def_237,type,
    hAPP_a_fun_a_bool: ( fun_a_fun_a_bool * x_a ) > fun_a_bool ).

tff(func_def_238,type,
    hAPP_a93125764e_bool: ( fun_a_fun_pname_bool * x_a ) > fun_pname_bool ).

tff(func_def_239,type,
    hAPP_a_fun_bool_bool: ( fun_a_fun_bool_bool * x_a ) > fun_bool_bool ).

tff(func_def_240,type,
    hAPP_a_fun_int_bool: ( fun_a_fun_int_bool * x_a ) > fun_int_bool ).

tff(func_def_241,type,
    hAPP_a85458249l_bool: ( fun_a_1255737515l_bool * x_a ) > fun_fun_a_bool_bool ).

tff(func_def_242,type,
    hAPP_a1206381875a_bool: ( fun_a_1752562919a_bool * x_a ) > fun_fu1731003005a_bool ).

tff(func_def_243,type,
    hAPP_pname_a: ( fun_pname_a * pname ) > x_a ).

tff(func_def_244,type,
    hAPP_pname_pname: ( fun_pname_pname * pname ) > pname ).

tff(func_def_245,type,
    hAPP_pname_bool: ( fun_pname_bool * pname ) > bool ).

tff(func_def_246,type,
    hAPP_p1534023578a_bool: ( fun_pname_fun_a_bool * pname ) > fun_a_bool ).

tff(func_def_247,type,
    hAPP_p1170154830_pname: ( fun_pn1208287926_pname * pname ) > fun_pname_pname ).

tff(func_def_248,type,
    hAPP_p61793385e_bool: ( fun_pn800050071e_bool * pname ) > fun_pname_bool ).

tff(func_def_249,type,
    hAPP_p393069232l_bool: ( fun_pn250273176l_bool * pname ) > fun_bool_bool ).

tff(func_def_250,type,
    hAPP_p338031245l_bool: ( fun_pn422929397l_bool * pname ) > fun_fu1430349052l_bool ).

tff(func_def_251,type,
    hAPP_p905327722e_bool: ( fun_pn479984722e_bool * pname ) > fun_fu410713561e_bool ).

tff(func_def_252,type,
    hAPP_bool_bool: ( fun_bool_bool * bool ) > bool ).

tff(func_def_253,type,
    hAPP_b589554111l_bool: ( fun_bo1549164019l_bool * bool ) > fun_bool_bool ).

tff(func_def_254,type,
    hAPP_int_a: ( fun_int_a * int ) > x_a ).

tff(func_def_255,type,
    hAPP_int_bool: ( fun_int_bool * int ) > bool ).

tff(func_def_256,type,
    hAPP_int_int: ( fun_int_int * int ) > int ).

tff(func_def_257,type,
    hAPP_int_fun_a_bool: ( fun_int_fun_a_bool * int ) > fun_a_bool ).

tff(func_def_258,type,
    hAPP_i7355787e_bool: ( fun_in2065004473e_bool * int ) > fun_pname_bool ).

tff(func_def_259,type,
    hAPP_i68813070l_bool: ( fun_in531499254l_bool * int ) > fun_bool_bool ).

tff(func_def_260,type,
    hAPP_i1948725293t_bool: ( fun_int_fun_int_bool * int ) > fun_int_bool ).

tff(func_def_261,type,
    hAPP_int_fun_int_int: ( fun_int_fun_int_int * int ) > fun_int_int ).

tff(func_def_262,type,
    hAPP_i418383825t_bool: ( fun_int_fun_nat_bool * int ) > fun_nat_bool ).

tff(func_def_263,type,
    hAPP_i888906320l_bool: ( fun_in1106722302l_bool * int ) > fun_fun_a_bool_bool ).

tff(func_def_264,type,
    hAPP_i1587699435l_bool: ( fun_in711834963l_bool * int ) > fun_fu1430349052l_bool ).

tff(func_def_265,type,
    hAPP_i2112223885l_bool: ( fun_in938817141l_bool * int ) > fun_fu819804446l_bool ).

tff(func_def_266,type,
    hAPP_i1529485324t_bool: ( fun_in719570932t_bool * int ) > fun_fu554825757t_bool ).

tff(func_def_267,type,
    hAPP_i1718399025l_bool: ( fun_in791894553l_bool * int ) > fun_fu425979586l_bool ).

tff(func_def_268,type,
    hAPP_nat_bool: ( fun_nat_bool * nat ) > bool ).

tff(func_def_269,type,
    hAPP_nat_int: ( fun_nat_int * nat ) > int ).

tff(func_def_270,type,
    hAPP_nat_nat: ( fun_nat_nat * nat ) > nat ).

tff(func_def_271,type,
    hAPP_nat_fun_a_bool: ( fun_nat_fun_a_bool * nat ) > fun_a_bool ).

tff(func_def_272,type,
    hAPP_n1025906991e_bool: ( fun_na936072029e_bool * nat ) > fun_pname_bool ).

tff(func_def_273,type,
    hAPP_n1006566506l_bool: ( fun_na1469252690l_bool * nat ) > fun_bool_bool ).

tff(func_def_274,type,
    hAPP_n1082236369t_bool: ( fun_nat_fun_int_bool * nat ) > fun_int_bool ).

tff(func_def_275,type,
    hAPP_n1699378549t_bool: ( fun_nat_fun_nat_bool * nat ) > fun_nat_bool ).

tff(func_def_276,type,
    hAPP_nat_fun_nat_nat: ( fun_nat_fun_nat_nat * nat ) > fun_nat_nat ).

tff(func_def_277,type,
    hAPP_n1414589940l_bool: ( fun_na1632405922l_bool * nat ) > fun_fun_a_bool_bool ).

tff(func_def_278,type,
    hAPP_n850744903l_bool: ( fun_na2122364079l_bool * nat ) > fun_fu1430349052l_bool ).

tff(func_def_279,type,
    hAPP_n609083369l_bool: ( fun_na1583160273l_bool * nat ) > fun_fu819804446l_bool ).

tff(func_def_280,type,
    hAPP_n215258509l_bool: ( fun_na1436237685l_bool * nat ) > fun_fu425979586l_bool ).

tff(func_def_281,type,
    hAPP_n1512601776t_bool: ( fun_na35521688t_bool * nat ) > fun_fu821463397t_bool ).

tff(func_def_282,type,
    hAPP_fun_a_bool_a: ( fun_fun_a_bool_a * fun_a_bool ) > x_a ).

tff(func_def_283,type,
    hAPP_fun_a_bool_bool: ( fun_fun_a_bool_bool * fun_a_bool ) > bool ).

tff(func_def_284,type,
    hAPP_fun_a_bool_nat: ( fun_fun_a_bool_nat * fun_a_bool ) > nat ).

tff(func_def_285,type,
    hAPP_f2050579477a_bool: ( fun_fu1731003005a_bool * fun_a_bool ) > fun_a_bool ).

tff(func_def_286,type,
    hAPP_f1038053735a_bool: ( fun_fu868269973a_bool * fun_a_bool ) > fun_a_fun_a_bool ).

tff(func_def_287,type,
    hAPP_f198738859l_bool: ( fun_fu554186387l_bool * fun_a_bool ) > fun_bool_bool ).

tff(func_def_288,type,
    hAPP_f1812805200t_bool: ( fun_fu859530750t_bool * fun_a_bool ) > fun_int_bool ).

tff(func_def_289,type,
    hAPP_f282463732t_bool: ( fun_fu600484770t_bool * fun_a_bool ) > fun_nat_bool ).

tff(func_def_290,type,
    hAPP_f1631501043l_bool: ( fun_fu1471507361l_bool * fun_a_bool ) > fun_fun_a_bool_bool ).

tff(func_def_291,type,
    hAPP_f1791771145a_bool: ( fun_fu1663643505a_bool * fun_a_bool ) > fun_fu1731003005a_bool ).

tff(func_def_292,type,
    hAPP_f285962445l_bool: ( fun_fu386216885l_bool * fun_a_bool ) > fun_fu885608257l_bool ).

tff(func_def_293,type,
    hAPP_f1531278575l_bool: ( fun_fu1434634199l_bool * fun_a_bool ) > fun_fu911136611l_bool ).

tff(func_def_294,type,
    hAPP_f1297739591_pname: ( fun_fu1499449723_pname * fun_pname_bool ) > pname ).

tff(func_def_295,type,
    hAPP_f1664156314l_bool: ( fun_fu1430349052l_bool * fun_pname_bool ) > bool ).

tff(func_def_296,type,
    hAPP_f921600141ol_nat: ( fun_fu1668467777ol_nat * fun_pname_bool ) > nat ).

tff(func_def_297,type,
    hAPP_f759274231e_bool: ( fun_fu410713561e_bool * fun_pname_bool ) > fun_pname_bool ).

tff(func_def_298,type,
    hAPP_f1476298914l_bool: ( fun_fu31783638l_bool * fun_pname_bool ) > fun_bool_bool ).

tff(func_def_299,type,
    hAPP_f449020825t_bool: ( fun_fu1159356667t_bool * fun_pname_bool ) > fun_int_bool ).

tff(func_def_300,type,
    hAPP_f1066163005t_bool: ( fun_fu900310687t_bool * fun_pname_bool ) > fun_nat_bool ).

tff(func_def_301,type,
    hAPP_f434788991l_bool: ( fun_fu802393907l_bool * fun_pname_bool ) > fun_fu1430349052l_bool ).

tff(func_def_302,type,
    hAPP_f1388330588e_bool: ( fun_fu2101097872e_bool * fun_pname_bool ) > fun_fu410713561e_bool ).

tff(func_def_303,type,
    hAPP_f556039215l_bool: ( fun_fu931343505l_bool * fun_pname_bool ) > fun_fu399576434l_bool ).

tff(func_def_304,type,
    hAPP_f1320879424l_bool: ( fun_fu1232732404l_bool * fun_pname_bool ) > fun_fu2087345469l_bool ).

tff(func_def_305,type,
    hAPP_f448129468l_bool: ( fun_fu819804446l_bool * fun_int_bool ) > bool ).

tff(func_def_306,type,
    hAPP_f1594865479ol_int: ( fun_fun_int_bool_int * fun_int_bool ) > int ).

tff(func_def_307,type,
    hAPP_f957591787ol_nat: ( fun_fun_int_bool_nat * fun_int_bool ) > nat ).

tff(func_def_308,type,
    hAPP_f1721100032l_bool: ( fun_fu989146164l_bool * fun_int_bool ) > fun_bool_bool ).

tff(func_def_309,type,
    hAPP_f1805168059t_bool: ( fun_fu554825757t_bool * fun_int_bool ) > fun_int_bool ).

tff(func_def_310,type,
    hAPP_f1048215610t_bool: ( fun_fu380257692t_bool * fun_int_bool ) > fun_int_fun_int_bool ).

tff(func_def_311,type,
    hAPP_f274826591t_bool: ( fun_fu295779777t_bool * fun_int_bool ) > fun_nat_bool ).

tff(func_def_312,type,
    hAPP_f284875647l_bool: ( fun_fu1151772339l_bool * fun_int_bool ) > fun_fu819804446l_bool ).

tff(func_def_313,type,
    hAPP_f1223193598t_bool: ( fun_fu1075512626t_bool * fun_int_bool ) > fun_fu554825757t_bool ).

tff(func_def_314,type,
    hAPP_f628503027l_bool: ( fun_fu1637550549l_bool * fun_int_bool ) > fun_fu1540142484l_bool ).

tff(func_def_315,type,
    hAPP_f587666462l_bool: ( fun_fu587680722l_bool * fun_int_bool ) > fun_fu1070826941l_bool ).

tff(func_def_316,type,
    hAPP_f54304608l_bool: ( fun_fu425979586l_bool * fun_nat_bool ) > bool ).

tff(func_def_317,type,
    hAPP_f22106695ol_nat: ( fun_fun_nat_bool_nat * fun_nat_bool ) > nat ).

tff(func_def_318,type,
    hAPP_f1748468828l_bool: ( fun_fu1016514960l_bool * fun_nat_bool ) > fun_bool_bool ).

tff(func_def_319,type,
    hAPP_f183368031t_bool: ( fun_fu1080509377t_bool * fun_nat_bool ) > fun_int_bool ).

tff(func_def_320,type,
    hAPP_f800510211t_bool: ( fun_fu821463397t_bool * fun_nat_bool ) > fun_nat_bool ).

tff(func_def_321,type,
    hAPP_f1570313510t_bool: ( fun_fu429110920t_bool * fun_nat_bool ) > fun_nat_fun_nat_bool ).

tff(func_def_322,type,
    hAPP_f103356543l_bool: ( fun_fu1217155507l_bool * fun_nat_bool ) > fun_fu425979586l_bool ).

tff(func_def_323,type,
    hAPP_f1730770594t_bool: ( fun_fu915923926t_bool * fun_nat_bool ) > fun_fu821463397t_bool ).

tff(func_def_324,type,
    hAPP_f1951378235l_bool: ( fun_fu1436348701l_bool * fun_nat_bool ) > fun_fu814369080l_bool ).

tff(func_def_325,type,
    hAPP_f633452666l_bool: ( fun_fu1516990510l_bool * fun_nat_bool ) > fun_fu616551101l_bool ).

tff(func_def_326,type,
    hAPP_f621171935l_bool: ( fun_fu885608257l_bool * fun_fun_a_bool_bool ) > bool ).

tff(func_def_327,type,
    hAPP_f2009550088ol_nat: ( fun_fu2020802748ol_nat * fun_fun_a_bool_bool ) > nat ).

tff(func_def_328,type,
    hAPP_f2117159681l_bool: ( fun_fu911136611l_bool * fun_fun_a_bool_bool ) > fun_fun_a_bool_bool ).

tff(func_def_329,type,
    hAPP_f1434722111l_bool: ( fun_fu418465139l_bool * fun_fun_a_bool_bool ) > fun_fu885608257l_bool ).

tff(func_def_330,type,
    hAPP_f1935102916l_bool: ( fun_fu399576434l_bool * fun_fu1430349052l_bool ) > bool ).

tff(func_def_331,type,
    hAPP_f55526627ol_nat: ( fun_fu1730389579ol_nat * fun_fu1430349052l_bool ) > nat ).

tff(func_def_332,type,
    hAPP_f559147733l_bool: ( fun_fu2087345469l_bool * fun_fu1430349052l_bool ) > fun_fu1430349052l_bool ).

tff(func_def_333,type,
    hAPP_f510955609l_bool: ( fun_fu1911931399l_bool * fun_fu1430349052l_bool ) > fun_fu399576434l_bool ).

tff(func_def_334,type,
    hAPP_f215623910l_bool: ( fun_fu1540142484l_bool * fun_fu819804446l_bool ) > bool ).

tff(func_def_335,type,
    hAPP_f521865025ol_nat: ( fun_fu236049833ol_nat * fun_fu819804446l_bool ) > nat ).

tff(func_def_336,type,
    hAPP_f1948010709l_bool: ( fun_fu1070826941l_bool * fun_fu819804446l_bool ) > fun_fu819804446l_bool ).

tff(func_def_337,type,
    hAPP_f317860125l_bool: ( fun_fu209342027l_bool * fun_fu819804446l_bool ) > fun_fu1540142484l_bool ).

tff(func_def_338,type,
    hAPP_f1637334154l_bool: ( fun_fu814369080l_bool * fun_fu425979586l_bool ) > bool ).

tff(func_def_339,type,
    hAPP_f696928925ol_nat: ( fun_fu411113733ol_nat * fun_fu425979586l_bool ) > nat ).

tff(func_def_340,type,
    hAPP_f1246832597l_bool: ( fun_fu616551101l_bool * fun_fu425979586l_bool ) > fun_fu425979586l_bool ).

tff(func_def_341,type,
    hAPP_f1772781669l_bool: ( fun_fu140186515l_bool * fun_fu425979586l_bool ) > fun_fu814369080l_bool ).

tff(func_def_342,type,
    hAPP_f292226953l_bool: ( fun_fu255076663l_bool * fun_fu885608257l_bool ) > bool ).

tff(func_def_343,type,
    hAPP_f389811538l_bool: ( fun_fu1438281908l_bool * fun_fu399576434l_bool ) > bool ).

tff(func_def_344,type,
    hAPP_f1593524852l_bool: ( fun_fu717296342l_bool * fun_fu1540142484l_bool ) > bool ).

tff(func_def_345,type,
    hAPP_f937997336l_bool: ( fun_fu61768826l_bool * fun_fu814369080l_bool ) > bool ).

tff(func_def_346,type,
    member_a: fun_a_1255737515l_bool ).

tff(func_def_347,type,
    member_pname: fun_pn422929397l_bool ).

tff(func_def_348,type,
    member_int: fun_in938817141l_bool ).

tff(func_def_349,type,
    member_nat: fun_na1436237685l_bool ).

tff(func_def_350,type,
    member_fun_a_bool: fun_fu386216885l_bool ).

tff(func_def_351,type,
    member799430823e_bool: fun_fu931343505l_bool ).

tff(func_def_352,type,
    member_fun_int_bool: fun_fu1637550549l_bool ).

tff(func_def_353,type,
    member_fun_nat_bool: fun_fu1436348701l_bool ).

tff(func_def_354,type,
    g: fun_a_bool ).

tff(func_def_355,type,
    p: fun_a_bool > fun_fun_a_bool_bool ).

tff(func_def_356,type,
    u: fun_pname_bool ).

tff(func_def_357,type,
    mgt: com > x_a ).

tff(func_def_358,type,
    mgt_call: fun_pname_a ).

tff(func_def_359,type,
    na: nat ).

tff(func_def_360,type,
    pn: pname ).

tff(func_def_361,type,
    wt: com > bool ).

tff(func_def_362,type,
    sK29: nat > nat ).

tff(func_def_363,type,
    sK30: nat > nat ).

tff(func_def_364,type,
    sK31: int > nat ).

tff(func_def_365,type,
    sK32: int > nat ).

tff(func_def_366,type,
    sK33: int > nat ).

tff(func_def_367,type,
    sK34: int > nat ).

tff(func_def_368,type,
    sK35: nat > nat ).

tff(func_def_369,type,
    sK36: fun_pname_bool > pname ).

tff(func_def_370,type,
    sK37: fun_pname_bool > fun_pname_bool ).

tff(func_def_371,type,
    sK38: fun_nat_bool > nat ).

tff(func_def_372,type,
    sK39: fun_nat_bool > fun_nat_bool ).

tff(func_def_373,type,
    sK40: fun_int_bool > int ).

tff(func_def_374,type,
    sK41: fun_int_bool > fun_int_bool ).

tff(func_def_375,type,
    sK42: fun_a_bool > x_a ).

tff(func_def_376,type,
    sK43: fun_a_bool > fun_a_bool ).

tff(func_def_377,type,
    sK44: fun_a_bool > x_a ).

tff(func_def_378,type,
    sK45: fun_a_bool > x_a ).

tff(func_def_379,type,
    sK46: fun_int_bool > int ).

tff(func_def_380,type,
    sK47: fun_int_bool > int ).

tff(func_def_381,type,
    sK48: fun_nat_bool > nat ).

tff(func_def_382,type,
    sK49: fun_nat_bool > nat ).

tff(func_def_383,type,
    sK50: fun_pname_bool > fun_pname_bool ).

tff(func_def_384,type,
    sK51: fun_pname_bool > pname ).

tff(func_def_385,type,
    sK52: fun_a_bool > fun_a_bool ).

tff(func_def_386,type,
    sK53: fun_a_bool > x_a ).

tff(func_def_387,type,
    sK54: fun_int_bool > fun_int_bool ).

tff(func_def_388,type,
    sK55: fun_int_bool > int ).

tff(func_def_389,type,
    sK56: fun_nat_bool > fun_nat_bool ).

tff(func_def_390,type,
    sK57: fun_nat_bool > nat ).

tff(func_def_391,type,
    sK58: ( fun_nat_bool * nat ) > nat ).

tff(func_def_392,type,
    sK59: fun_nat_bool > nat ).

tff(func_def_393,type,
    sK60: ( fun_nat_bool * nat ) > nat ).

tff(func_def_394,type,
    sK61: fun_nat_bool > nat ).

tff(func_def_395,type,
    sK62: nat > nat ).

tff(func_def_396,type,
    sK63: fun_pname_bool > pname ).

tff(func_def_397,type,
    sK64: fun_a_bool > x_a ).

tff(func_def_398,type,
    sK65: fun_int_bool > int ).

tff(func_def_399,type,
    sK66: fun_nat_bool > nat ).

tff(func_def_400,type,
    sK67: fun_int_bool > nat ).

tff(func_def_401,type,
    sK68: fun_int_bool > int ).

tff(func_def_402,type,
    sK69: fun_pname_bool > pname ).

tff(func_def_403,type,
    sK70: fun_a_bool > x_a ).

tff(func_def_404,type,
    sK71: fun_int_bool > int ).

tff(func_def_405,type,
    sK72: fun_nat_bool > nat ).

tff(func_def_406,type,
    sK73: fun_int_bool > int ).

tff(func_def_407,type,
    sK74: fun_int_bool > nat ).

tff(func_def_408,type,
    sK75: int > nat ).

tff(func_def_409,type,
    sK76: int > nat ).

tff(func_def_410,type,
    sK77: fun_a_bool > pname ).

tff(func_def_411,type,
    sK78: ( fun_pname_a * fun_pname_bool ) > pname ).

tff(func_def_412,type,
    sK79: ( fun_in2065004473e_bool * fun_int_bool ) > int ).

tff(func_def_413,type,
    sK80: ( fun_int_fun_a_bool * fun_int_bool ) > int ).

tff(func_def_414,type,
    sK81: ( fun_int_fun_nat_bool * fun_int_bool ) > int ).

tff(func_def_415,type,
    sK82: ( fun_int_fun_int_bool * fun_int_bool ) > int ).

tff(func_def_416,type,
    sK83: ( fun_int_a * fun_int_bool ) > int ).

tff(func_def_417,type,
    sK84: ( fun_na936072029e_bool * fun_nat_bool ) > nat ).

tff(func_def_418,type,
    sK85: ( fun_nat_fun_a_bool * fun_nat_bool ) > nat ).

tff(func_def_419,type,
    sK86: ( fun_nat_fun_int_bool * fun_nat_bool ) > nat ).

tff(func_def_420,type,
    sK87: ( fun_nat_fun_nat_bool * fun_nat_bool ) > nat ).

tff(func_def_421,type,
    sK88: ( fun_nat_int * fun_nat_bool ) > nat ).

tff(func_def_422,type,
    sK89: ( nat * fun_nat_bool ) > nat ).

tff(func_def_423,type,
    sK90: ( nat * fun_nat_bool ) > nat ).

tff(func_def_424,type,
    sK91: fun_fu1430349052l_bool > pname ).

tff(func_def_425,type,
    sK92: fun_fu1430349052l_bool > fun_pname_bool ).

tff(func_def_426,type,
    sK93: fun_fu1430349052l_bool > pname ).

tff(func_def_427,type,
    sK94: fun_fu1430349052l_bool > pname ).

tff(func_def_428,type,
    sK95: fun_fu1430349052l_bool > fun_pname_bool ).

tff(func_def_429,type,
    sK96: fun_fu1430349052l_bool > pname ).

tff(func_def_430,type,
    sK97: fun_fu1430349052l_bool > fun_pname_bool ).

tff(func_def_431,type,
    sK98: fun_fun_a_bool_bool > x_a ).

tff(func_def_432,type,
    sK99: fun_fun_a_bool_bool > fun_a_bool ).

tff(func_def_433,type,
    sK100: fun_fun_a_bool_bool > x_a ).

tff(func_def_434,type,
    sK101: fun_fun_a_bool_bool > x_a ).

tff(func_def_435,type,
    sK102: fun_fun_a_bool_bool > fun_a_bool ).

tff(func_def_436,type,
    sK103: fun_fun_a_bool_bool > x_a ).

tff(func_def_437,type,
    sK104: fun_fun_a_bool_bool > fun_a_bool ).

tff(func_def_438,type,
    sK105: fun_fu819804446l_bool > int ).

tff(func_def_439,type,
    sK106: fun_fu819804446l_bool > fun_int_bool ).

tff(func_def_440,type,
    sK107: fun_fu819804446l_bool > int ).

tff(func_def_441,type,
    sK108: fun_fu819804446l_bool > int ).

tff(func_def_442,type,
    sK109: fun_fu819804446l_bool > fun_int_bool ).

tff(func_def_443,type,
    sK110: fun_fu819804446l_bool > int ).

tff(func_def_444,type,
    sK111: fun_fu819804446l_bool > fun_int_bool ).

tff(func_def_445,type,
    sK112: fun_fu425979586l_bool > nat ).

tff(func_def_446,type,
    sK113: fun_fu425979586l_bool > fun_nat_bool ).

tff(func_def_447,type,
    sK114: fun_fu425979586l_bool > nat ).

tff(func_def_448,type,
    sK115: fun_fu425979586l_bool > nat ).

tff(func_def_449,type,
    sK116: fun_fu425979586l_bool > fun_nat_bool ).

tff(func_def_450,type,
    sK117: fun_fu425979586l_bool > nat ).

tff(func_def_451,type,
    sK118: fun_fu425979586l_bool > fun_nat_bool ).

tff(func_def_452,type,
    sK119: fun_nat_bool > nat ).

tff(func_def_453,type,
    sK120: fun_nat_bool > nat ).

tff(func_def_454,type,
    sK121: ( nat * nat ) > nat ).

tff(func_def_455,type,
    sK122: ( nat * nat ) > nat ).

tff(func_def_456,type,
    sK123: ( nat * nat ) > nat ).

tff(func_def_457,type,
    sK124: ( nat * nat ) > nat ).

tff(func_def_458,type,
    sK125: nat > nat ).

tff(func_def_459,type,
    sK126: fun_nat_nat > nat ).

tff(func_def_460,type,
    sK127: ( fun_a_bool * fun_a_bool ) > x_a ).

tff(func_def_461,type,
    sK128: ( fun_int_bool * fun_int_bool ) > int ).

tff(func_def_462,type,
    sK129: ( fun_nat_bool * fun_nat_bool ) > nat ).

tff(func_def_463,type,
    sK130: ( fun_int_bool * fun_int_bool ) > int ).

tff(func_def_464,type,
    sK131: ( fun_pname_bool * fun_pname_bool ) > pname ).

tff(func_def_465,type,
    sK132: ( fun_a_bool * fun_a_bool ) > x_a ).

tff(func_def_466,type,
    sK133: ( fun_int_bool * fun_int_bool ) > int ).

tff(func_def_467,type,
    sK134: ( fun_nat_bool * fun_nat_bool ) > nat ).

tff(func_def_468,type,
    sK135: ( nat * fun_nat_bool ) > nat ).

tff(func_def_469,type,
    sK136: ( fun_a_bool * fun_a_bool ) > x_a ).

tff(func_def_470,type,
    sK137: ( fun_int_bool * fun_int_bool ) > int ).

tff(func_def_471,type,
    sK138: ( fun_nat_bool * fun_nat_bool ) > nat ).

tff(func_def_472,type,
    sK139: ( int * int ) > nat ).

tff(func_def_473,type,
    sK140: ( int * int ) > nat ).

tff(func_def_474,type,
    sK141: ( nat * nat ) > nat ).

tff(func_def_475,type,
    sK142: ( nat * nat ) > nat ).

tff(func_def_476,type,
    sK143: ( nat * nat ) > nat ).

tff(func_def_477,type,
    sK144: ( fun_a_fun_a_bool * fun_a_bool * fun_fun_a_bool_bool ) > fun_a_bool ).

tff(func_def_478,type,
    sK145: ( fun_a_fun_pname_bool * fun_a_bool * fun_fu1430349052l_bool ) > fun_a_bool ).

tff(func_def_479,type,
    sK146: ( fun_a_fun_nat_bool * fun_a_bool * fun_fu425979586l_bool ) > fun_a_bool ).

tff(func_def_480,type,
    sK147: ( fun_a_fun_int_bool * fun_a_bool * fun_fu819804446l_bool ) > fun_a_bool ).

tff(func_def_481,type,
    sK148: ( fun_pname_fun_a_bool * fun_pname_bool * fun_fun_a_bool_bool ) > fun_pname_bool ).

tff(func_def_482,type,
    sK149: ( fun_pn406123357t_bool * fun_pname_bool * fun_fu425979586l_bool ) > fun_pname_bool ).

tff(func_def_483,type,
    sK150: ( fun_pn665169337t_bool * fun_pname_bool * fun_fu819804446l_bool ) > fun_pname_bool ).

tff(func_def_484,type,
    sK151: ( fun_pn800050071e_bool * fun_pname_bool * fun_fu1430349052l_bool ) > fun_pname_bool ).

tff(func_def_485,type,
    sK152: ( fun_int_fun_nat_bool * fun_int_bool * fun_fu425979586l_bool ) > fun_int_bool ).

tff(func_def_486,type,
    sK153: ( fun_int_fun_int_bool * fun_int_bool * fun_fu819804446l_bool ) > fun_int_bool ).

tff(func_def_487,type,
    sK154: ( fun_int_fun_a_bool * fun_int_bool * fun_fun_a_bool_bool ) > fun_int_bool ).

tff(func_def_488,type,
    sK155: ( fun_in2065004473e_bool * fun_int_bool * fun_fu1430349052l_bool ) > fun_int_bool ).

tff(func_def_489,type,
    sK156: ( fun_nat_fun_a_bool * fun_nat_bool * fun_fun_a_bool_bool ) > fun_nat_bool ).

tff(func_def_490,type,
    sK157: ( fun_nat_fun_int_bool * fun_nat_bool * fun_fu819804446l_bool ) > fun_nat_bool ).

tff(func_def_491,type,
    sK158: ( fun_na936072029e_bool * fun_nat_bool * fun_fu1430349052l_bool ) > fun_nat_bool ).

tff(func_def_492,type,
    sK159: ( fun_nat_fun_nat_bool * fun_nat_bool * fun_fu425979586l_bool ) > fun_nat_bool ).

tff(func_def_493,type,
    sK160: ( fun_fu1430349052l_bool * fun_pname_bool ) > pname ).

tff(func_def_494,type,
    sK161: ( fun_fu1430349052l_bool * fun_pname_bool ) > fun_pname_bool ).

tff(func_def_495,type,
    sK162: ( fun_fun_a_bool_pname * fun_fun_a_bool_bool * fun_pname_bool ) > fun_fun_a_bool_bool ).

tff(func_def_496,type,
    sK163: ( fun_fu665170229_pname * fun_fu425979586l_bool * fun_pname_bool ) > fun_fu425979586l_bool ).

tff(func_def_497,type,
    sK164: ( fun_fu953875929_pname * fun_fu819804446l_bool * fun_pname_bool ) > fun_fu819804446l_bool ).

tff(func_def_498,type,
    sK165: ( fun_fu1499449723_pname * fun_fu1430349052l_bool * fun_pname_bool ) > fun_fu1430349052l_bool ).

tff(func_def_499,type,
    sK166: ( fun_pname_pname * fun_pname_bool * fun_pname_bool ) > fun_pname_bool ).

tff(func_def_500,type,
    sK167: ( fun_int_pname * fun_int_bool * fun_pname_bool ) > fun_int_bool ).

tff(func_def_501,type,
    sK168: ( fun_nat_pname * fun_nat_bool * fun_pname_bool ) > fun_nat_bool ).

tff(func_def_502,type,
    sK169: ( fun_a_pname * fun_a_bool * fun_pname_bool ) > fun_a_bool ).

tff(func_def_503,type,
    sK170: ( fun_fun_a_bool_bool * fun_a_bool ) > x_a ).

tff(func_def_504,type,
    sK171: ( fun_fun_a_bool_bool * fun_a_bool ) > fun_a_bool ).

tff(func_def_505,type,
    sK172: ( fun_fun_a_bool_a * fun_fun_a_bool_bool * fun_a_bool ) > fun_fun_a_bool_bool ).

tff(func_def_506,type,
    sK173: ( fun_fun_pname_bool_a * fun_fu1430349052l_bool * fun_a_bool ) > fun_fu1430349052l_bool ).

tff(func_def_507,type,
    sK174: ( fun_fun_int_bool_a * fun_fu819804446l_bool * fun_a_bool ) > fun_fu819804446l_bool ).

tff(func_def_508,type,
    sK175: ( fun_fun_nat_bool_a * fun_fu425979586l_bool * fun_a_bool ) > fun_fu425979586l_bool ).

tff(func_def_509,type,
    sK176: ( fun_a_a * fun_a_bool * fun_a_bool ) > fun_a_bool ).

tff(func_def_510,type,
    sK177: ( fun_nat_a * fun_nat_bool * fun_a_bool ) > fun_nat_bool ).

tff(func_def_511,type,
    sK178: ( fun_int_a * fun_int_bool * fun_a_bool ) > fun_int_bool ).

tff(func_def_512,type,
    sK179: ( fun_pname_a * fun_pname_bool * fun_a_bool ) > fun_pname_bool ).

tff(func_def_513,type,
    sK180: ( fun_fu819804446l_bool * fun_int_bool ) > int ).

tff(func_def_514,type,
    sK181: ( fun_fu819804446l_bool * fun_int_bool ) > fun_int_bool ).

tff(func_def_515,type,
    sK182: ( fun_pname_int * fun_pname_bool * fun_int_bool ) > fun_pname_bool ).

tff(func_def_516,type,
    sK183: ( fun_fun_int_bool_int * fun_fu819804446l_bool * fun_int_bool ) > fun_fu819804446l_bool ).

tff(func_def_517,type,
    sK184: ( fun_fun_nat_bool_int * fun_fu425979586l_bool * fun_int_bool ) > fun_fu425979586l_bool ).

tff(func_def_518,type,
    sK185: ( fun_fu1830380701ol_int * fun_fu1430349052l_bool * fun_int_bool ) > fun_fu1430349052l_bool ).

tff(func_def_519,type,
    sK186: ( fun_fun_a_bool_int * fun_fun_a_bool_bool * fun_int_bool ) > fun_fun_a_bool_bool ).

tff(func_def_520,type,
    sK187: ( fun_a_int * fun_a_bool * fun_int_bool ) > fun_a_bool ).

tff(func_def_521,type,
    sK188: ( fun_nat_int * fun_nat_bool * fun_int_bool ) > fun_nat_bool ).

tff(func_def_522,type,
    sK189: ( fun_fu425979586l_bool * fun_nat_bool ) > nat ).

tff(func_def_523,type,
    sK190: ( fun_fu425979586l_bool * fun_nat_bool ) > fun_nat_bool ).

tff(func_def_524,type,
    sK191: ( fun_pname_nat * fun_pname_bool * fun_nat_bool ) > fun_pname_bool ).

tff(func_def_525,type,
    sK192: ( fun_fun_int_bool_nat * fun_fu819804446l_bool * fun_nat_bool ) > fun_fu819804446l_bool ).

tff(func_def_526,type,
    sK193: ( fun_fun_a_bool_nat * fun_fun_a_bool_bool * fun_nat_bool ) > fun_fun_a_bool_bool ).

tff(func_def_527,type,
    sK194: ( fun_fun_nat_bool_nat * fun_fu425979586l_bool * fun_nat_bool ) > fun_fu425979586l_bool ).

tff(func_def_528,type,
    sK195: ( fun_fu1668467777ol_nat * fun_fu1430349052l_bool * fun_nat_bool ) > fun_fu1430349052l_bool ).

tff(func_def_529,type,
    sK196: ( fun_a_nat * fun_a_bool * fun_nat_bool ) > fun_a_bool ).

tff(func_def_530,type,
    sK197: fun_pn1208287926_pname > pname ).

tff(func_def_531,type,
    sK198: fun_pn1208287926_pname > pname ).

tff(func_def_532,type,
    sK199: fun_a_fun_a_a > x_a ).

tff(func_def_533,type,
    sK200: fun_a_fun_a_a > x_a ).

tff(func_def_534,type,
    sK201: fun_int_fun_int_int > int ).

tff(func_def_535,type,
    sK202: fun_int_fun_int_int > int ).

tff(func_def_536,type,
    sK203: fun_nat_fun_nat_nat > nat ).

tff(func_def_537,type,
    sK204: fun_nat_fun_nat_nat > nat ).

tff(func_def_538,type,
    sK205: ( fun_int_bool * int ) > int ).

tff(func_def_539,type,
    sK206: ( fun_int_bool * int ) > int ).

tff(func_def_540,type,
    sK207: fun_nat_bool > nat ).

tff(func_def_541,type,
    sK208: ( fun_int_bool * int ) > int ).

tff(func_def_542,type,
    sK209: ( fun_int_bool * int ) > int ).

tff(func_def_543,type,
    sK210: ( fun_int_bool * fun_int_bool * int ) > int ).

tff(func_def_544,type,
    sK211: fun_int_bool > int ).

tff(func_def_545,type,
    sK212: ( fun_int_bool * int ) > int ).

tff(func_def_546,type,
    sK213: ( fun_int_bool * int ) > int ).

tff(func_def_547,type,
    sK214: ( fun_int_bool * fun_int_bool * int ) > int ).

tff(func_def_548,type,
    sK215: fun_int_bool > int ).

tff(func_def_549,type,
    sK216: ( fun_int_bool * int ) > int ).

tff(func_def_550,type,
    sK217: ( fun_int_bool * int ) > int ).

tff(func_def_551,type,
    sK218: ( fun_int_bool * int ) > int ).

tff(func_def_552,type,
    sK219: ( fun_int_bool * int ) > int ).

tff(func_def_553,type,
    sK220: ( fun_int_bool * int ) > int ).

tff(func_def_554,type,
    sK221: ( fun_int_bool * int ) > int ).

tff(func_def_555,type,
    sK222: ( fun_nat_bool * nat ) > nat ).

tff(func_def_556,type,
    sK223: ( x_a * fun_pname_a * fun_pname_bool ) > pname ).

tff(func_def_557,type,
    sK224: ( int * fun_nat_int * fun_nat_bool ) > nat ).

tff(func_def_558,type,
    sK225: fun_nat_bool > nat ).

tff(func_def_559,type,
    sK226: fun_na936072029e_bool > nat ).

tff(func_def_560,type,
    sK227: fun_nat_fun_a_bool > nat ).

tff(func_def_561,type,
    sK228: fun_nat_fun_int_bool > nat ).

tff(func_def_562,type,
    sK229: fun_nat_fun_nat_bool > nat ).

tff(func_def_563,type,
    sK230: fun_nat_int > nat ).

tff(func_def_564,type,
    sK231: fun_nat_nat > nat ).

tff(func_def_565,type,
    sK232: ( fun_pname_a * fun_a_bool * fun_pname_bool ) > pname ).

tff(func_def_566,type,
    sK233: ( fun_nat_int * fun_int_bool * fun_nat_bool ) > nat ).

tff(func_def_567,type,
    sK234: ( int * fun_nat_int * nat ) > nat ).

tff(func_def_568,type,
    sK235: ( fun_nat_int * nat ) > nat ).

tff(func_def_569,type,
    sK236: ( int * fun_nat_int * nat ) > nat ).

tff(func_def_570,type,
    sK237: ( fun_nat_int * nat ) > nat ).

tff(func_def_571,type,
    sK238: fun_nat_nat > nat ).

tff(func_def_572,type,
    sK239: fun_nat_nat > nat ).

tff(func_def_573,type,
    sK240: fun_nat_nat > nat ).

tff(func_def_574,type,
    sK241: fun_nat_nat > nat ).

tff(func_def_575,type,
    sK242: ( x_a * fun_pname_a * fun_pname_bool ) > pname ).

tff(func_def_576,type,
    sK243: ( fun_a_bool * fun_pname_a * fun_pname_bool ) > fun_pname_bool ).

tff(func_def_577,type,
    sK244: ( int * fun_nat_int * fun_nat_bool ) > nat ).

tff(func_def_578,type,
    sK245: ( fun_int_bool * fun_nat_int * fun_nat_bool ) > fun_nat_bool ).

tff(func_def_579,type,
    sK246: ( fun_nat_bool * nat * nat ) > nat ).

tff(func_def_580,type,
    sK247: ( fun_nat_bool * nat * nat ) > nat ).

tff(func_def_581,type,
    sK248: ( fun_nat_int * nat * nat ) > nat ).

tff(func_def_582,type,
    sK249: ( int * fun_nat_int * nat * nat ) > nat ).

tff(pred_def_1,type,
    hBOOL: bool > $o ).

tff(pred_def_2,type,
    sP0: fun_fu1430349052l_bool > $o ).

tff(pred_def_3,type,
    sP1: fun_fun_a_bool_bool > $o ).

tff(pred_def_4,type,
    sP2: fun_fu819804446l_bool > $o ).

tff(pred_def_5,type,
    sP3: fun_fu425979586l_bool > $o ).

tff(pred_def_6,type,
    sP4: ( int * int ) > $o ).

tff(pred_def_7,type,
    sP5: ( int * int ) > $o ).

tff(pred_def_8,type,
    sP6: ( nat * nat ) > $o ).

tff(pred_def_9,type,
    sP7: ( nat * nat ) > $o ).

tff(pred_def_10,type,
    sP8: ( fun_fu1430349052l_bool * fun_pname_bool ) > $o ).

tff(pred_def_11,type,
    sP9: ( fun_fun_a_bool_bool * fun_a_bool ) > $o ).

tff(pred_def_12,type,
    sP10: ( fun_fu819804446l_bool * fun_int_bool ) > $o ).

tff(pred_def_13,type,
    sP11: ( fun_fu425979586l_bool * fun_nat_bool ) > $o ).

tff(pred_def_14,type,
    sP12: ( fun_int_bool * int ) > $o ).

tff(pred_def_15,type,
    sP13: ( fun_int_bool * fun_int_bool ) > $o ).

tff(pred_def_16,type,
    sP14: ( fun_int_bool * fun_int_bool ) > $o ).

tff(pred_def_17,type,
    sP15: ( bool * int * bool ) > $o ).

tff(pred_def_18,type,
    sP16: ( bool * int * bool ) > $o ).

tff(pred_def_19,type,
    sP17: ( nat * nat * fun_nat_fun_nat_bool ) > $o ).

tff(pred_def_20,type,
    sP18: ( fun_nat_bool * nat * nat ) > $o ).

tff(pred_def_21,type,
    sP19: ( fun_nat_bool * nat * nat ) > $o ).

tff(pred_def_22,type,
    sP20: ( fun_pname_bool * fun_pname_bool * pname ) > $o ).

tff(pred_def_23,type,
    sP21: ( fun_a_bool * fun_a_bool * x_a ) > $o ).

tff(pred_def_24,type,
    sP22: ( fun_int_bool * fun_int_bool * int ) > $o ).

tff(pred_def_25,type,
    sP23: ( fun_nat_bool * fun_nat_bool * nat ) > $o ).

tff(pred_def_26,type,
    sP24: ( fun_int_bool * nat * nat ) > $o ).

tff(pred_def_27,type,
    sP25: ( fun_nat_int * nat * nat ) > $o ).

tff(pred_def_28,type,
    sP26: ( int * int * int * int ) > $o ).

tff(pred_def_29,type,
    sP27: ( nat * nat * nat * nat ) > $o ).

tff(pred_def_30,type,
    sP28: ( x_a * x_a * x_a * x_a ) > $o ).

tff(f31324,plain,
    $false,
    inference(avatar_sat_refutation,[],[f7317,f7322,f7327,f7332,f7337,f7342,f7347,f7352,f7357,f7362,f7367,f7372,f7377,f7382,f7386,f7390,f7394,f7399,f7404,f7409,f7414,f7419,f7424,f7428,f7432,f7436,f7440,f7444,f7449,f7453,f7457,f7461,f7465,f7469,f7473,f7480,f7489,f7494,f7498,f7502,f7506,f7510,f7514,f7518,f7522,f7526,f7530,f7534,f7538,f7542,f7546,f7550,f7555,f7559,f7563,f7567,f7575,f7579,f7583,f7588,f7592,f7594,f7598,f7602,f7606,f7610,f7614,f7619,f7623,f7627,f7631,f7636,f7641,f7645,f7649,f7653,f7657,f7661,f7665,f7669,f7673,f7677,f7681,f7685,f7735,f7749,f7761,f7765,f7769,f7773,f7778,f7782,f7786,f7790,f7794,f7798,f7802,f7806,f7810,f7814,f7819,f7823,f7827,f7831,f7835,f7839,f7843,f7847,f7851,f7855,f7859,f7863,f7867,f7871,f7875,f7879,f7883,f7887,f7891,f7895,f7899,f7931,f7936,f7940,f7944,f7948,f7952,f7956,f7961,f7968,f8005,f8010,f8015,f8022,f8027,f8031,f8035,f8039,f8043,f8047,f8051,f8055,f8059,f8063,f8067,f8071,f8075,f8079,f8083,f8087,f8091,f8095,f8100,f8104,f8108,f8112,f8117,f8121,f8125,f8129,f8133,f8137,f8142,f8146,f8150,f8154,f8158,f8162,f8193,f8198,f8228,f8232,f8237,f8241,f8245,f8249,f8254,f8258,f8263,f8267,f8272,f8277,f8281,f8285,f8289,f8293,f8297,f8301,f8305,f8309,f8313,f8317,f8321,f8325,f8329,f8333,f8337,f8341,f8345,f8349,f8353,f8358,f8362,f8366,f8370,f8374,f8378,f8382,f8386,f8390,f8394,f8398,f8403,f8407,f8411,f8415,f8419,f8423,f8427,f8431,f8435,f8437,f8503,f8644,f8652,f8656,f8660,f8664,f8668,f8672,f8676,f8680,f8686,f8690,f8694,f8698,f8702,f8706,f8710,f8714,f8718,f8722,f8791,f8795,f8799,f8803,f8807,f8811,f8815,f8819,f8823,f8827,f8831,f8835,f8839,f8843,f8847,f8851,f8855,f8859,f8863,f8867,f8871,f8875,f8879,f8883,f8887,f8891,f8895,f8899,f8903,f8907,f8911,f8915,f8919,f8923,f8927,f8931,f8935,f8939,f8943,f8947,f8951,f8955,f8959,f8963,f8967,f8971,f8975,f8979,f8983,f8987,f8991,f8995,f9001,f9005,f9009,f9013,f9017,f9021,f9025,f9029,f9033,f9037,f9042,f9046,f9050,f9054,f9058,f9062,f9066,f9070,f9074,f9078,f9082,f9087,f9091,f9095,f9099,f9103,f9107,f9111,f9115,f9119,f9123,f9127,f9132,f9136,f9140,f9144,f9148,f9152,f9156,f9175,f9422,f9514,f9552,f9556,f9560,f9564,f9568,f9572,f9576,f9580,f9584,f9588,f9592,f9596,f9600,f9604,f9608,f9612,f9616,f9620,f9624,f9628,f9632,f9636,f9640,f9644,f9648,f9652,f9656,f9660,f9664,f9668,f9672,f9676,f9680,f9685,f9689,f9693,f9697,f9701,f9705,f9709,f9713,f9717,f9721,f9725,f9729,f9733,f9737,f9741,f9745,f9749,f9753,f9757,f9761,f9765,f9769,f9773,f9777,f9781,f9785,f9789,f9793,f9797,f9801,f9805,f9809,f9813,f9817,f9821,f9825,f9830,f9834,f9838,f9842,f9847,f9851,f9855,f9903,f10104,f10216,f10273,f10326,f10337,f10356,f10362,f10369,f10373,f10377,f10381,f10385,f10389,f10393,f10397,f10401,f10405,f10409,f10413,f10417,f10421,f10425,f10429,f10433,f10437,f10441,f10445,f10449,f10453,f10457,f10461,f10465,f10469,f10473,f10477,f10481,f10485,f10489,f10493,f10497,f10501,f10505,f10509,f10513,f10517,f10521,f10525,f10529,f10533,f10537,f10541,f10545,f10549,f10553,f10557,f10561,f10565,f10569,f10573,f10577,f10581,f10587,f10591,f10595,f10599,f10603,f10607,f10611,f10615,f10619,f10623,f10630,f10634,f10638,f10642,f10646,f10650,f10654,f10658,f10662,f10666,f10674,f10678,f10682,f10686,f10690,f10694,f10698,f10702,f10706,f10710,f10714,f10718,f10722,f10726,f10730,f10734,f10738,f10743,f10751,f10759,f10765,f10769,f10773,f10777,f10781,f10785,f10789,f10793,f10797,f10801,f10806,f10810,f10814,f10818,f10822,f10826,f10830,f10834,f10838,f10842,f10846,f10851,f10855,f10859,f10863,f10867,f10871,f10875,f10879,f10883,f10890,f10926,f10957,f11039,f11087,f11123,f11162,f11569,f11631,f11666,f11670,f11674,f11678,f11682,f11686,f11690,f11694,f11698,f11702,f11706,f11710,f11714,f11718,f11722,f11727,f11732,f11736,f11740,f11744,f11748,f11752,f11756,f11760,f11764,f11768,f11772,f11776,f11780,f11784,f11788,f11792,f11796,f11800,f11804,f11808,f11812,f11816,f11820,f11824,f11828,f11944,f12028,f12089,f12298,f12302,f12306,f12310,f12314,f12318,f12322,f12326,f12330,f12334,f12346,f12350,f12354,f12358,f12362,f12366,f12370,f12374,f12378,f12382,f12387,f12391,f12395,f12399,f12403,f12407,f12411,f12415,f12419,f12423,f12427,f12431,f12435,f12439,f12443,f12447,f12451,f12455,f12459,f12463,f12467,f12594,f12598,f12602,f12606,f12610,f12614,f12618,f12622,f12626,f12630,f12635,f12639,f12643,f12647,f12651,f12655,f12659,f12663,f12667,f12671,f12675,f12682,f12686,f12690,f12694,f12698,f12702,f12706,f12710,f12714,f12718,f12723,f12727,f12731,f12735,f12739,f12743,f12747,f12751,f12755,f12759,f12763,f12772,f12776,f12780,f12784,f12788,f12793,f12800,f12804,f12808,f12813,f12817,f13016,f13089,f13622,f13763,f13963,f14120,f14133,f14137,f14141,f14145,f14149,f14153,f14157,f14161,f14165,f14169,f14173,f14177,f14181,f14185,f14189,f14193,f14197,f14201,f14205,f14209,f14213,f14217,f14221,f14225,f14229,f14233,f14237,f14241,f14245,f14250,f14255,f14259,f14263,f14267,f14271,f14457,f14772,f15107,f15111,f15115,f15119,f15123,f15127,f15131,f15135,f15139,f15143,f15147,f15151,f15155,f15159,f15163,f15167,f15171,f15175,f15179,f15183,f15187,f15191,f15195,f15199,f15203,f15207,f15211,f15215,f15219,f15223,f15227,f15231,f15235,f15239,f15243,f15247,f15251,f15257,f15264,f15270,f15284,f15288,f15292,f15296,f15300,f15306,f15322,f15326,f15330,f15334,f15338,f15342,f15347,f15352,f15356,f15361,f15366,f15370,f15374,f15378,f15382,f15386,f15390,f15394,f15398,f15402,f15406,f15410,f15414,f15418,f15422,f15426,f15430,f15434,f15438,f15442,f15446,f15450,f15454,f15458,f15462,f15466,f15470,f15474,f15478,f15482,f15486,f15490,f15494,f15498,f15502,f15506,f15510,f15514,f15518,f15522,f15526,f15530,f15534,f15538,f15542,f15546,f15550,f15554,f15558,f15562,f15566,f15570,f15574,f15578,f15582,f15586,f15590,f15594,f15598,f15602,f15609,f15613,f15617,f15621,f15625,f15629,f15633,f15637,f15641,f15645,f15841,f15845,f15849,f15853,f15857,f15861,f15865,f15869,f15873,f15877,f15884,f15888,f15892,f15896,f15900,f15904,f15908,f15912,f15916,f15920,f15924,f15928,f15932,f15936,f15940,f15944,f15948,f15952,f15956,f15960,f15964,f15968,f15972,f15977,f15982,f15987,f15991,f15995,f15999,f16003,f16007,f16011,f16016,f16020,f16176,f16291,f16401,f16564,f16654,f16658,f16662,f16666,f16671,f16813,f16980,f17139,f17469,f17783,f17787,f17791,f17996,f18000,f18004,f18008,f18012,f18016,f18020,f18024,f18029,f18033,f18037,f18041,f18045,f18049,f18053,f18057,f18061,f18065,f18070,f18074,f18078,f18082,f18086,f18090,f18094,f18098,f18102,f18106,f18110,f18114,f18118,f18122,f18126,f18130,f18134,f18138,f18142,f18146,f18150,f18154,f18158,f18162,f18166,f18170,f18174,f18178,f18182,f18186,f18190,f18194,f18198,f18202,f18206,f18210,f18214,f18218,f18222,f18226,f18230,f18234,f18238,f18242,f18246,f18250,f18254,f18258,f18262,f18266,f18270,f18274,f19734,f20235,f20239,f20243,f20247,f20251,f20255,f20316,f20320,f20324,f20328,f20332,f20336,f20340,f20344,f20348,f20352,f20357,f20361,f20365,f20369,f20373,f20377,f20381,f20385,f20389,f20393,f20397,f20402,f20406,f20410,f20414,f20418,f20422,f20426,f20430,f20434,f20438,f20479,f20483,f20487,f20491,f20714,f21311,f21315,f21319,f21323,f21327,f21331,f21337,f21341,f21345,f21349,f21353,f21357,f21361,f21365,f21369,f21373,f21380,f21384,f21388,f21392,f21396,f21400,f21404,f21408,f21412,f21416,f21437,f21441,f21445,f21449,f21453,f21457,f21461,f21465,f21469,f21473,f21477,f21481,f21485,f21489,f21493,f21497,f21501,f21505,f21509,f21513,f21517,f21522,f21526,f21530,f21534,f21538,f21542,f21546,f21550,f21554,f21558,f21562,f21567,f21571,f21575,f21579,f21583,f21587,f21591,f21595,f21599,f21603,f21607,f21611,f21615,f21619,f21623,f21627,f21631,f21635,f21639,f21643,f21647,f21651,f21655,f21659,f21663,f21667,f22595,f22789,f22900,f23387,f23549,f23553,f23557,f23561,f23566,f23570,f23575,f23579,f23583,f23587,f23591,f23595,f23599,f23603,f23607,f23612,f23616,f23620,f23624,f23628,f23632,f23636,f23640,f23644,f23648,f23652,f23658,f23662,f23673,f23679,f23689,f23695,f23705,f23711,f23715,f23726,f23732,f23742,f23748,f23758,f23762,f23766,f23771,f23775,f23779,f23783,f23787,f23791,f23795,f23799,f23803,f23807,f23811,f23816,f23820,f23824,f23828,f23832,f23836,f23840,f23844,f23848,f23852,f23856,f23860,f23864,f23868,f23872,f23876,f23880,f23884,f23888,f23892,f23896,f23900,f23904,f23908,f23912,f23916,f23920,f23924,f23928,f23932,f23936,f23940,f23944,f23949,f23953,f23957,f23961,f23965,f23969,f23973,f23977,f23981,f23985,f23989,f23994,f23998,f24002,f24006,f24010,f24014,f24018,f24022,f24026,f24030,f24034,f24043,f24047,f24051,f24055,f24059,f24063,f24067,f24071,f24075,f24079,f24091,f24095,f24099,f24103,f24107,f24111,f24115,f24119,f24123,f24127,f24207,f24211,f24215,f24219,f24223,f24227,f24231,f24235,f24239,f24243,f24249,f24253,f24258,f24263,f24268,f24273,f24278,f24283,f24288,f24292,f24296,f24301,f24305,f24309,f24313,f24317,f24321,f24325,f24329,f24342,f24769,f24826,f25644,f26216,f27006,f27010,f27014,f27018,f27022,f27026,f27030,f27034,f27208,f27478,f27492,f27496,f27500,f27504,f27508,f27512,f27516,f27520,f27524,f27528,f27537,f27541,f27545,f27549,f27553,f27557,f27561,f27565,f27569,f27573,f27577,f27581,f27585,f27589,f27593,f27597,f27601,f27605,f27609,f27613,f27617,f27626,f27630,f27634,f27638,f27642,f27646,f27650,f27654,f27658,f27662,f27671,f27675,f27679,f27683,f27687,f27691,f27695,f27699,f27703,f27707,f27712,f27716,f27720,f27724,f27728,f27732,f27736,f27740,f27744,f27748,f27752,f27777,f27781,f27785,f27789,f27793,f27797,f27801,f27805,f27809,f27813,f27961,f29579,f29612,f29617,f29621,f29625,f29629,f29633,f29637,f29641,f29645,f29650,f29654,f29658,f29662,f29666,f29670,f29674,f29678,f29682,f29686,f29690,f29694,f29698,f29702,f29706,f29710,f29714,f29718,f29722,f29726,f29730,f29735,f29739,f29743,f29747,f29751,f29755,f29759,f29763,f29767,f29771,f29775,f29779,f29783,f29787,f29791,f29795,f29799,f29803,f30106,f30945,f31294,f31298,f31302,f31306,f31310,f31314,f31318,f31322,f31323]) ).

tff(f31323,plain,
    ( ~ spl250_130
    | ~ spl250_38
    | ~ spl250_85
    | ~ spl250_837
    | spl250_1415 ),
    inference(avatar_split_clause,[],[f31198,f30942,f15556,f7733,f7491,f7965]) ).

tff(f7965,plain,
    ( spl250_130
  <=> hBOOL(fTrue) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_130])]) ).

tff(f7491,plain,
    ( spl250_38
  <=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_38])]) ).

tff(f7733,plain,
    ( spl250_85
  <=> ! [X0: bool] :
        ( ~ hBOOL(X0)
        | ( fTrue = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_85])]) ).

tff(f15556,plain,
    ( spl250_837
  <=> ! [X2: fun_pname_bool,X0: fun_pname_a,X1: pname] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_837])]) ).

tff(f30942,plain,
    ( spl250_1415
  <=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1415])]) ).

tff(f31198,plain,
    ( ~ hBOOL(fTrue)
    | ~ spl250_38
    | ~ spl250_85
    | ~ spl250_837
    | spl250_1415 ),
    inference(forward_demodulation,[],[f31191,f7918]) ).

tff(f7918,plain,
    ( ( fTrue = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u) )
    | ~ spl250_38
    | ~ spl250_85 ),
    inference(resolution,[],[f7734,f7493]) ).

tff(f7493,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u))
    | ~ spl250_38 ),
    inference(avatar_component_clause,[],[f7491]) ).

tff(f7734,plain,
    ( ! [X0: bool] :
        ( ~ hBOOL(X0)
        | ( fTrue = X0 ) )
    | ~ spl250_85 ),
    inference(avatar_component_clause,[],[f7733]) ).

tff(f31191,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u))
    | ~ spl250_837
    | spl250_1415 ),
    inference(resolution,[],[f30944,f15557]) ).

tff(f15557,plain,
    ( ! [X2: fun_pname_bool,X0: fun_pname_a,X1: pname] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) )
    | ~ spl250_837 ),
    inference(avatar_component_clause,[],[f15556]) ).

tff(f30944,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u)))
    | spl250_1415 ),
    inference(avatar_component_clause,[],[f30942]) ).

tff(f31322,plain,
    spl250_1423,
    inference(avatar_split_clause,[],[f5108,f31320]) ).

tff(f31320,plain,
    ( spl250_1423
  <=> ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
        ( ( X0 = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,X0)))
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1423])]) ).

tff(f5108,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,X0)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(cnf_transformation,[],[f2739]) ).

tff(f2739,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,X0)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(flattening,[],[f2738]) ).

tff(f2738,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,X0)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(ennf_transformation,[],[f1721]) ).

tff(f1721,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,X0)))
         => ( X0 = X1 ) ) ) ),
    inference(rectify,[],[f82]) ).

tff(f82,axiom,
    ! [X2: fun_fu1430349052l_bool,X7: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),X7))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X7)),hAPP_f55526627ol_nat(finite1340463720e_bool,X2)))
         => ( X2 = X7 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_card__seteq) ).

tff(f31318,plain,
    spl250_1422,
    inference(avatar_split_clause,[],[f5107,f31316]) ).

tff(f31316,plain,
    ( spl250_1422
  <=> ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
        ( ( X0 = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)))
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1422])]) ).

tff(f5107,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(cnf_transformation,[],[f2737]) ).

tff(f2737,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(flattening,[],[f2736]) ).

tff(f2736,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(ennf_transformation,[],[f1720]) ).

tff(f1720,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)))
         => ( X0 = X1 ) ) ) ),
    inference(rectify,[],[f83]) ).

tff(f83,axiom,
    ! [X2: fun_fun_a_bool_bool,X7: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),X7))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X7)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)))
         => ( X2 = X7 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_card__seteq) ).

tff(f31314,plain,
    spl250_1421,
    inference(avatar_split_clause,[],[f5106,f31312]) ).

tff(f31312,plain,
    ( spl250_1421
  <=> ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
        ( ( X0 = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,X0)))
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1421])]) ).

tff(f5106,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,X0)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(cnf_transformation,[],[f2735]) ).

tff(f2735,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,X0)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(flattening,[],[f2734]) ).

tff(f2734,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,X0)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(ennf_transformation,[],[f1719]) ).

tff(f1719,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,X0)))
         => ( X0 = X1 ) ) ) ),
    inference(rectify,[],[f81]) ).

tff(f81,axiom,
    ! [X2: fun_fu425979586l_bool,X7: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),X7))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X7)),hAPP_f696928925ol_nat(finite346522414t_bool,X2)))
         => ( X2 = X7 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_card__seteq) ).

tff(f31310,plain,
    spl250_1420,
    inference(avatar_split_clause,[],[f5105,f31308]) ).

tff(f31308,plain,
    ( spl250_1420
  <=> ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
        ( ( X0 = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X1)),hAPP_f521865025ol_nat(finite1876863882t_bool,X0)))
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1420])]) ).

tff(f5105,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X1)),hAPP_f521865025ol_nat(finite1876863882t_bool,X0)))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(cnf_transformation,[],[f2733]) ).

tff(f2733,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X1)),hAPP_f521865025ol_nat(finite1876863882t_bool,X0)))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(flattening,[],[f2732]) ).

tff(f2732,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X1)),hAPP_f521865025ol_nat(finite1876863882t_bool,X0)))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(ennf_transformation,[],[f1718]) ).

tff(f1718,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X1)),hAPP_f521865025ol_nat(finite1876863882t_bool,X0)))
         => ( X0 = X1 ) ) ) ),
    inference(rectify,[],[f80]) ).

tff(f80,axiom,
    ! [X2: fun_fu819804446l_bool,X7: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X7))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),X7))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X7)),hAPP_f521865025ol_nat(finite1876863882t_bool,X2)))
         => ( X2 = X7 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_card__seteq) ).

tff(f31306,plain,
    spl250_1419,
    inference(avatar_split_clause,[],[f5092,f31304]) ).

tff(f31304,plain,
    ( spl250_1419
  <=> ! [X0: fun_int_bool,X1: fun_fu819804446l_bool] :
        ( ( hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,X1)) )
        | hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X0),X1))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1419])]) ).

tff(f5092,plain,
    ! [X0: fun_int_bool,X1: fun_fu819804446l_bool] :
      ( ( hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,X1)) )
      | hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X0),X1))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(cnf_transformation,[],[f2707]) ).

tff(f2707,plain,
    ! [X0: fun_int_bool,X1: fun_fu819804446l_bool] :
      ( ( ( ( hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,X1)) )
          | hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X0),X1)) )
        & ( ( hAPP_f521865025ol_nat(finite1876863882t_bool,X1) = hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1)) )
          | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X0),X1)) ) )
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(ennf_transformation,[],[f1705]) ).

tff(f1705,plain,
    ! [X0: fun_int_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
     => ( ( ~ hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X0),X1))
         => ( hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,X1)) ) )
        & ( hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X0),X1))
         => ( hAPP_f521865025ol_nat(finite1876863882t_bool,X1) = hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1)) ) ) ) ),
    inference(rectify,[],[f96]) ).

tff(f96,axiom,
    ! [X8: fun_int_bool,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
     => ( ( ~ hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X8),X2))
         => ( hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X8),X2)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,X2)) ) )
        & ( hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X8),X2))
         => ( hAPP_f521865025ol_nat(finite1876863882t_bool,X2) = hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X8),X2)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_card__insert__if) ).

tff(f31302,plain,
    spl250_1418,
    inference(avatar_split_clause,[],[f5090,f31300]) ).

tff(f31300,plain,
    ( spl250_1418
  <=> ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
        ( ( hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1)) )
        | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1418])]) ).

tff(f5090,plain,
    ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
      ( ( hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1)) )
      | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(cnf_transformation,[],[f2706]) ).

tff(f2706,plain,
    ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
      ( ( ( ( hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1)) )
          | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1)) )
        & ( ( hAPP_f696928925ol_nat(finite346522414t_bool,X1) = hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1)) )
          | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1)) ) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(ennf_transformation,[],[f1704]) ).

tff(f1704,plain,
    ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
     => ( ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1))
         => ( hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1)) ) )
        & ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1))
         => ( hAPP_f696928925ol_nat(finite346522414t_bool,X1) = hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1)) ) ) ) ),
    inference(rectify,[],[f97]) ).

tff(f97,axiom,
    ! [X8: fun_nat_bool,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
     => ( ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X8),X2))
         => ( hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X8),X2)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X2)) ) )
        & ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X8),X2))
         => ( hAPP_f696928925ol_nat(finite346522414t_bool,X2) = hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X8),X2)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_card__insert__if) ).

tff(f31298,plain,
    spl250_1417,
    inference(avatar_split_clause,[],[f5088,f31296]) ).

tff(f31296,plain,
    ( spl250_1417
  <=> ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
        ( ( hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)) )
        | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1417])]) ).

tff(f5088,plain,
    ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
      ( ( hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)) )
      | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(cnf_transformation,[],[f2705]) ).

tff(f2705,plain,
    ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
      ( ( ( ( hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)) )
          | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1)) )
        & ( ( hAPP_f55526627ol_nat(finite1340463720e_bool,X1) = hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1)) )
          | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1)) ) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(ennf_transformation,[],[f1703]) ).

tff(f1703,plain,
    ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
     => ( ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1))
         => ( hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)) ) )
        & ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1))
         => ( hAPP_f55526627ol_nat(finite1340463720e_bool,X1) = hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1)) ) ) ) ),
    inference(rectify,[],[f98]) ).

tff(f98,axiom,
    ! [X8: fun_pname_bool,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
     => ( ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X8),X2))
         => ( hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X8),X2)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X2)) ) )
        & ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X8),X2))
         => ( hAPP_f55526627ol_nat(finite1340463720e_bool,X2) = hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X8),X2)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_card__insert__if) ).

tff(f31294,plain,
    spl250_1416,
    inference(avatar_split_clause,[],[f5086,f31292]) ).

tff(f31292,plain,
    ( spl250_1416
  <=> ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
        ( ( hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)) )
        | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1416])]) ).

tff(f5086,plain,
    ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
      ( ( hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)) )
      | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(cnf_transformation,[],[f2704]) ).

tff(f2704,plain,
    ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
      ( ( ( ( hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)) )
          | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1)) )
        & ( ( hAPP_f2009550088ol_nat(finite1306199131a_bool,X1) = hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1)) )
          | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1)) ) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(ennf_transformation,[],[f1702]) ).

tff(f1702,plain,
    ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
     => ( ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1))
         => ( hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)) ) )
        & ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1))
         => ( hAPP_f2009550088ol_nat(finite1306199131a_bool,X1) = hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1)) ) ) ) ),
    inference(rectify,[],[f99]) ).

tff(f99,axiom,
    ! [X8: fun_a_bool,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
     => ( ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X8),X2))
         => ( hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X8),X2)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)) ) )
        & ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X8),X2))
         => ( hAPP_f2009550088ol_nat(finite1306199131a_bool,X2) = hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X8),X2)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_card__insert__if) ).

tff(f30945,plain,
    ( ~ spl250_1415
    | ~ spl250_130
    | spl250_7
    | ~ spl250_85
    | ~ spl250_132
    | ~ spl250_1391 ),
    inference(avatar_split_clause,[],[f30522,f29712,f8007,f7733,f7344,f7965,f30942]) ).

tff(f7344,plain,
    ( spl250_7
  <=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_7])]) ).

tff(f8007,plain,
    ( spl250_132
  <=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_132])]) ).

tff(f29712,plain,
    ( spl250_1391
  <=> ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1391])]) ).

tff(f30522,plain,
    ( ~ hBOOL(fTrue)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u)))
    | spl250_7
    | ~ spl250_85
    | ~ spl250_132
    | ~ spl250_1391 ),
    inference(forward_demodulation,[],[f30481,f8017]) ).

tff(f8017,plain,
    ( ( fTrue = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)) )
    | ~ spl250_85
    | ~ spl250_132 ),
    inference(resolution,[],[f8009,f7734]) ).

tff(f8009,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)))
    | ~ spl250_132 ),
    inference(avatar_component_clause,[],[f8007]) ).

tff(f30481,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),image_pname_a(mgt_call,u)))
    | spl250_7
    | ~ spl250_1391 ),
    inference(resolution,[],[f29713,f7346]) ).

tff(f7346,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u)))
    | spl250_7 ),
    inference(avatar_component_clause,[],[f7344]) ).

tff(f29713,plain,
    ( ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
    | ~ spl250_1391 ),
    inference(avatar_component_clause,[],[f29712]) ).

tff(f30106,plain,
    ( spl250_1414
    | ~ spl250_55
    | ~ spl250_692 ),
    inference(avatar_split_clause,[],[f15603,f13620,f7561,f30104]) ).

tff(f30104,plain,
    ( spl250_1414
  <=> ! [X0: fun_fu554186387l_bool] :
        ( ( fFalse = hAPP_bool_bool(hAPP_f198738859l_bool(X0,image_pname_a(mgt_call,u)),fFalse) )
        | ( fTrue = hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X0,hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g))),image_pname_a(mgt_call,u)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1414])]) ).

tff(f7561,plain,
    ( spl250_55
  <=> ! [X0: bool] :
        ( ( fFalse = X0 )
        | ( fTrue = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_55])]) ).

tff(f13620,plain,
    ( spl250_692
  <=> ! [X0: fun_fu554186387l_bool] : ( hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X0,hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g))),image_pname_a(mgt_call,u)) = hAPP_bool_bool(hAPP_f198738859l_bool(X0,image_pname_a(mgt_call,u)),fFalse) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_692])]) ).

tff(f15603,plain,
    ( ! [X0: fun_fu554186387l_bool] :
        ( ( fFalse = hAPP_bool_bool(hAPP_f198738859l_bool(X0,image_pname_a(mgt_call,u)),fFalse) )
        | ( fTrue = hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X0,hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g))),image_pname_a(mgt_call,u)) ) )
    | ~ spl250_55
    | ~ spl250_692 ),
    inference(superposition,[],[f13621,f7562]) ).

tff(f7562,plain,
    ( ! [X0: bool] :
        ( ( fFalse = X0 )
        | ( fTrue = X0 ) )
    | ~ spl250_55 ),
    inference(avatar_component_clause,[],[f7561]) ).

tff(f13621,plain,
    ( ! [X0: fun_fu554186387l_bool] : ( hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X0,hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g))),image_pname_a(mgt_call,u)) = hAPP_bool_bool(hAPP_f198738859l_bool(X0,image_pname_a(mgt_call,u)),fFalse) )
    | ~ spl250_692 ),
    inference(avatar_component_clause,[],[f13620]) ).

tff(f29803,plain,
    ( spl250_1413
    | ~ spl250_20
    | ~ spl250_110
    | ~ spl250_922
    | ~ spl250_1366 ),
    inference(avatar_split_clause,[],[f29613,f29610,f18006,f7853,f7406,f29801]) ).

tff(f29801,plain,
    ( spl250_1413
  <=> ! [X0: nat,X1: nat] :
        ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),X1)),X0)) )
        | ( zero_zero_nat = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1413])]) ).

tff(f7406,plain,
    ( spl250_20
  <=> ( one_one_nat = hAPP_nat_nat(suc,zero_zero_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_20])]) ).

tff(f7853,plain,
    ( spl250_110
  <=> ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),zero_zero_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_110])]) ).

tff(f18006,plain,
    ( spl250_922
  <=> ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_922])]) ).

tff(f29610,plain,
    ( spl250_1366
  <=> ! [X0: nat,X1: nat] :
        ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)),X0)) )
        | ( zero_zero_nat = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1366])]) ).

tff(f29613,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),X1)),X0)) )
        | ( zero_zero_nat = X1 ) )
    | ~ spl250_20
    | ~ spl250_110
    | ~ spl250_922
    | ~ spl250_1366 ),
    inference(forward_demodulation,[],[f29611,f18373]) ).

tff(f18373,plain,
    ( ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),one_one_nat) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),X0) )
    | ~ spl250_20
    | ~ spl250_110
    | ~ spl250_922 ),
    inference(forward_demodulation,[],[f18367,f7408]) ).

tff(f7408,plain,
    ( ( one_one_nat = hAPP_nat_nat(suc,zero_zero_nat) )
    | ~ spl250_20 ),
    inference(avatar_component_clause,[],[f7406]) ).

tff(f18367,plain,
    ( ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(suc,zero_zero_nat)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),X0) )
    | ~ spl250_110
    | ~ spl250_922 ),
    inference(superposition,[],[f18007,f7854]) ).

tff(f7854,plain,
    ( ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),zero_zero_nat) = X0 )
    | ~ spl250_110 ),
    inference(avatar_component_clause,[],[f7853]) ).

tff(f18007,plain,
    ( ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)) )
    | ~ spl250_922 ),
    inference(avatar_component_clause,[],[f18006]) ).

tff(f29611,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)),X0)) )
        | ( zero_zero_nat = X1 ) )
    | ~ spl250_1366 ),
    inference(avatar_component_clause,[],[f29610]) ).

tff(f29799,plain,
    spl250_1412,
    inference(avatar_split_clause,[],[f7310,f29797]) ).

tff(f29797,plain,
    ( spl250_1412
  <=> ! [X0: x_a,X3: x_a,X2: x_a,X1: x_a] :
        ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),collect_a(hAPP_a_fun_a_bool(fequal_a,X3))) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),collect_a(hAPP_a_fun_a_bool(fequal_a,X1))) )
        | sP28(X2,X1,X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1412])]) ).

tff(f7310,plain,
    ! [X2: x_a,X3: x_a,X0: x_a,X1: x_a] :
      ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),collect_a(hAPP_a_fun_a_bool(fequal_a,X3))) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),collect_a(hAPP_a_fun_a_bool(fequal_a,X1))) )
      | sP28(X2,X1,X3,X0) ),
    inference(forward_demodulation,[],[f7309,f4680]) ).

tff(f4680,plain,
    ! [X0: x_a] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = collect_a(hAPP_a_fun_a_bool(fequal_a,X0)) ),
    inference(cnf_transformation,[],[f1408]) ).

tff(f1408,plain,
    ! [X0: x_a] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = collect_a(hAPP_a_fun_a_bool(fequal_a,X0)) ),
    inference(rectify,[],[f640]) ).

tff(f640,axiom,
    ! [X5: x_a] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),bot_bot_fun_a_bool) = collect_a(hAPP_a_fun_a_bool(fequal_a,X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_639_singleton__conv2) ).

tff(f7309,plain,
    ! [X2: x_a,X3: x_a,X0: x_a,X1: x_a] :
      ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),collect_a(hAPP_a_fun_a_bool(fequal_a,X3))) )
      | sP28(X2,X1,X3,X0) ),
    inference(forward_demodulation,[],[f6538,f4680]) ).

tff(f6538,plain,
    ! [X2: x_a,X3: x_a,X0: x_a,X1: x_a] :
      ( sP28(X2,X1,X3,X0)
      | ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),bot_bot_fun_a_bool)) ) ),
    inference(cnf_transformation,[],[f4533]) ).

tff(f4533,plain,
    ! [X0: x_a,X1: x_a,X2: x_a,X3: x_a] :
      ( ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),bot_bot_fun_a_bool)) )
        | ~ sP28(X2,X1,X3,X0) )
      & ( sP28(X2,X1,X3,X0)
        | ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),bot_bot_fun_a_bool)) ) ) ),
    inference(nnf_transformation,[],[f3740]) ).

tff(f3740,plain,
    ! [X0: x_a,X1: x_a,X2: x_a,X3: x_a] :
      ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),bot_bot_fun_a_bool)) )
    <=> sP28(X2,X1,X3,X0) ),
    inference(definition_folding,[],[f2563,f3739]) ).

tff(f3739,plain,
    ! [X2: x_a,X1: x_a,X3: x_a,X0: x_a] :
      ( sP28(X2,X1,X3,X0)
    <=> ( ( ( X1 = X2 )
          & ( X0 = X3 ) )
        | ( ( X1 = X3 )
          & ( X0 = X2 ) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP28])]) ).

tff(f2563,plain,
    ! [X0: x_a,X1: x_a,X2: x_a,X3: x_a] :
      ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),bot_bot_fun_a_bool)) )
    <=> ( ( ( X1 = X2 )
          & ( X0 = X3 ) )
        | ( ( X1 = X3 )
          & ( X0 = X2 ) ) ) ),
    inference(rectify,[],[f597]) ).

tff(f597,axiom,
    ! [X5: x_a,X28: x_a,X29: x_a,X70: x_a] :
      ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X28),bot_bot_fun_a_bool)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X29),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X70),bot_bot_fun_a_bool)) )
    <=> ( ( ( X28 = X29 )
          & ( X5 = X70 ) )
        | ( ( X28 = X70 )
          & ( X5 = X29 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_doubleton__eq__iff) ).

tff(f29795,plain,
    spl250_1411,
    inference(avatar_split_clause,[],[f7308,f29793]) ).

tff(f29793,plain,
    ( spl250_1411
  <=> ! [X0: x_a,X3: x_a,X2: x_a,X1: x_a] :
        ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),collect_a(hAPP_a_fun_a_bool(fequal_a,X3))) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),collect_a(hAPP_a_fun_a_bool(fequal_a,X1))) )
        | ~ sP28(X2,X1,X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1411])]) ).

tff(f7308,plain,
    ! [X2: x_a,X3: x_a,X0: x_a,X1: x_a] :
      ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),collect_a(hAPP_a_fun_a_bool(fequal_a,X3))) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),collect_a(hAPP_a_fun_a_bool(fequal_a,X1))) )
      | ~ sP28(X2,X1,X3,X0) ),
    inference(forward_demodulation,[],[f7307,f4680]) ).

tff(f7307,plain,
    ! [X2: x_a,X3: x_a,X0: x_a,X1: x_a] :
      ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),collect_a(hAPP_a_fun_a_bool(fequal_a,X3))) )
      | ~ sP28(X2,X1,X3,X0) ),
    inference(forward_demodulation,[],[f6539,f4680]) ).

tff(f6539,plain,
    ! [X2: x_a,X3: x_a,X0: x_a,X1: x_a] :
      ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),bot_bot_fun_a_bool)) )
      | ~ sP28(X2,X1,X3,X0) ),
    inference(cnf_transformation,[],[f4533]) ).

tff(f29791,plain,
    spl250_1410,
    inference(avatar_split_clause,[],[f7273,f29789]) ).

tff(f29789,plain,
    ( spl250_1410
  <=> ! [X2: nat,X0: fun_nat_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_n1699378549t_bool(fequal_nat,X2))),X0))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
        | ~ sP23(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1410])]) ).

tff(f7273,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_n1699378549t_bool(fequal_nat,X2))),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
      | ~ sP23(X0,X1,X2) ),
    inference(forward_demodulation,[],[f6381,f6931]) ).

tff(f6931,plain,
    ! [X0: nat] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) = hAPP_n1699378549t_bool(fequal_nat,X0) ),
    inference(forward_demodulation,[],[f4679,f4588]) ).

tff(f4588,plain,
    ! [X0: fun_nat_bool] : ( collect_nat(X0) = X0 ),
    inference(cnf_transformation,[],[f1316]) ).

tff(f1316,plain,
    ! [X0: fun_nat_bool] : ( collect_nat(X0) = X0 ),
    inference(rectify,[],[f382]) ).

tff(f382,axiom,
    ! [X10: fun_nat_bool] : ( collect_nat(X10) = X10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_381_Collect__def) ).

tff(f4679,plain,
    ! [X0: nat] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) = collect_nat(hAPP_n1699378549t_bool(fequal_nat,X0)) ),
    inference(cnf_transformation,[],[f1407]) ).

tff(f1407,plain,
    ! [X0: nat] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) = collect_nat(hAPP_n1699378549t_bool(fequal_nat,X0)) ),
    inference(rectify,[],[f642]) ).

tff(f642,axiom,
    ! [X5: nat] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5),bot_bot_fun_nat_bool) = collect_nat(hAPP_n1699378549t_bool(fequal_nat,X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_641_singleton__conv2) ).

tff(f6381,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
      | ~ sP23(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4470]) ).

tff(f4470,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool,X2: nat] :
      ( ( sP23(X0,X1,X2)
        | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
        | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))),X0))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ) )
      & ( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
            | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
          & ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))),X0))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ) )
        | ~ sP23(X0,X1,X2) ) ),
    inference(rectify,[],[f4469]) ).

tff(f4469,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
      ( ( sP23(X2,X0,X1)
        | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X2))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) )
        | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))),X2))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) ) )
      & ( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X2))
            | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) )
          & ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))),X2))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) ) )
        | ~ sP23(X2,X0,X1) ) ),
    inference(flattening,[],[f4468]) ).

tff(f4468,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
      ( ( sP23(X2,X0,X1)
        | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X2))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) )
        | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))),X2))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) ) )
      & ( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X2))
            | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) )
          & ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))),X2))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) ) )
        | ~ sP23(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f3729]) ).

tff(f3729,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
      ( sP23(X2,X0,X1)
    <=> ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X2))
          | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) )
        & ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))),X2))
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP23])]) ).

tff(f29787,plain,
    spl250_1409,
    inference(avatar_split_clause,[],[f7272,f29785]) ).

tff(f29785,plain,
    ( spl250_1409
  <=> ! [X2: nat,X0: fun_nat_bool,X1: fun_nat_bool] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_n1699378549t_bool(fequal_nat,X2))),X0))
        | sP23(X0,X1,X2)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1409])]) ).

tff(f7272,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_n1699378549t_bool(fequal_nat,X2))),X0))
      | sP23(X0,X1,X2)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ),
    inference(forward_demodulation,[],[f6384,f6931]) ).

tff(f6384,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: fun_nat_bool] :
      ( sP23(X0,X1,X2)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))),X0)) ),
    inference(cnf_transformation,[],[f4470]) ).

tff(f29783,plain,
    spl250_1408,
    inference(avatar_split_clause,[],[f7270,f29781]) ).

tff(f29781,plain,
    ( spl250_1408
  <=> ! [X2: int,X0: fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_i1948725293t_bool(fequal_int,X2))),X0))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
        | ~ sP22(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1408])]) ).

tff(f7270,plain,
    ! [X2: int,X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_i1948725293t_bool(fequal_int,X2))),X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
      | ~ sP22(X0,X1,X2) ),
    inference(forward_demodulation,[],[f6364,f6930]) ).

tff(f6930,plain,
    ! [X0: int] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = hAPP_i1948725293t_bool(fequal_int,X0) ),
    inference(forward_demodulation,[],[f4678,f4586]) ).

tff(f4586,plain,
    ! [X0: fun_int_bool] : ( collect_int(X0) = X0 ),
    inference(cnf_transformation,[],[f1314]) ).

tff(f1314,plain,
    ! [X0: fun_int_bool] : ( collect_int(X0) = X0 ),
    inference(rectify,[],[f381]) ).

tff(f381,axiom,
    ! [X10: fun_int_bool] : ( collect_int(X10) = X10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_380_Collect__def) ).

tff(f4678,plain,
    ! [X0: int] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = collect_int(hAPP_i1948725293t_bool(fequal_int,X0)) ),
    inference(cnf_transformation,[],[f1406]) ).

tff(f1406,plain,
    ! [X0: int] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = collect_int(hAPP_i1948725293t_bool(fequal_int,X0)) ),
    inference(rectify,[],[f641]) ).

tff(f641,axiom,
    ! [X5: int] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5),bot_bot_fun_int_bool) = collect_int(hAPP_i1948725293t_bool(fequal_int,X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_640_singleton__conv2) ).

tff(f6364,plain,
    ! [X2: int,X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))),X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
      | ~ sP22(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4460]) ).

tff(f4460,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool,X2: int] :
      ( ( sP22(X0,X1,X2)
        | ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
        | ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))),X0))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ) )
      & ( ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
            | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
          & ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))),X0))
            | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ) )
        | ~ sP22(X0,X1,X2) ) ),
    inference(rectify,[],[f4459]) ).

tff(f4459,plain,
    ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] :
      ( ( sP22(X2,X0,X1)
        | ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X2))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) )
        | ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))),X2))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) ) )
      & ( ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X2))
            | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) )
          & ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))),X2))
            | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) ) )
        | ~ sP22(X2,X0,X1) ) ),
    inference(flattening,[],[f4458]) ).

tff(f4458,plain,
    ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] :
      ( ( sP22(X2,X0,X1)
        | ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X2))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) )
        | ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))),X2))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) ) )
      & ( ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X2))
            | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) )
          & ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))),X2))
            | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) ) )
        | ~ sP22(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f3727]) ).

tff(f3727,plain,
    ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] :
      ( sP22(X2,X0,X1)
    <=> ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X2))
          | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) )
        & ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))),X2))
          | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP22])]) ).

tff(f29779,plain,
    spl250_1407,
    inference(avatar_split_clause,[],[f7269,f29777]) ).

tff(f29777,plain,
    ( spl250_1407
  <=> ! [X2: int,X0: fun_int_bool,X1: fun_int_bool] :
        ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_i1948725293t_bool(fequal_int,X2))),X0))
        | sP22(X0,X1,X2)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1407])]) ).

tff(f7269,plain,
    ! [X2: int,X0: fun_int_bool,X1: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_i1948725293t_bool(fequal_int,X2))),X0))
      | sP22(X0,X1,X2)
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ),
    inference(forward_demodulation,[],[f6367,f6930]) ).

tff(f6367,plain,
    ! [X2: int,X0: fun_int_bool,X1: fun_int_bool] :
      ( sP22(X0,X1,X2)
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))),X0)) ),
    inference(cnf_transformation,[],[f4460]) ).

tff(f29775,plain,
    ( spl250_1406
    | spl250_1
    | ~ spl250_152
    | ~ spl250_673 ),
    inference(avatar_split_clause,[],[f13881,f12741,f8093,f7314,f29773]) ).

tff(f29773,plain,
    ( spl250_1406
  <=> ! [X0: nat,X1: nat] : ~ sP24(bot_bot_fun_int_bool,X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1406])]) ).

tff(f7314,plain,
    ( spl250_1
  <=> hBOOL(fFalse) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1])]) ).

tff(f8093,plain,
    ( spl250_152
  <=> ! [X0: int] : ( fFalse = hAPP_int_bool(bot_bot_fun_int_bool,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_152])]) ).

tff(f12741,plain,
    ( spl250_673
  <=> ! [X2: nat,X0: fun_int_bool,X1: nat] :
        ( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))))
        | ~ sP24(X0,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_673])]) ).

tff(f13881,plain,
    ( ! [X0: nat,X1: nat] :
        ( hBOOL(fFalse)
        | ~ sP24(bot_bot_fun_int_bool,X1,X0) )
    | ~ spl250_152
    | ~ spl250_673 ),
    inference(superposition,[],[f12742,f8094]) ).

tff(f8094,plain,
    ( ! [X0: int] : ( fFalse = hAPP_int_bool(bot_bot_fun_int_bool,X0) )
    | ~ spl250_152 ),
    inference(avatar_component_clause,[],[f8093]) ).

tff(f12742,plain,
    ( ! [X2: nat,X0: fun_int_bool,X1: nat] :
        ( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))))
        | ~ sP24(X0,X2,X1) )
    | ~ spl250_673 ),
    inference(avatar_component_clause,[],[f12741]) ).

tff(f29771,plain,
    spl250_1405,
    inference(avatar_split_clause,[],[f7215,f29769]) ).

tff(f29769,plain,
    ( spl250_1405
  <=> ! [X2: int,X0: int,X1: nat] :
        ( ~ hBOOL(hAPP_int_bool(nat_neg,X2))
        | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1405])]) ).

tff(f7215,plain,
    ! [X2: int,X0: int,X1: nat] :
      ( ~ hBOOL(hAPP_int_bool(nat_neg,X2))
      | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1)) ) ),
    inference(forward_demodulation,[],[f5779,f4587]) ).

tff(f4587,plain,
    ! [X0: int] : ( number_number_of_int(X0) = X0 ),
    inference(cnf_transformation,[],[f1315]) ).

tff(f1315,plain,
    ! [X0: int] : ( number_number_of_int(X0) = X0 ),
    inference(rectify,[],[f1072]) ).

tff(f1072,axiom,
    ! [X19: int] : ( number_number_of_int(X19) = X19 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1071_number__of__is__id) ).

tff(f5779,plain,
    ! [X2: int,X0: int,X1: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1)) )
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X2))) ),
    inference(cnf_transformation,[],[f3068]) ).

tff(f3068,plain,
    ! [X0: int,X1: nat,X2: int] :
      ( ( ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X0))),X1) )
            | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
          & ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),X1) )
            | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) )
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X2))) )
      & ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1)) )
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X2))) ) ),
    inference(ennf_transformation,[],[f2154]) ).

tff(f2154,plain,
    ! [X0: int,X1: nat,X2: int] :
      ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X2)))
       => ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
           => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X0))),X1) ) )
          & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
           => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),X1) ) ) ) )
      & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X2)))
       => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),X1)) ) ) ),
    inference(rectify,[],[f1156]) ).

tff(f1156,axiom,
    ! [X153: int,X19: nat,X130: int] :
      ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X130)))
       => ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X153)))
           => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X130)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X153)),X19)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X130),X153))),X19) ) )
          & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X153)))
           => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X130)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X153)),X19)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X130)),X19) ) ) ) )
      & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X130)))
       => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X153)),X19) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X130)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X153)),X19)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1155_nat__number__of__add__left) ).

tff(f29767,plain,
    spl250_1404,
    inference(avatar_split_clause,[],[f7209,f29765]) ).

tff(f29765,plain,
    ( spl250_1404
  <=> ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] : ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),collect_a(hAPP_a_fun_a_bool(fequal_a,X1)))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1404])]) ).

tff(f7209,plain,
    ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] : ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),collect_a(hAPP_a_fun_a_bool(fequal_a,X1)))),X2) ),
    inference(forward_demodulation,[],[f5766,f4680]) ).

tff(f5766,plain,
    ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] : ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))),X2) ),
    inference(cnf_transformation,[],[f2142]) ).

tff(f2142,plain,
    ! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))),X2) ),
    inference(rectify,[],[f556]) ).

tff(f556,axiom,
    ! [X2: fun_a_bool,X5: x_a,X7: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),X7)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),bot_bot_fun_a_bool))),X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_555_Diff__insert2) ).

tff(f29763,plain,
    spl250_1403,
    inference(avatar_split_clause,[],[f7208,f29761]) ).

tff(f29761,plain,
    ( spl250_1403
  <=> ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] : ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2)),collect_a(hAPP_a_fun_a_bool(fequal_a,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1403])]) ).

tff(f7208,plain,
    ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] : ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2)),collect_a(hAPP_a_fun_a_bool(fequal_a,X1))) ),
    inference(forward_demodulation,[],[f5765,f4680]) ).

tff(f5765,plain,
    ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] : ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)) ),
    inference(cnf_transformation,[],[f2141]) ).

tff(f2141,plain,
    ! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)) ),
    inference(rectify,[],[f559]) ).

tff(f559,axiom,
    ! [X2: fun_a_bool,X5: x_a,X7: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),X7)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X7)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),bot_bot_fun_a_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_558_Diff__insert) ).

tff(f29759,plain,
    spl250_1402,
    inference(avatar_split_clause,[],[f7080,f29757]) ).

tff(f29757,plain,
    ( spl250_1402
  <=> ! [X0: nat,X1: nat] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1402])]) ).

tff(f7080,plain,
    ! [X0: nat,X1: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ),
    inference(forward_demodulation,[],[f7079,f4566]) ).

tff(f4566,plain,
    one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
    inference(cnf_transformation,[],[f958]) ).

tff(f958,axiom,
    one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_957_One__nat__def) ).

tff(f7079,plain,
    ! [X0: nat,X1: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
    inference(forward_demodulation,[],[f7078,f4566]) ).

tff(f7078,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
    inference(forward_demodulation,[],[f5377,f4566]) ).

tff(f5377,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
    inference(cnf_transformation,[],[f3022]) ).

tff(f3022,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
    inference(flattening,[],[f3021]) ).

tff(f3021,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
    inference(ennf_transformation,[],[f1921]) ).

tff(f1921,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ) ),
    inference(rectify,[],[f1011]) ).

tff(f1011,axiom,
    ! [X12: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X11))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X12))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X12),X11))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1010_one__less__mult) ).

tff(f29755,plain,
    spl250_1401,
    inference(avatar_split_clause,[],[f7077,f29753]) ).

tff(f29753,plain,
    ( spl250_1401
  <=> ! [X0: nat,X1: nat] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1401])]) ).

tff(f7077,plain,
    ! [X0: nat,X1: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0))) ),
    inference(forward_demodulation,[],[f7076,f4566]) ).

tff(f7076,plain,
    ! [X0: nat,X1: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
    inference(forward_demodulation,[],[f5376,f4566]) ).

tff(f5376,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
    inference(cnf_transformation,[],[f3020]) ).

tff(f3020,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
    inference(flattening,[],[f3019]) ).

tff(f3019,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
    inference(ennf_transformation,[],[f1920]) ).

tff(f1920,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0))) ) ),
    inference(rectify,[],[f1010]) ).

tff(f1010,axiom,
    ! [X12: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X11))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X12))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X11),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X11),X12))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1009_n__less__n__mult__m) ).

tff(f29751,plain,
    spl250_1400,
    inference(avatar_split_clause,[],[f7075,f29749]) ).

tff(f29749,plain,
    ( spl250_1400
  <=> ! [X0: nat,X1: nat] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1400])]) ).

tff(f7075,plain,
    ! [X0: nat,X1: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ),
    inference(forward_demodulation,[],[f7074,f4566]) ).

tff(f7074,plain,
    ! [X0: nat,X1: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
    inference(forward_demodulation,[],[f5375,f4566]) ).

tff(f5375,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
    inference(cnf_transformation,[],[f3018]) ).

tff(f3018,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
    inference(flattening,[],[f3017]) ).

tff(f3017,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1)) ),
    inference(ennf_transformation,[],[f1919]) ).

tff(f1919,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X0))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ) ),
    inference(rectify,[],[f1009]) ).

tff(f1009,axiom,
    ! [X12: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X11))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X12))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X11),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X12),X11))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1008_n__less__m__mult__n) ).

tff(f29747,plain,
    spl250_1399,
    inference(avatar_split_clause,[],[f6641,f29745]) ).

tff(f29745,plain,
    ( spl250_1399
  <=> ! [X0: int,X1: int] :
        ( ( X0 = X1 )
        | ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1399])]) ).

tff(f6641,plain,
    ! [X0: int,X1: int] :
      ( ( X0 = X1 )
      | ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1) ) ),
    inference(definition_unfolding,[],[f5462,f4687,f4687]) ).

tff(f4687,plain,
    ! [X0: int] : ( bit1(X0) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0) ),
    inference(cnf_transformation,[],[f1415]) ).

tff(f1415,plain,
    ! [X0: int] : ( bit1(X0) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0) ),
    inference(rectify,[],[f1178]) ).

tff(f1178,axiom,
    ! [X19: int] : ( bit1(X19) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X19)),X19) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1177_Bit1__def) ).

tff(f5462,plain,
    ! [X0: int,X1: int] :
      ( ( X0 = X1 )
      | ( bit1(X0) != bit1(X1) ) ),
    inference(cnf_transformation,[],[f4040]) ).

tff(f4040,plain,
    ! [X0: int,X1: int] :
      ( ( ( bit1(X0) = bit1(X1) )
        | ( X0 != X1 ) )
      & ( ( X0 = X1 )
        | ( bit1(X0) != bit1(X1) ) ) ),
    inference(nnf_transformation,[],[f1970]) ).

tff(f1970,plain,
    ! [X0: int,X1: int] :
      ( ( bit1(X0) = bit1(X1) )
    <=> ( X0 = X1 ) ),
    inference(rectify,[],[f1182]) ).

tff(f1182,axiom,
    ! [X13: int,X131: int] :
      ( ( bit1(X13) = bit1(X131) )
    <=> ( X13 = X131 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1181_rel__simps_I51_J) ).

tff(f29743,plain,
    spl250_1398,
    inference(avatar_split_clause,[],[f6636,f29741]) ).

tff(f29741,plain,
    ( spl250_1398
  <=> ! [X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1398])]) ).

tff(f6636,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
    inference(definition_unfolding,[],[f5298,f4550,f4550,f4550]) ).

tff(f4550,plain,
    zero_zero_int = pls,
    inference(cnf_transformation,[],[f1181]) ).

tff(f1181,axiom,
    zero_zero_int = pls,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1180_Pls__def) ).

tff(f5298,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
    inference(cnf_transformation,[],[f2919]) ).

tff(f2919,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
    inference(flattening,[],[f2918]) ).

tff(f2918,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
    inference(ennf_transformation,[],[f1851]) ).

tff(f1851,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0))) ) ),
    inference(rectify,[],[f1086]) ).

tff(f1086,axiom,
    ! [X16: int,X15: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X15))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X16))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X15),X16))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1085_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).

tff(f29739,plain,
    spl250_1397,
    inference(avatar_split_clause,[],[f6635,f29737]) ).

tff(f29737,plain,
    ( spl250_1397
  <=> ! [X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1397])]) ).

tff(f6635,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
    inference(definition_unfolding,[],[f5297,f4550,f4550,f4550]) ).

tff(f5297,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
    inference(cnf_transformation,[],[f2917]) ).

tff(f2917,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
    inference(flattening,[],[f2916]) ).

tff(f2916,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
    inference(ennf_transformation,[],[f1850]) ).

tff(f1850,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0))) ) ),
    inference(rectify,[],[f1084]) ).

tff(f1084,axiom,
    ! [X16: int,X15: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X15))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X16))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X15),X16))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1083_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).

tff(f29735,plain,
    spl250_1396,
    inference(avatar_split_clause,[],[f6634,f29733]) ).

tff(f29733,plain,
    ( spl250_1396
  <=> ! [X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1396])]) ).

tff(f6634,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
    inference(definition_unfolding,[],[f5296,f4550,f4550,f4550]) ).

tff(f5296,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
    inference(cnf_transformation,[],[f2915]) ).

tff(f2915,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
    inference(flattening,[],[f2914]) ).

tff(f2914,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
    inference(ennf_transformation,[],[f1849]) ).

tff(f1849,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0))) ) ),
    inference(rectify,[],[f1129]) ).

tff(f1129,axiom,
    ! [X16: int,X15: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X15))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X16))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X15),X16))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1128_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).

tff(f29730,plain,
    spl250_1395,
    inference(avatar_split_clause,[],[f6395,f29728]) ).

tff(f29728,plain,
    ( spl250_1395
  <=> ! [X2: nat,X0: fun_int_bool,X1: nat] :
        ( sP24(X0,X1,X2)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
        | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X2)),hAPP_nat_int(semiri1621563631at_int,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1395])]) ).

tff(f6395,plain,
    ! [X2: nat,X0: fun_int_bool,X1: nat] :
      ( sP24(X0,X1,X2)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X2)),hAPP_nat_int(semiri1621563631at_int,X1)))) ),
    inference(cnf_transformation,[],[f4476]) ).

tff(f4476,plain,
    ! [X0: fun_int_bool,X1: nat,X2: nat] :
      ( ( sP24(X0,X1,X2)
        | ( ~ hBOOL(hAPP_int_bool(X0,zero_zero_int))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) )
        | ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X2)),hAPP_nat_int(semiri1621563631at_int,X1))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) )
      & ( ( ( hBOOL(hAPP_int_bool(X0,zero_zero_int))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) )
          & ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X2)),hAPP_nat_int(semiri1621563631at_int,X1))))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) )
        | ~ sP24(X0,X1,X2) ) ),
    inference(rectify,[],[f4475]) ).

tff(f4475,plain,
    ! [X0: fun_int_bool,X2: nat,X1: nat] :
      ( ( sP24(X0,X2,X1)
        | ( ~ hBOOL(hAPP_int_bool(X0,zero_zero_int))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
        | ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ) )
      & ( ( ( hBOOL(hAPP_int_bool(X0,zero_zero_int))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
          & ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ) )
        | ~ sP24(X0,X2,X1) ) ),
    inference(flattening,[],[f4474]) ).

tff(f4474,plain,
    ! [X0: fun_int_bool,X2: nat,X1: nat] :
      ( ( sP24(X0,X2,X1)
        | ( ~ hBOOL(hAPP_int_bool(X0,zero_zero_int))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
        | ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ) )
      & ( ( ( hBOOL(hAPP_int_bool(X0,zero_zero_int))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
          & ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ) )
        | ~ sP24(X0,X2,X1) ) ),
    inference(nnf_transformation,[],[f3731]) ).

tff(f3731,plain,
    ! [X0: fun_int_bool,X2: nat,X1: nat] :
      ( sP24(X0,X2,X1)
    <=> ( ( hBOOL(hAPP_int_bool(X0,zero_zero_int))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
        & ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP24])]) ).

tff(f29726,plain,
    spl250_1394,
    inference(avatar_split_clause,[],[f6392,f29724]) ).

tff(f29724,plain,
    ( spl250_1394
  <=> ! [X2: nat,X0: fun_int_bool,X1: nat] :
        ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X2)),hAPP_nat_int(semiri1621563631at_int,X1))))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
        | ~ sP24(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1394])]) ).

tff(f6392,plain,
    ! [X2: nat,X0: fun_int_bool,X1: nat] :
      ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X2)),hAPP_nat_int(semiri1621563631at_int,X1))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ sP24(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4476]) ).

tff(f29722,plain,
    spl250_1393,
    inference(avatar_split_clause,[],[f6391,f29720]) ).

tff(f29720,plain,
    ( spl250_1393
  <=> ! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),X2))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1393])]) ).

tff(f6391,plain,
    ! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),X2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) ),
    inference(cnf_transformation,[],[f4473]) ).

tff(f4473,plain,
    ! [X0: nat,X1: fun_nat_bool,X2: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),X2))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) )
      & ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),X2)) ) ),
    inference(flattening,[],[f4472]) ).

tff(f4472,plain,
    ! [X0: nat,X1: fun_nat_bool,X2: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),X2))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) )
      & ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),X2)) ) ),
    inference(nnf_transformation,[],[f2493]) ).

tff(f2493,plain,
    ! [X0: nat,X1: fun_nat_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),X2))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) ) ),
    inference(rectify,[],[f456]) ).

tff(f456,axiom,
    ! [X8: nat,X2: fun_nat_bool,X7: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X2)),X7))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X7))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_455_insert__subset) ).

tff(f29718,plain,
    spl250_1392,
    inference(avatar_split_clause,[],[f6374,f29716]) ).

tff(f29716,plain,
    ( spl250_1392
  <=> ! [X2: fun_int_bool,X0: int,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),X2))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1392])]) ).

tff(f6374,plain,
    ! [X2: fun_int_bool,X0: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),X2))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2)) ),
    inference(cnf_transformation,[],[f4463]) ).

tff(f4463,plain,
    ! [X0: int,X1: fun_int_bool,X2: fun_int_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),X2))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2)) )
      & ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2)) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),X2)) ) ),
    inference(flattening,[],[f4462]) ).

tff(f4462,plain,
    ! [X0: int,X1: fun_int_bool,X2: fun_int_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),X2))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2)) )
      & ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2)) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),X2)) ) ),
    inference(nnf_transformation,[],[f2489]) ).

tff(f2489,plain,
    ! [X0: int,X1: fun_int_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),X2))
    <=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2)) ) ),
    inference(rectify,[],[f455]) ).

tff(f455,axiom,
    ! [X8: int,X2: fun_int_bool,X7: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X2)),X7))
    <=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X7))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_454_insert__subset) ).

tff(f29714,plain,
    spl250_1391,
    inference(avatar_split_clause,[],[f6357,f29712]) ).

tff(f6357,plain,
    ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ),
    inference(cnf_transformation,[],[f4453]) ).

tff(f4453,plain,
    ! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
      & ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2)) ) ),
    inference(flattening,[],[f4452]) ).

tff(f4452,plain,
    ! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
      & ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2)) ) ),
    inference(nnf_transformation,[],[f2485]) ).

tff(f2485,plain,
    ! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2))
    <=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ) ),
    inference(rectify,[],[f454]) ).

tff(f454,axiom,
    ! [X8: x_a,X2: fun_a_bool,X7: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X2)),X7))
    <=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_453_insert__subset) ).

tff(f29710,plain,
    spl250_1390,
    inference(avatar_split_clause,[],[f6340,f29708]) ).

tff(f29708,plain,
    ( spl250_1390
  <=> ! [X2: fun_pname_bool,X0: pname,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),X2))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1390])]) ).

tff(f6340,plain,
    ! [X2: fun_pname_bool,X0: pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),X2))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) ),
    inference(cnf_transformation,[],[f4443]) ).

tff(f4443,plain,
    ! [X0: pname,X1: fun_pname_bool,X2: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),X2))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) )
      & ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),X2)) ) ),
    inference(flattening,[],[f4442]) ).

tff(f4442,plain,
    ! [X0: pname,X1: fun_pname_bool,X2: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),X2))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) )
      & ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),X2)) ) ),
    inference(nnf_transformation,[],[f2481]) ).

tff(f2481,plain,
    ! [X0: pname,X1: fun_pname_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),X2))
    <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) ) ),
    inference(rectify,[],[f457]) ).

tff(f457,axiom,
    ! [X8: pname,X2: fun_pname_bool,X7: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),X2)),X7))
    <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X7))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_456_insert__subset) ).

tff(f29706,plain,
    spl250_1389,
    inference(avatar_split_clause,[],[f6179,f29704]) ).

tff(f29704,plain,
    ( spl250_1389
  <=> ! [X2: nat,X0: fun_nat_bool,X1: nat] :
        ( hBOOL(hAPP_nat_bool(X0,X1))
        | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,sK222(X0,X2))))
        | ~ hBOOL(hAPP_nat_bool(X0,X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1389])]) ).

tff(f6179,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_nat_bool(X0,X1))
      | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,sK222(X0,X2))))
      | ~ hBOOL(hAPP_nat_bool(X0,X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f4351]) ).

tff(f4351,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(X0,X1))
      | ( ~ hBOOL(hAPP_nat_bool(X0,sK222(X0,X2)))
        & hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,sK222(X0,X2))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK222(X0,X2)),X2)) )
      | ~ hBOOL(hAPP_nat_bool(X0,X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK222])],[f3491,f4350]) ).

tff(f4350,plain,
    ! [X0: fun_nat_bool,X2: nat] :
      ( ? [X3: nat] :
          ( ~ hBOOL(hAPP_nat_bool(X0,X3))
          & hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,X3)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) )
     => ( ~ hBOOL(hAPP_nat_bool(X0,sK222(X0,X2)))
        & hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,sK222(X0,X2))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK222(X0,X2)),X2)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3491,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(X0,X1))
      | ? [X3: nat] :
          ( ~ hBOOL(hAPP_nat_bool(X0,X3))
          & hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,X3)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) )
      | ~ hBOOL(hAPP_nat_bool(X0,X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(flattening,[],[f3490]) ).

tff(f3490,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(X0,X1))
      | ? [X3: nat] :
          ( ~ hBOOL(hAPP_nat_bool(X0,X3))
          & hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,X3)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) )
      | ~ hBOOL(hAPP_nat_bool(X0,X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f2402]) ).

tff(f2402,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => ( hBOOL(hAPP_nat_bool(X0,X2))
       => ( ! [X3: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2))
             => ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,X3)))
               => hBOOL(hAPP_nat_bool(X0,X3)) ) )
         => hBOOL(hAPP_nat_bool(X0,X1)) ) ) ),
    inference(rectify,[],[f916]) ).

tff(f916,axiom,
    ! [X10: fun_nat_bool,X30: nat,X117: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X30),X117))
     => ( hBOOL(hAPP_nat_bool(X10,X117))
       => ( ! [X123: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X123),X117))
             => ( hBOOL(hAPP_nat_bool(X10,hAPP_nat_nat(suc,X123)))
               => hBOOL(hAPP_nat_bool(X10,X123)) ) )
         => hBOOL(hAPP_nat_bool(X10,X30)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_915_inc__induct) ).

tff(f29702,plain,
    spl250_1388,
    inference(avatar_split_clause,[],[f6178,f29700]) ).

tff(f29700,plain,
    ( spl250_1388
  <=> ! [X2: nat,X0: fun_nat_bool,X1: nat] :
        ( hBOOL(hAPP_nat_bool(X0,X1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK222(X0,X2)),X2))
        | ~ hBOOL(hAPP_nat_bool(X0,X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1388])]) ).

tff(f6178,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_nat_bool(X0,X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK222(X0,X2)),X2))
      | ~ hBOOL(hAPP_nat_bool(X0,X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f4351]) ).

tff(f29698,plain,
    spl250_1387,
    inference(avatar_split_clause,[],[f6140,f29696]) ).

tff(f29696,plain,
    ( spl250_1387
  <=> ! [X2: int,X0: fun_int_bool,X1: int] :
        ( hBOOL(hAPP_int_bool(X0,X2))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),sK221(X0,X1)))
        | ~ hBOOL(hAPP_int_bool(X0,X1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1387])]) ).

tff(f6140,plain,
    ! [X2: int,X0: fun_int_bool,X1: int] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),sK221(X0,X1)))
      | ~ hBOOL(hAPP_int_bool(X0,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
    inference(cnf_transformation,[],[f4349]) ).

tff(f4349,plain,
    ! [X0: fun_int_bool,X1: int,X2: int] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,sK221(X0,X1)),one_one_int)))
        & hBOOL(hAPP_int_bool(X0,sK221(X0,X1)))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),sK221(X0,X1))) )
      | ~ hBOOL(hAPP_int_bool(X0,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK221])],[f3444,f4348]) ).

tff(f4348,plain,
    ! [X0: fun_int_bool,X1: int] :
      ( ? [X3: int] :
          ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),one_one_int)))
          & hBOOL(hAPP_int_bool(X0,X3))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) )
     => ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,sK221(X0,X1)),one_one_int)))
        & hBOOL(hAPP_int_bool(X0,sK221(X0,X1)))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),sK221(X0,X1))) ) ),
    introduced(choice_axiom,[]) ).

tff(f3444,plain,
    ! [X0: fun_int_bool,X1: int,X2: int] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | ? [X3: int] :
          ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),one_one_int)))
          & hBOOL(hAPP_int_bool(X0,X3))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) )
      | ~ hBOOL(hAPP_int_bool(X0,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
    inference(flattening,[],[f3443]) ).

tff(f3443,plain,
    ! [X0: fun_int_bool,X1: int,X2: int] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | ? [X3: int] :
          ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),one_one_int)))
          & hBOOL(hAPP_int_bool(X0,X3))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) )
      | ~ hBOOL(hAPP_int_bool(X0,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
    inference(ennf_transformation,[],[f2366]) ).

tff(f2366,plain,
    ! [X0: fun_int_bool,X1: int,X2: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
     => ( hBOOL(hAPP_int_bool(X0,X1))
       => ( ! [X3: int] :
              ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
             => ( hBOOL(hAPP_int_bool(X0,X3))
               => hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),one_one_int))) ) )
         => hBOOL(hAPP_int_bool(X0,X2)) ) ) ),
    inference(rectify,[],[f1083]) ).

tff(f1083,axiom,
    ! [X10: fun_int_bool,X13: int,X30: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X13),X30))
     => ( hBOOL(hAPP_int_bool(X10,X13))
       => ( ! [X123: int] :
              ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X13),X123))
             => ( hBOOL(hAPP_int_bool(X10,X123))
               => hBOOL(hAPP_int_bool(X10,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X123),one_one_int))) ) )
         => hBOOL(hAPP_int_bool(X10,X30)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1082_int__ge__induct) ).

tff(f29694,plain,
    spl250_1386,
    inference(avatar_split_clause,[],[f6137,f29692]) ).

tff(f29692,plain,
    ( spl250_1386
  <=> ! [X2: int,X0: fun_int_bool,X1: int] :
        ( hBOOL(hAPP_int_bool(X0,X1))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK220(X0,X2)),X2))
        | ~ hBOOL(hAPP_int_bool(X0,X2))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1386])]) ).

tff(f6137,plain,
    ! [X2: int,X0: fun_int_bool,X1: int] :
      ( hBOOL(hAPP_int_bool(X0,X1))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK220(X0,X2)),X2))
      | ~ hBOOL(hAPP_int_bool(X0,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
    inference(cnf_transformation,[],[f4347]) ).

tff(f4347,plain,
    ! [X0: fun_int_bool,X1: int,X2: int] :
      ( hBOOL(hAPP_int_bool(X0,X1))
      | ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK220(X0,X2)),one_one_int)))
        & hBOOL(hAPP_int_bool(X0,sK220(X0,X2)))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK220(X0,X2)),X2)) )
      | ~ hBOOL(hAPP_int_bool(X0,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK220])],[f3442,f4346]) ).

tff(f4346,plain,
    ! [X0: fun_int_bool,X2: int] :
      ( ? [X3: int] :
          ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),one_one_int)))
          & hBOOL(hAPP_int_bool(X0,X3))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2)) )
     => ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK220(X0,X2)),one_one_int)))
        & hBOOL(hAPP_int_bool(X0,sK220(X0,X2)))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK220(X0,X2)),X2)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3442,plain,
    ! [X0: fun_int_bool,X1: int,X2: int] :
      ( hBOOL(hAPP_int_bool(X0,X1))
      | ? [X3: int] :
          ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),one_one_int)))
          & hBOOL(hAPP_int_bool(X0,X3))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2)) )
      | ~ hBOOL(hAPP_int_bool(X0,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
    inference(flattening,[],[f3441]) ).

tff(f3441,plain,
    ! [X0: fun_int_bool,X1: int,X2: int] :
      ( hBOOL(hAPP_int_bool(X0,X1))
      | ? [X3: int] :
          ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),one_one_int)))
          & hBOOL(hAPP_int_bool(X0,X3))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2)) )
      | ~ hBOOL(hAPP_int_bool(X0,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
    inference(ennf_transformation,[],[f2365]) ).

tff(f2365,plain,
    ! [X0: fun_int_bool,X1: int,X2: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
     => ( hBOOL(hAPP_int_bool(X0,X2))
       => ( ! [X3: int] :
              ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2))
             => ( hBOOL(hAPP_int_bool(X0,X3))
               => hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),one_one_int))) ) )
         => hBOOL(hAPP_int_bool(X0,X1)) ) ) ),
    inference(rectify,[],[f1081]) ).

tff(f1081,axiom,
    ! [X10: fun_int_bool,X30: int,X13: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X30),X13))
     => ( hBOOL(hAPP_int_bool(X10,X13))
       => ( ! [X123: int] :
              ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X123),X13))
             => ( hBOOL(hAPP_int_bool(X10,X123))
               => hBOOL(hAPP_int_bool(X10,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X123),one_one_int))) ) )
         => hBOOL(hAPP_int_bool(X10,X30)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1080_int__le__induct) ).

tff(f29690,plain,
    ( spl250_1385
    | spl250_1
    | ~ spl250_212
    | ~ spl250_507 ),
    inference(avatar_split_clause,[],[f11423,f10728,f8396,f7314,f29688]) ).

tff(f29688,plain,
    ( spl250_1385
  <=> ! [X0: nat,X1: nat] : ~ sP19(bot_bot_fun_nat_bool,X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1385])]) ).

tff(f8396,plain,
    ( spl250_212
  <=> ! [X0: nat] : ( fFalse = hAPP_nat_bool(bot_bot_fun_nat_bool,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_212])]) ).

tff(f10728,plain,
    ( spl250_507
  <=> ! [X2: nat,X0: fun_nat_bool,X1: nat] :
        ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
        | ~ sP19(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_507])]) ).

tff(f11423,plain,
    ( ! [X0: nat,X1: nat] :
        ( hBOOL(fFalse)
        | ~ sP19(bot_bot_fun_nat_bool,X0,X1) )
    | ~ spl250_212
    | ~ spl250_507 ),
    inference(superposition,[],[f10729,f8397]) ).

tff(f8397,plain,
    ( ! [X0: nat] : ( fFalse = hAPP_nat_bool(bot_bot_fun_nat_bool,X0) )
    | ~ spl250_212 ),
    inference(avatar_component_clause,[],[f8396]) ).

tff(f10729,plain,
    ( ! [X2: nat,X0: fun_nat_bool,X1: nat] :
        ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
        | ~ sP19(X0,X1,X2) )
    | ~ spl250_507 ),
    inference(avatar_component_clause,[],[f10728]) ).

tff(f29686,plain,
    spl250_1384,
    inference(avatar_split_clause,[],[f6107,f29684]) ).

tff(f29684,plain,
    ( spl250_1384
  <=> ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X0)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1384])]) ).

tff(f6107,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X0)))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f3399]) ).

tff(f3399,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X0)))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
    inference(flattening,[],[f3398]) ).

tff(f3398,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X0)))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f2339]) ).

tff(f2339,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X0))) ) ),
    inference(rectify,[],[f710]) ).

tff(f710,axiom,
    ! [X7: fun_nat_bool,X29: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),X2))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),X7))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X7))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_709_DiffI) ).

tff(f29682,plain,
    spl250_1383,
    inference(avatar_split_clause,[],[f6087,f29680]) ).

tff(f29680,plain,
    ( spl250_1383
  <=> ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X0)))
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1383])]) ).

tff(f6087,plain,
    ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X0)))
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
    inference(cnf_transformation,[],[f3368]) ).

tff(f3368,plain,
    ! [X0: fun_int_bool,X1: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X0)))
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
    inference(flattening,[],[f3367]) ).

tff(f3367,plain,
    ! [X0: fun_int_bool,X1: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X0)))
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
    inference(ennf_transformation,[],[f2319]) ).

tff(f2319,plain,
    ! [X0: fun_int_bool,X1: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
     => ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
       => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X0))) ) ),
    inference(rectify,[],[f709]) ).

tff(f709,axiom,
    ! [X7: fun_int_bool,X29: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X29),X2))
     => ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X29),X7))
       => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X29),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X7))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_708_DiffI) ).

tff(f29678,plain,
    spl250_1382,
    inference(avatar_split_clause,[],[f6070,f29676]) ).

tff(f29676,plain,
    ( spl250_1382
  <=> ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X0)))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1382])]) ).

tff(f6070,plain,
    ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X0)))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
    inference(cnf_transformation,[],[f3340]) ).

tff(f3340,plain,
    ! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X0)))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
    inference(flattening,[],[f3339]) ).

tff(f3339,plain,
    ! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X0)))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
    inference(ennf_transformation,[],[f2302]) ).

tff(f2302,plain,
    ! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
     => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X0))) ) ),
    inference(rectify,[],[f711]) ).

tff(f711,axiom,
    ! [X7: fun_a_bool,X29: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X29),X2))
     => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X29),X7))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X29),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X7))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_710_DiffI) ).

tff(f29674,plain,
    spl250_1381,
    inference(avatar_split_clause,[],[f6066,f29672]) ).

tff(f29672,plain,
    ( spl250_1381
  <=> ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X0)))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1381])]) ).

tff(f6066,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X0)))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
    inference(cnf_transformation,[],[f3334]) ).

tff(f3334,plain,
    ! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X0)))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
    inference(flattening,[],[f3333]) ).

tff(f3333,plain,
    ! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X0)))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
    inference(ennf_transformation,[],[f2298]) ).

tff(f2298,plain,
    ! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
     => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X0))) ) ),
    inference(rectify,[],[f712]) ).

tff(f712,axiom,
    ! [X7: fun_pname_bool,X29: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X29),X2))
     => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X29),X7))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X29),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X7))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_711_DiffI) ).

tff(f29670,plain,
    spl250_1380,
    inference(avatar_split_clause,[],[f6031,f29668]) ).

tff(f29668,plain,
    ( spl250_1380
  <=> ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1380])]) ).

tff(f6031,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f4312]) ).

tff(f4312,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
      ( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)))
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0)) )
        & ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0))) ) )
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
    inference(nnf_transformation,[],[f3303]) ).

tff(f3303,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)))
      <=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0)) )
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f2277]) ).

tff(f2277,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)))
      <=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0)) ) ),
    inference(rectify,[],[f460]) ).

tff(f460,axiom,
    ! [X7: fun_nat_bool,X8: nat,X2: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X7)))
      <=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_459_subset__insert) ).

tff(f29666,plain,
    spl250_1379,
    inference(avatar_split_clause,[],[f6027,f29664]) ).

tff(f29664,plain,
    ( spl250_1379
  <=> ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)))
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1379])]) ).

tff(f6027,plain,
    ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)))
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
    inference(cnf_transformation,[],[f4310]) ).

tff(f4310,plain,
    ! [X0: fun_int_bool,X1: int,X2: fun_int_bool] :
      ( ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)))
          | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0)) )
        & ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
          | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0))) ) )
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
    inference(nnf_transformation,[],[f3300]) ).

tff(f3300,plain,
    ! [X0: fun_int_bool,X1: int,X2: fun_int_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)))
      <=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0)) )
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
    inference(ennf_transformation,[],[f2275]) ).

tff(f2275,plain,
    ! [X0: fun_int_bool,X1: int,X2: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)))
      <=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0)) ) ),
    inference(rectify,[],[f459]) ).

tff(f459,axiom,
    ! [X7: fun_int_bool,X8: int,X2: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X7)))
      <=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_458_subset__insert) ).

tff(f29662,plain,
    spl250_1378,
    inference(avatar_split_clause,[],[f6023,f29660]) ).

tff(f29660,plain,
    ( spl250_1378
  <=> ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1378])]) ).

tff(f6023,plain,
    ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
    inference(cnf_transformation,[],[f4308]) ).

tff(f4308,plain,
    ! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0)) )
        & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0))) ) )
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
    inference(nnf_transformation,[],[f3297]) ).

tff(f3297,plain,
    ! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)))
      <=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0)) )
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
    inference(ennf_transformation,[],[f2273]) ).

tff(f2273,plain,
    ! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)))
      <=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0)) ) ),
    inference(rectify,[],[f458]) ).

tff(f458,axiom,
    ! [X7: fun_a_bool,X8: x_a,X2: fun_a_bool] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X7)))
      <=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_457_subset__insert) ).

tff(f29658,plain,
    spl250_1377,
    inference(avatar_split_clause,[],[f6020,f29656]) ).

tff(f29656,plain,
    ( spl250_1377
  <=> ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1377])]) ).

tff(f6020,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
    inference(cnf_transformation,[],[f4306]) ).

tff(f4306,plain,
    ! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0)) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0))) ) )
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
    inference(nnf_transformation,[],[f3294]) ).

tff(f3294,plain,
    ! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)))
      <=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0)) )
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
    inference(ennf_transformation,[],[f2271]) ).

tff(f2271,plain,
    ! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)))
      <=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0)) ) ),
    inference(rectify,[],[f461]) ).

tff(f461,axiom,
    ! [X7: fun_pname_bool,X8: pname,X2: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),X7)))
      <=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_460_subset__insert) ).

tff(f29654,plain,
    spl250_1376,
    inference(avatar_split_clause,[],[f6019,f29652]) ).

tff(f29652,plain,
    ( spl250_1376
  <=> ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1376])]) ).

tff(f6019,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
    inference(cnf_transformation,[],[f4306]) ).

tff(f29650,plain,
    spl250_1375,
    inference(avatar_split_clause,[],[f5668,f29648]) ).

tff(f29648,plain,
    ( spl250_1375
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1375])]) ).

tff(f5668,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1))) ),
    inference(cnf_transformation,[],[f4177]) ).

tff(f4177,plain,
    ! [X0: nat,X1: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1))) ) ),
    inference(flattening,[],[f4176]) ).

tff(f4176,plain,
    ! [X0: nat,X1: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1))) ) ),
    inference(nnf_transformation,[],[f2050]) ).

tff(f2050,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
    inference(rectify,[],[f952]) ).

tff(f952,axiom,
    ! [X22: nat,X14: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X22),X14)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X14))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X22)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_951_add__gr__0) ).

tff(f29645,plain,
    spl250_1374,
    inference(avatar_split_clause,[],[f5665,f29643]) ).

tff(f29643,plain,
    ( spl250_1374
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1374])]) ).

tff(f5665,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f4174]) ).

tff(f4174,plain,
    ! [X0: nat,X1: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ) ),
    inference(flattening,[],[f4173]) ).

tff(f4173,plain,
    ! [X0: nat,X1: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ) ),
    inference(nnf_transformation,[],[f2048]) ).

tff(f2048,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
    inference(rectify,[],[f1003]) ).

tff(f1003,axiom,
    ! [X22: nat,X14: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X22),X14)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X14))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X22)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1002_nat__0__less__mult__iff) ).

tff(f29641,plain,
    spl250_1373,
    inference(avatar_split_clause,[],[f5300,f29639]) ).

tff(f29639,plain,
    ( spl250_1373
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X0))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1373])]) ).

tff(f5300,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
    inference(cnf_transformation,[],[f2922]) ).

tff(f2922,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
    inference(flattening,[],[f2921]) ).

tff(f2921,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
    inference(ennf_transformation,[],[f1853]) ).

tff(f1853,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X0)) ) ),
    inference(rectify,[],[f954]) ).

tff(f954,axiom,
    ! [X12: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X11))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X12))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X12),X11)),X12)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_953_diff__less) ).

tff(f29637,plain,
    spl250_1372,
    inference(avatar_split_clause,[],[f5261,f29635]) ).

tff(f29635,plain,
    ( spl250_1372
  <=> ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(X0,X1))
        | ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK115(X0)),sK116(X0))))
        | ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1372])]) ).

tff(f5261,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,X1))
      | ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK115(X0)),sK116(X0))))
      | ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f3972]) ).

tff(f3972,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,X1))
      | ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK115(X0)),sK116(X0))))
        & hBOOL(hAPP_f54304608l_bool(X0,sK116(X0)))
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK115(X0)),sK116(X0)))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK116(X0))) )
      | ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK115,sK116])],[f2876,f3971]) ).

tff(f3971,plain,
    ! [X0: fun_fu425979586l_bool] :
      ( ? [X2: nat,X3: fun_nat_bool] :
          ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3)))
          & hBOOL(hAPP_f54304608l_bool(X0,X3))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) )
     => ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK115(X0)),sK116(X0))))
        & hBOOL(hAPP_f54304608l_bool(X0,sK116(X0)))
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK115(X0)),sK116(X0)))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK116(X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f2876,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,X1))
      | ? [X2: nat,X3: fun_nat_bool] :
          ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3)))
          & hBOOL(hAPP_f54304608l_bool(X0,X3))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) )
      | ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(flattening,[],[f2875]) ).

tff(f2875,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,X1))
      | ? [X2: nat,X3: fun_nat_bool] :
          ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3)))
          & hBOOL(hAPP_f54304608l_bool(X0,X3))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) )
      | ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(ennf_transformation,[],[f1823]) ).

tff(f1823,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
     => ( hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
       => ( ! [X2: nat,X3: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
             => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3))
               => ( hBOOL(hAPP_f54304608l_bool(X0,X3))
                 => hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3))) ) ) )
         => hBOOL(hAPP_f54304608l_bool(X0,X1)) ) ) ),
    inference(rectify,[],[f690]) ).

tff(f690,axiom,
    ! [X10: fun_fu425979586l_bool,X4: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
     => ( hBOOL(hAPP_f54304608l_bool(X10,bot_bot_fun_nat_bool))
       => ( ! [X27: nat,X76: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X76))
             => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X27),X76))
               => ( hBOOL(hAPP_f54304608l_bool(X10,X76))
                 => hBOOL(hAPP_f54304608l_bool(X10,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X27),X76))) ) ) )
         => hBOOL(hAPP_f54304608l_bool(X10,X4)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_689_finite__induct) ).

tff(f29633,plain,
    spl250_1371,
    inference(avatar_split_clause,[],[f5218,f29631]) ).

tff(f29631,plain,
    ( spl250_1371
  <=> ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(X0,X1))
        | ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK108(X0)),sK109(X0))))
        | ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1371])]) ).

tff(f5218,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,X1))
      | ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK108(X0)),sK109(X0))))
      | ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f3961]) ).

tff(f3961,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,X1))
      | ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK108(X0)),sK109(X0))))
        & hBOOL(hAPP_f448129468l_bool(X0,sK109(X0)))
        & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK108(X0)),sK109(X0)))
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK109(X0))) )
      | ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK108,sK109])],[f2836,f3960]) ).

tff(f3960,plain,
    ! [X0: fun_fu819804446l_bool] :
      ( ? [X2: int,X3: fun_int_bool] :
          ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3)))
          & hBOOL(hAPP_f448129468l_bool(X0,X3))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X3))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) )
     => ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK108(X0)),sK109(X0))))
        & hBOOL(hAPP_f448129468l_bool(X0,sK109(X0)))
        & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK108(X0)),sK109(X0)))
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK109(X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f2836,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,X1))
      | ? [X2: int,X3: fun_int_bool] :
          ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3)))
          & hBOOL(hAPP_f448129468l_bool(X0,X3))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X3))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) )
      | ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(flattening,[],[f2835]) ).

tff(f2835,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,X1))
      | ? [X2: int,X3: fun_int_bool] :
          ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3)))
          & hBOOL(hAPP_f448129468l_bool(X0,X3))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X3))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) )
      | ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(ennf_transformation,[],[f1794]) ).

tff(f1794,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
     => ( hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
       => ( ! [X2: int,X3: fun_int_bool] :
              ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
             => ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X3))
               => ( hBOOL(hAPP_f448129468l_bool(X0,X3))
                 => hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3))) ) ) )
         => hBOOL(hAPP_f448129468l_bool(X0,X1)) ) ) ),
    inference(rectify,[],[f689]) ).

tff(f689,axiom,
    ! [X10: fun_fu819804446l_bool,X4: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
     => ( hBOOL(hAPP_f448129468l_bool(X10,bot_bot_fun_int_bool))
       => ( ! [X27: int,X76: fun_int_bool] :
              ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X76))
             => ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X27),X76))
               => ( hBOOL(hAPP_f448129468l_bool(X10,X76))
                 => hBOOL(hAPP_f448129468l_bool(X10,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X27),X76))) ) ) )
         => hBOOL(hAPP_f448129468l_bool(X10,X4)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_688_finite__induct) ).

tff(f29629,plain,
    spl250_1370,
    inference(avatar_split_clause,[],[f5179,f29627]) ).

tff(f29627,plain,
    ( spl250_1370
  <=> ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK101(X0)),sK102(X0))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1370])]) ).

tff(f5179,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK101(X0)),sK102(X0))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(cnf_transformation,[],[f3951]) ).

tff(f3951,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK101(X0)),sK102(X0))))
        & hBOOL(hAPP_fun_a_bool_bool(X0,sK102(X0)))
        & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK101(X0)),sK102(X0)))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK102(X0))) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK101,sK102])],[f2799,f3950]) ).

tff(f3950,plain,
    ! [X0: fun_fun_a_bool_bool] :
      ( ? [X2: x_a,X3: fun_a_bool] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3)))
          & hBOOL(hAPP_fun_a_bool_bool(X0,X3))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3)) )
     => ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK101(X0)),sK102(X0))))
        & hBOOL(hAPP_fun_a_bool_bool(X0,sK102(X0)))
        & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK101(X0)),sK102(X0)))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK102(X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f2799,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
      | ? [X2: x_a,X3: fun_a_bool] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3)))
          & hBOOL(hAPP_fun_a_bool_bool(X0,X3))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(flattening,[],[f2798]) ).

tff(f2798,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
      | ? [X2: x_a,X3: fun_a_bool] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3)))
          & hBOOL(hAPP_fun_a_bool_bool(X0,X3))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(ennf_transformation,[],[f1768]) ).

tff(f1768,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
     => ( hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
       => ( ! [X2: x_a,X3: fun_a_bool] :
              ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
             => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
               => ( hBOOL(hAPP_fun_a_bool_bool(X0,X3))
                 => hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3))) ) ) )
         => hBOOL(hAPP_fun_a_bool_bool(X0,X1)) ) ) ),
    inference(rectify,[],[f688]) ).

tff(f688,axiom,
    ! [X10: fun_fun_a_bool_bool,X4: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
     => ( hBOOL(hAPP_fun_a_bool_bool(X10,bot_bot_fun_a_bool))
       => ( ! [X27: x_a,X76: fun_a_bool] :
              ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X76))
             => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X27),X76))
               => ( hBOOL(hAPP_fun_a_bool_bool(X10,X76))
                 => hBOOL(hAPP_fun_a_bool_bool(X10,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X27),X76))) ) ) )
         => hBOOL(hAPP_fun_a_bool_bool(X10,X4)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_687_finite__induct) ).

tff(f29625,plain,
    spl250_1369,
    inference(avatar_split_clause,[],[f5138,f29623]) ).

tff(f29623,plain,
    ( spl250_1369
  <=> ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(X0,X1))
        | ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK94(X0)),sK95(X0))))
        | ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1369])]) ).

tff(f5138,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK94(X0)),sK95(X0))))
      | ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f3940]) ).

tff(f3940,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,X1))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK94(X0)),sK95(X0))))
        & hBOOL(hAPP_f1664156314l_bool(X0,sK95(X0)))
        & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK94(X0)),sK95(X0)))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK95(X0))) )
      | ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK94,sK95])],[f2761,f3939]) ).

tff(f3939,plain,
    ! [X0: fun_fu1430349052l_bool] :
      ( ? [X2: pname,X3: fun_pname_bool] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X3)))
          & hBOOL(hAPP_f1664156314l_bool(X0,X3))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3)) )
     => ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK94(X0)),sK95(X0))))
        & hBOOL(hAPP_f1664156314l_bool(X0,sK95(X0)))
        & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK94(X0)),sK95(X0)))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK95(X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f2761,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,X1))
      | ? [X2: pname,X3: fun_pname_bool] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X3)))
          & hBOOL(hAPP_f1664156314l_bool(X0,X3))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(flattening,[],[f2760]) ).

tff(f2760,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,X1))
      | ? [X2: pname,X3: fun_pname_bool] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X3)))
          & hBOOL(hAPP_f1664156314l_bool(X0,X3))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(ennf_transformation,[],[f1741]) ).

tff(f1741,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
     => ( hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
       => ( ! [X2: pname,X3: fun_pname_bool] :
              ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
             => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
               => ( hBOOL(hAPP_f1664156314l_bool(X0,X3))
                 => hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X3))) ) ) )
         => hBOOL(hAPP_f1664156314l_bool(X0,X1)) ) ) ),
    inference(rectify,[],[f691]) ).

tff(f691,axiom,
    ! [X10: fun_fu1430349052l_bool,X4: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
     => ( hBOOL(hAPP_f1664156314l_bool(X10,bot_bo844097828e_bool))
       => ( ! [X27: pname,X76: fun_pname_bool] :
              ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X76))
             => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X27),X76))
               => ( hBOOL(hAPP_f1664156314l_bool(X10,X76))
                 => hBOOL(hAPP_f1664156314l_bool(X10,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X27),X76))) ) ) )
         => hBOOL(hAPP_f1664156314l_bool(X10,X4)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_690_finite__induct) ).

tff(f29621,plain,
    spl250_1368,
    inference(avatar_split_clause,[],[f5134,f29619]) ).

tff(f29619,plain,
    ( spl250_1368
  <=> ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(X0,X1))
        | sP0(X0)
        | ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK93(X0)),bot_bo844097828e_bool)))
        | ( bot_bo844097828e_bool = X1 )
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1368])]) ).

tff(f5134,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,X1))
      | sP0(X0)
      | ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK93(X0)),bot_bo844097828e_bool)))
      | ( bot_bo844097828e_bool = X1 )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f3938]) ).

tff(f3938,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,X1))
      | sP0(X0)
      | ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK93(X0)),bot_bo844097828e_bool)))
      | ( bot_bo844097828e_bool = X1 )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK93])],[f3685,f3937]) ).

tff(f3937,plain,
    ! [X0: fun_fu1430349052l_bool] :
      ( ? [X2: pname] : ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool)))
     => ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK93(X0)),bot_bo844097828e_bool))) ),
    introduced(choice_axiom,[]) ).

tff(f3685,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,X1))
      | sP0(X0)
      | ? [X2: pname] : ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool)))
      | ( bot_bo844097828e_bool = X1 )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(definition_folding,[],[f2759,f3684]) ).

tff(f3684,plain,
    ! [X0: fun_fu1430349052l_bool] :
      ( ? [X3: pname,X4: fun_pname_bool] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4)))
          & hBOOL(hAPP_f1664156314l_bool(X0,X4))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
          & ( bot_bo844097828e_bool != X4 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4)) )
      | ~ sP0(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

tff(f2759,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,X1))
      | ? [X3: pname,X4: fun_pname_bool] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4)))
          & hBOOL(hAPP_f1664156314l_bool(X0,X4))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
          & ( bot_bo844097828e_bool != X4 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4)) )
      | ? [X2: pname] : ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool)))
      | ( bot_bo844097828e_bool = X1 )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(flattening,[],[f2758]) ).

tff(f2758,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,X1))
      | ? [X3: pname,X4: fun_pname_bool] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4)))
          & hBOOL(hAPP_f1664156314l_bool(X0,X4))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
          & ( bot_bo844097828e_bool != X4 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4)) )
      | ? [X2: pname] : ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool)))
      | ( bot_bo844097828e_bool = X1 )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(ennf_transformation,[],[f1740]) ).

tff(f1740,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
     => ( ( bot_bo844097828e_bool != X1 )
       => ( ! [X2: pname] : hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool)))
         => ( ! [X3: pname,X4: fun_pname_bool] :
                ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
               => ( ( bot_bo844097828e_bool != X4 )
                 => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
                   => ( hBOOL(hAPP_f1664156314l_bool(X0,X4))
                     => hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4))) ) ) ) )
           => hBOOL(hAPP_f1664156314l_bool(X0,X1)) ) ) ) ),
    inference(rectify,[],[f783]) ).

tff(f783,axiom,
    ! [X10: fun_fu1430349052l_bool,X4: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
     => ( ( bot_bo844097828e_bool != X4 )
       => ( ! [X27: pname] : hBOOL(hAPP_f1664156314l_bool(X10,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X27),bot_bo844097828e_bool)))
         => ( ! [X27: pname,X76: fun_pname_bool] :
                ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X76))
               => ( ( bot_bo844097828e_bool != X76 )
                 => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X27),X76))
                   => ( hBOOL(hAPP_f1664156314l_bool(X10,X76))
                     => hBOOL(hAPP_f1664156314l_bool(X10,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X27),X76))) ) ) ) )
           => hBOOL(hAPP_f1664156314l_bool(X10,X4)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_782_finite__ne__induct) ).

tff(f29617,plain,
    spl250_1367,
    inference(avatar_split_clause,[],[f5121,f29615]) ).

tff(f29615,plain,
    ( spl250_1367
  <=> ! [X0: pname,X1: fun_pname_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool)))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1367])]) ).

tff(f5121,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool)))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f2752]) ).

tff(f2752,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool)))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(ennf_transformation,[],[f1734]) ).

tff(f1734,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool)))),hAPP_f921600141ol_nat(finite_card_pname,X1))) ),
    inference(rectify,[],[f654]) ).

tff(f654,axiom,
    ! [X8: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),bot_bo844097828e_bool)))),hAPP_f921600141ol_nat(finite_card_pname,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_653_card__Diff1__le) ).

tff(f29612,plain,
    spl250_1366,
    inference(avatar_split_clause,[],[f4951,f29610]) ).

tff(f4951,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)),X0)) )
      | ( zero_zero_nat = X1 ) ),
    inference(cnf_transformation,[],[f2613]) ).

tff(f2613,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)),X0)) )
        | ( zero_zero_nat = X1 ) )
      & ( ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0) )
        | ( zero_zero_nat != X1 ) ) ),
    inference(ennf_transformation,[],[f1596]) ).

tff(f1596,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( zero_zero_nat != X1 )
       => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)),X0)) ) )
      & ( ( zero_zero_nat = X1 )
       => ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0) ) ) ),
    inference(rectify,[],[f1015]) ).

tff(f1015,axiom,
    ! [X11: nat,X12: nat] :
      ( ( ( zero_zero_nat != X12 )
       => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X12),X11) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X11),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X12),one_one_nat)),X11)) ) )
      & ( ( zero_zero_nat = X12 )
       => ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X12),X11) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1014_mult__eq__if) ).

tff(f29579,plain,
    ( spl250_1365
    | spl250_1
    | ~ spl250_212
    | ~ spl250_505 ),
    inference(avatar_split_clause,[],[f11362,f10720,f8396,f7314,f29577]) ).

tff(f29577,plain,
    ( spl250_1365
  <=> ! [X0: nat,X1: nat] : ~ sP18(bot_bot_fun_nat_bool,X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1365])]) ).

tff(f10720,plain,
    ( spl250_505
  <=> ! [X2: nat,X0: fun_nat_bool,X1: nat] :
        ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
        | ~ sP18(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_505])]) ).

tff(f11362,plain,
    ( ! [X0: nat,X1: nat] :
        ( hBOOL(fFalse)
        | ~ sP18(bot_bot_fun_nat_bool,X0,X1) )
    | ~ spl250_212
    | ~ spl250_505 ),
    inference(superposition,[],[f10721,f8397]) ).

tff(f10721,plain,
    ( ! [X2: nat,X0: fun_nat_bool,X1: nat] :
        ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
        | ~ sP18(X0,X1,X2) )
    | ~ spl250_505 ),
    inference(avatar_component_clause,[],[f10720]) ).

tff(f27961,plain,
    ( spl250_1364
    | ~ spl250_66
    | ~ spl250_152
    | ~ spl250_1173 ),
    inference(avatar_split_clause,[],[f27818,f23813,f8093,f7608,f27958]) ).

tff(f27958,plain,
    ( spl250_1364
  <=> ( fFalse = hAPP_int_bool(nat_neg,pls) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1364])]) ).

tff(f7608,plain,
    ( spl250_66
  <=> ! [X0: bool,X1: int] : ( hAPP_int_bool(cOMBK_bool_int(X0),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_66])]) ).

tff(f23813,plain,
    ( spl250_1173
  <=> ( bot_bot_fun_int_bool = cOMBK_bool_int(hAPP_int_bool(nat_neg,pls)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1173])]) ).

tff(f27818,plain,
    ( ( fFalse = hAPP_int_bool(nat_neg,pls) )
    | ~ spl250_66
    | ~ spl250_152
    | ~ spl250_1173 ),
    inference(forward_demodulation,[],[f27817,f8094]) ).

tff(f27817,plain,
    ( ! [X0: int] : ( hAPP_int_bool(bot_bot_fun_int_bool,X0) = hAPP_int_bool(nat_neg,pls) )
    | ~ spl250_66
    | ~ spl250_1173 ),
    inference(superposition,[],[f7609,f23815]) ).

tff(f23815,plain,
    ( ( bot_bot_fun_int_bool = cOMBK_bool_int(hAPP_int_bool(nat_neg,pls)) )
    | ~ spl250_1173 ),
    inference(avatar_component_clause,[],[f23813]) ).

tff(f7609,plain,
    ( ! [X0: bool,X1: int] : ( hAPP_int_bool(cOMBK_bool_int(X0),X1) = X0 )
    | ~ spl250_66 ),
    inference(avatar_component_clause,[],[f7608]) ).

tff(f27813,plain,
    spl250_1363,
    inference(avatar_split_clause,[],[f7207,f27811]) ).

tff(f27811,plain,
    ( spl250_1363
  <=> ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] : ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_n1699378549t_bool(fequal_nat,X1))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1363])]) ).

tff(f7207,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] : ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_n1699378549t_bool(fequal_nat,X1))),X2) ),
    inference(forward_demodulation,[],[f5764,f6931]) ).

tff(f5764,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] : ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))),X2) ),
    inference(cnf_transformation,[],[f2140]) ).

tff(f2140,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))),X2) ),
    inference(rectify,[],[f557]) ).

tff(f557,axiom,
    ! [X2: fun_nat_bool,X5: nat,X7: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5),X7)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5),bot_bot_fun_nat_bool))),X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_556_Diff__insert2) ).

tff(f27809,plain,
    spl250_1362,
    inference(avatar_split_clause,[],[f7206,f27807]) ).

tff(f27807,plain,
    ( spl250_1362
  <=> ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] : ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2)),hAPP_n1699378549t_bool(fequal_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1362])]) ).

tff(f7206,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] : ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2)),hAPP_n1699378549t_bool(fequal_nat,X1)) ),
    inference(forward_demodulation,[],[f5763,f6931]) ).

tff(f5763,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] : ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)) ),
    inference(cnf_transformation,[],[f2139]) ).

tff(f2139,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)) ),
    inference(rectify,[],[f560]) ).

tff(f560,axiom,
    ! [X2: fun_nat_bool,X5: nat,X7: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5),X7)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X7)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5),bot_bot_fun_nat_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_559_Diff__insert) ).

tff(f27805,plain,
    spl250_1361,
    inference(avatar_split_clause,[],[f7205,f27803]) ).

tff(f27803,plain,
    ( spl250_1361
  <=> ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] : ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_i1948725293t_bool(fequal_int,X1))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1361])]) ).

tff(f7205,plain,
    ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] : ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_i1948725293t_bool(fequal_int,X1))),X2) ),
    inference(forward_demodulation,[],[f5762,f6930]) ).

tff(f5762,plain,
    ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] : ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))),X2) ),
    inference(cnf_transformation,[],[f2138]) ).

tff(f2138,plain,
    ! [X0: fun_int_bool,X1: int,X2: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))),X2) ),
    inference(rectify,[],[f558]) ).

tff(f558,axiom,
    ! [X2: fun_int_bool,X5: int,X7: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5),X7)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5),bot_bot_fun_int_bool))),X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_557_Diff__insert2) ).

tff(f27801,plain,
    spl250_1360,
    inference(avatar_split_clause,[],[f7204,f27799]) ).

tff(f27799,plain,
    ( spl250_1360
  <=> ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] : ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2)),hAPP_i1948725293t_bool(fequal_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1360])]) ).

tff(f7204,plain,
    ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] : ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2)),hAPP_i1948725293t_bool(fequal_int,X1)) ),
    inference(forward_demodulation,[],[f5761,f6930]) ).

tff(f5761,plain,
    ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] : ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)) ),
    inference(cnf_transformation,[],[f2137]) ).

tff(f2137,plain,
    ! [X0: fun_int_bool,X1: int,X2: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)) ),
    inference(rectify,[],[f561]) ).

tff(f561,axiom,
    ! [X2: fun_int_bool,X5: int,X7: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5),X7)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X7)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5),bot_bot_fun_int_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_560_Diff__insert) ).

tff(f27797,plain,
    spl250_1359,
    inference(avatar_split_clause,[],[f7028,f27795]) ).

tff(f27795,plain,
    ( spl250_1359
  <=> ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,collect_a(hAPP_a_fun_a_bool(fequal_a,sK100(X0)))))
        | hBOOL(hAPP_fun_a_bool_bool(X0,X1))
        | sP1(X0)
        | ( bot_bot_fun_a_bool = X1 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1359])]) ).

tff(f7028,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,collect_a(hAPP_a_fun_a_bool(fequal_a,sK100(X0)))))
      | hBOOL(hAPP_fun_a_bool_bool(X0,X1))
      | sP1(X0)
      | ( bot_bot_fun_a_bool = X1 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(forward_demodulation,[],[f5175,f4680]) ).

tff(f5175,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
      | sP1(X0)
      | ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK100(X0)),bot_bot_fun_a_bool)))
      | ( bot_bot_fun_a_bool = X1 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(cnf_transformation,[],[f3949]) ).

tff(f3949,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
      | sP1(X0)
      | ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK100(X0)),bot_bot_fun_a_bool)))
      | ( bot_bot_fun_a_bool = X1 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK100])],[f3687,f3948]) ).

tff(f3948,plain,
    ! [X0: fun_fun_a_bool_bool] :
      ( ? [X2: x_a] : ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)))
     => ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK100(X0)),bot_bot_fun_a_bool))) ),
    introduced(choice_axiom,[]) ).

tff(f3687,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
      | sP1(X0)
      | ? [X2: x_a] : ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)))
      | ( bot_bot_fun_a_bool = X1 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(definition_folding,[],[f2797,f3686]) ).

tff(f3686,plain,
    ! [X0: fun_fun_a_bool_bool] :
      ( ? [X3: x_a,X4: fun_a_bool] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4)))
          & hBOOL(hAPP_fun_a_bool_bool(X0,X4))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
          & ( bot_bot_fun_a_bool != X4 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4)) )
      | ~ sP1(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

tff(f2797,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
      | ? [X3: x_a,X4: fun_a_bool] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4)))
          & hBOOL(hAPP_fun_a_bool_bool(X0,X4))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
          & ( bot_bot_fun_a_bool != X4 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4)) )
      | ? [X2: x_a] : ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)))
      | ( bot_bot_fun_a_bool = X1 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(flattening,[],[f2796]) ).

tff(f2796,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
      | ? [X3: x_a,X4: fun_a_bool] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4)))
          & hBOOL(hAPP_fun_a_bool_bool(X0,X4))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
          & ( bot_bot_fun_a_bool != X4 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4)) )
      | ? [X2: x_a] : ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)))
      | ( bot_bot_fun_a_bool = X1 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(ennf_transformation,[],[f1767]) ).

tff(f1767,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
     => ( ( bot_bot_fun_a_bool != X1 )
       => ( ! [X2: x_a] : hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)))
         => ( ! [X3: x_a,X4: fun_a_bool] :
                ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
               => ( ( bot_bot_fun_a_bool != X4 )
                 => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
                   => ( hBOOL(hAPP_fun_a_bool_bool(X0,X4))
                     => hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4))) ) ) ) )
           => hBOOL(hAPP_fun_a_bool_bool(X0,X1)) ) ) ) ),
    inference(rectify,[],[f780]) ).

tff(f780,axiom,
    ! [X10: fun_fun_a_bool_bool,X4: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
     => ( ( bot_bot_fun_a_bool != X4 )
       => ( ! [X27: x_a] : hBOOL(hAPP_fun_a_bool_bool(X10,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X27),bot_bot_fun_a_bool)))
         => ( ! [X27: x_a,X76: fun_a_bool] :
                ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X76))
               => ( ( bot_bot_fun_a_bool != X76 )
                 => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X27),X76))
                   => ( hBOOL(hAPP_fun_a_bool_bool(X10,X76))
                     => hBOOL(hAPP_fun_a_bool_bool(X10,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X27),X76))) ) ) ) )
           => hBOOL(hAPP_fun_a_bool_bool(X10,X4)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_779_finite__ne__induct) ).

tff(f27793,plain,
    spl250_1358,
    inference(avatar_split_clause,[],[f7022,f27791]) ).

tff(f27791,plain,
    ( spl250_1358
  <=> ! [X0: x_a,X1: fun_a_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),collect_a(hAPP_a_fun_a_bool(fequal_a,X0))))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1358])]) ).

tff(f7022,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),collect_a(hAPP_a_fun_a_bool(fequal_a,X0))))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(forward_demodulation,[],[f5162,f4680]) ).

tff(f5162,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(cnf_transformation,[],[f2790]) ).

tff(f2790,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(ennf_transformation,[],[f1761]) ).

tff(f1761,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)))),hAPP_fun_a_bool_nat(finite_card_a,X1))) ),
    inference(rectify,[],[f651]) ).

tff(f651,axiom,
    ! [X8: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),bot_bot_fun_a_bool)))),hAPP_fun_a_bool_nat(finite_card_a,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_650_card__Diff1__le) ).

tff(f27789,plain,
    spl250_1357,
    inference(avatar_split_clause,[],[f6014,f27787]) ).

tff(f27787,plain,
    ( spl250_1357
  <=> ! [X2: int,X0: int,X1: fun_int_bool] :
        ( hBOOL(hAPP_int_bool(X1,X0))
        | ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK206(X1,X2)),one_one_int)))
        | sP12(X1,X2)
        | ~ hBOOL(hAPP_int_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1357])]) ).

tff(f6014,plain,
    ! [X2: int,X0: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_int_bool(X1,X0))
      | ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK206(X1,X2)),one_one_int)))
      | sP12(X1,X2)
      | ~ hBOOL(hAPP_int_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f4302]) ).

tff(f4302,plain,
    ! [X0: int,X1: fun_int_bool,X2: int] :
      ( hBOOL(hAPP_int_bool(X1,X0))
      | ( ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK206(X1,X2)),one_one_int)))
        & hBOOL(hAPP_int_bool(X1,sK206(X1,X2)))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK206(X1,X2)),X2)) )
      | sP12(X1,X2)
      | ~ hBOOL(hAPP_int_bool(X1,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK206])],[f4300,f4301]) ).

tff(f4301,plain,
    ! [X1: fun_int_bool,X2: int] :
      ( ? [X3: int] :
          ( ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),one_one_int)))
          & hBOOL(hAPP_int_bool(X1,X3))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2)) )
     => ( ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK206(X1,X2)),one_one_int)))
        & hBOOL(hAPP_int_bool(X1,sK206(X1,X2)))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK206(X1,X2)),X2)) ) ),
    introduced(choice_axiom,[]) ).

tff(f4300,plain,
    ! [X0: int,X1: fun_int_bool,X2: int] :
      ( hBOOL(hAPP_int_bool(X1,X0))
      | ? [X3: int] :
          ( ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),one_one_int)))
          & hBOOL(hAPP_int_bool(X1,X3))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2)) )
      | sP12(X1,X2)
      | ~ hBOOL(hAPP_int_bool(X1,X2)) ),
    inference(rectify,[],[f3708]) ).

tff(f3708,plain,
    ! [X0: int,X1: fun_int_bool,X2: int] :
      ( hBOOL(hAPP_int_bool(X1,X0))
      | ? [X4: int] :
          ( ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X4),one_one_int)))
          & hBOOL(hAPP_int_bool(X1,X4))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),X2)) )
      | sP12(X1,X2)
      | ~ hBOOL(hAPP_int_bool(X1,X2)) ),
    inference(definition_folding,[],[f3289,f3707]) ).

tff(f3707,plain,
    ! [X1: fun_int_bool,X2: int] :
      ( ? [X3: int] :
          ( ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),one_one_int)))
          & hBOOL(hAPP_int_bool(X1,X3))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) )
      | ~ sP12(X1,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).

tff(f3289,plain,
    ! [X0: int,X1: fun_int_bool,X2: int] :
      ( hBOOL(hAPP_int_bool(X1,X0))
      | ? [X4: int] :
          ( ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X4),one_one_int)))
          & hBOOL(hAPP_int_bool(X1,X4))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),X2)) )
      | ? [X3: int] :
          ( ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),one_one_int)))
          & hBOOL(hAPP_int_bool(X1,X3))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) )
      | ~ hBOOL(hAPP_int_bool(X1,X2)) ),
    inference(flattening,[],[f3288]) ).

tff(f3288,plain,
    ! [X0: int,X1: fun_int_bool,X2: int] :
      ( hBOOL(hAPP_int_bool(X1,X0))
      | ? [X4: int] :
          ( ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X4),one_one_int)))
          & hBOOL(hAPP_int_bool(X1,X4))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),X2)) )
      | ? [X3: int] :
          ( ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),one_one_int)))
          & hBOOL(hAPP_int_bool(X1,X3))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) )
      | ~ hBOOL(hAPP_int_bool(X1,X2)) ),
    inference(ennf_transformation,[],[f2268]) ).

tff(f2268,plain,
    ! [X0: int,X1: fun_int_bool,X2: int] :
      ( hBOOL(hAPP_int_bool(X1,X2))
     => ( ! [X3: int] :
            ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3))
           => ( hBOOL(hAPP_int_bool(X1,X3))
             => hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),one_one_int))) ) )
       => ( ! [X4: int] :
              ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),X2))
             => ( hBOOL(hAPP_int_bool(X1,X4))
               => hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X4),one_one_int))) ) )
         => hBOOL(hAPP_int_bool(X1,X0)) ) ) ),
    inference(rectify,[],[f1093]) ).

tff(f1093,axiom,
    ! [X30: int,X10: fun_int_bool,X13: int] :
      ( hBOOL(hAPP_int_bool(X10,X13))
     => ( ! [X123: int] :
            ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X13),X123))
           => ( hBOOL(hAPP_int_bool(X10,X123))
             => hBOOL(hAPP_int_bool(X10,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X123),one_one_int))) ) )
       => ( ! [X123: int] :
              ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X123),X13))
             => ( hBOOL(hAPP_int_bool(X10,X123))
               => hBOOL(hAPP_int_bool(X10,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X123),one_one_int))) ) )
         => hBOOL(hAPP_int_bool(X10,X30)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1092_int__induct) ).

tff(f27785,plain,
    spl250_1356,
    inference(avatar_split_clause,[],[f5999,f27783]) ).

tff(f27783,plain,
    ( spl250_1356
  <=> ! [X2: fun_nat_bool,X0: fun_a_nat,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK196(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_a_nat(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1356])]) ).

tff(f5999,plain,
    ! [X2: fun_nat_bool,X0: fun_a_nat,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK196(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_a_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f4287]) ).

tff(f4287,plain,
    ! [X0: fun_a_nat,X1: fun_a_bool,X2: fun_nat_bool] :
      ( ( ( image_a_nat(X0,sK196(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK196(X0,X1,X2)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK196(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_a_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK196])],[f3276,f4286]) ).

tff(f4286,plain,
    ! [X0: fun_a_nat,X1: fun_a_bool,X2: fun_nat_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_a_nat(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
     => ( ( image_a_nat(X0,sK196(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK196(X0,X1,X2)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK196(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3276,plain,
    ! [X0: fun_a_nat,X1: fun_a_bool,X2: fun_nat_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_a_nat(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_a_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(flattening,[],[f3275]) ).

tff(f3275,plain,
    ! [X0: fun_a_nat,X1: fun_a_bool,X2: fun_nat_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_a_nat(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_a_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(ennf_transformation,[],[f2260]) ).

tff(f2260,plain,
    ! [X0: fun_a_nat,X1: fun_a_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_a_nat(X0,X1)))
       => ? [X3: fun_a_bool] :
            ( ( image_a_nat(X0,X3) = X2 )
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f234]) ).

tff(f234,axiom,
    ! [X6: fun_a_nat,X2: fun_a_bool,X7: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7),image_a_nat(X6,X2)))
       => ? [X24: fun_a_bool] :
            ( ( image_a_nat(X6,X24) = X7 )
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X24))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_finite__subset__image) ).

tff(f27781,plain,
    spl250_1355,
    inference(avatar_split_clause,[],[f5996,f27779]) ).

tff(f27779,plain,
    ( spl250_1355
  <=> ! [X2: fun_nat_bool,X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK195(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1551609309ol_nat(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1355])]) ).

tff(f5996,plain,
    ! [X2: fun_nat_bool,X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK195(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1551609309ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f4285]) ).

tff(f4285,plain,
    ! [X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool,X2: fun_nat_bool] :
      ( ( ( image_1551609309ol_nat(X0,sK195(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK195(X0,X1,X2)))
        & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK195(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1551609309ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK195])],[f3274,f4284]) ).

tff(f4284,plain,
    ! [X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool,X2: fun_nat_bool] :
      ( ? [X3: fun_fu1430349052l_bool] :
          ( ( image_1551609309ol_nat(X0,X3) = X2 )
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1)) )
     => ( ( image_1551609309ol_nat(X0,sK195(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK195(X0,X1,X2)))
        & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK195(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3274,plain,
    ! [X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool,X2: fun_nat_bool] :
      ( ? [X3: fun_fu1430349052l_bool] :
          ( ( image_1551609309ol_nat(X0,X3) = X2 )
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1551609309ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(flattening,[],[f3273]) ).

tff(f3273,plain,
    ! [X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool,X2: fun_nat_bool] :
      ( ? [X3: fun_fu1430349052l_bool] :
          ( ( image_1551609309ol_nat(X0,X3) = X2 )
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1551609309ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(ennf_transformation,[],[f2259]) ).

tff(f2259,plain,
    ! [X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1551609309ol_nat(X0,X1)))
       => ? [X3: fun_fu1430349052l_bool] :
            ( ( image_1551609309ol_nat(X0,X3) = X2 )
            & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
            & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f237]) ).

tff(f237,axiom,
    ! [X6: fun_fu1668467777ol_nat,X2: fun_fu1430349052l_bool,X7: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7),image_1551609309ol_nat(X6,X2)))
       => ? [X24: fun_fu1430349052l_bool] :
            ( ( image_1551609309ol_nat(X6,X24) = X7 )
            & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X24))
            & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_finite__subset__image) ).

tff(f27777,plain,
    spl250_1354,
    inference(avatar_split_clause,[],[f5993,f27775]) ).

tff(f27775,plain,
    ( spl250_1354
  <=> ! [X2: fun_nat_bool,X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK194(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_496248727ol_nat(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1354])]) ).

tff(f5993,plain,
    ! [X2: fun_nat_bool,X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK194(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_496248727ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f4283]) ).

tff(f4283,plain,
    ! [X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool,X2: fun_nat_bool] :
      ( ( ( image_496248727ol_nat(X0,sK194(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK194(X0,X1,X2)))
        & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK194(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_496248727ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK194])],[f3272,f4282]) ).

tff(f4282,plain,
    ! [X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool,X2: fun_nat_bool] :
      ( ? [X3: fun_fu425979586l_bool] :
          ( ( image_496248727ol_nat(X0,X3) = X2 )
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
     => ( ( image_496248727ol_nat(X0,sK194(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK194(X0,X1,X2)))
        & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK194(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3272,plain,
    ! [X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool,X2: fun_nat_bool] :
      ( ? [X3: fun_fu425979586l_bool] :
          ( ( image_496248727ol_nat(X0,X3) = X2 )
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_496248727ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(flattening,[],[f3271]) ).

tff(f3271,plain,
    ! [X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool,X2: fun_nat_bool] :
      ( ? [X3: fun_fu425979586l_bool] :
          ( ( image_496248727ol_nat(X0,X3) = X2 )
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_496248727ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(ennf_transformation,[],[f2258]) ).

tff(f2258,plain,
    ! [X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_496248727ol_nat(X0,X1)))
       => ? [X3: fun_fu425979586l_bool] :
            ( ( image_496248727ol_nat(X0,X3) = X2 )
            & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
            & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f236]) ).

tff(f236,axiom,
    ! [X6: fun_fun_nat_bool_nat,X2: fun_fu425979586l_bool,X7: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7),image_496248727ol_nat(X6,X2)))
       => ? [X24: fun_fu425979586l_bool] :
            ( ( image_496248727ol_nat(X6,X24) = X7 )
            & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X24))
            & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_finite__subset__image) ).

tff(f27752,plain,
    spl250_1353,
    inference(avatar_split_clause,[],[f5990,f27750]) ).

tff(f27750,plain,
    ( spl250_1353
  <=> ! [X2: fun_nat_bool,X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK193(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_fun_a_bool_nat(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1353])]) ).

tff(f5990,plain,
    ! [X2: fun_nat_bool,X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK193(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_fun_a_bool_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f4281]) ).

tff(f4281,plain,
    ! [X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool,X2: fun_nat_bool] :
      ( ( ( image_fun_a_bool_nat(X0,sK193(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK193(X0,X1,X2)))
        & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK193(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_fun_a_bool_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK193])],[f3270,f4280]) ).

tff(f4280,plain,
    ! [X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool,X2: fun_nat_bool] :
      ( ? [X3: fun_fun_a_bool_bool] :
          ( ( image_fun_a_bool_nat(X0,X3) = X2 )
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1)) )
     => ( ( image_fun_a_bool_nat(X0,sK193(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK193(X0,X1,X2)))
        & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK193(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3270,plain,
    ! [X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool,X2: fun_nat_bool] :
      ( ? [X3: fun_fun_a_bool_bool] :
          ( ( image_fun_a_bool_nat(X0,X3) = X2 )
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_fun_a_bool_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(flattening,[],[f3269]) ).

tff(f3269,plain,
    ! [X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool,X2: fun_nat_bool] :
      ( ? [X3: fun_fun_a_bool_bool] :
          ( ( image_fun_a_bool_nat(X0,X3) = X2 )
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_fun_a_bool_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(ennf_transformation,[],[f2257]) ).

tff(f2257,plain,
    ! [X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_fun_a_bool_nat(X0,X1)))
       => ? [X3: fun_fun_a_bool_bool] :
            ( ( image_fun_a_bool_nat(X0,X3) = X2 )
            & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
            & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f238]) ).

tff(f238,axiom,
    ! [X6: fun_fun_a_bool_nat,X2: fun_fun_a_bool_bool,X7: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7),image_fun_a_bool_nat(X6,X2)))
       => ? [X24: fun_fun_a_bool_bool] :
            ( ( image_fun_a_bool_nat(X6,X24) = X7 )
            & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X24))
            & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_finite__subset__image) ).

tff(f27748,plain,
    spl250_1352,
    inference(avatar_split_clause,[],[f5987,f27746]) ).

tff(f27746,plain,
    ( spl250_1352
  <=> ! [X2: fun_nat_bool,X0: fun_fun_int_bool_nat,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK192(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1431733819ol_nat(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1352])]) ).

tff(f5987,plain,
    ! [X2: fun_nat_bool,X0: fun_fun_int_bool_nat,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK192(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1431733819ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f4279]) ).

tff(f4279,plain,
    ! [X0: fun_fun_int_bool_nat,X1: fun_fu819804446l_bool,X2: fun_nat_bool] :
      ( ( ( image_1431733819ol_nat(X0,sK192(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK192(X0,X1,X2)))
        & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK192(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1431733819ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK192])],[f3268,f4278]) ).

tff(f4278,plain,
    ! [X0: fun_fun_int_bool_nat,X1: fun_fu819804446l_bool,X2: fun_nat_bool] :
      ( ? [X3: fun_fu819804446l_bool] :
          ( ( image_1431733819ol_nat(X0,X3) = X2 )
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
          & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
     => ( ( image_1431733819ol_nat(X0,sK192(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK192(X0,X1,X2)))
        & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK192(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3268,plain,
    ! [X0: fun_fun_int_bool_nat,X1: fun_fu819804446l_bool,X2: fun_nat_bool] :
      ( ? [X3: fun_fu819804446l_bool] :
          ( ( image_1431733819ol_nat(X0,X3) = X2 )
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
          & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1431733819ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(flattening,[],[f3267]) ).

tff(f3267,plain,
    ! [X0: fun_fun_int_bool_nat,X1: fun_fu819804446l_bool,X2: fun_nat_bool] :
      ( ? [X3: fun_fu819804446l_bool] :
          ( ( image_1431733819ol_nat(X0,X3) = X2 )
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
          & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1431733819ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(ennf_transformation,[],[f2256]) ).

tff(f2256,plain,
    ! [X0: fun_fun_int_bool_nat,X1: fun_fu819804446l_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1431733819ol_nat(X0,X1)))
       => ? [X3: fun_fu819804446l_bool] :
            ( ( image_1431733819ol_nat(X0,X3) = X2 )
            & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
            & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f235]) ).

tff(f235,axiom,
    ! [X6: fun_fun_int_bool_nat,X2: fun_fu819804446l_bool,X7: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7),image_1431733819ol_nat(X6,X2)))
       => ? [X24: fun_fu819804446l_bool] :
            ( ( image_1431733819ol_nat(X6,X24) = X7 )
            & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X24))
            & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_finite__subset__image) ).

tff(f27744,plain,
    spl250_1351,
    inference(avatar_split_clause,[],[f5984,f27742]) ).

tff(f27742,plain,
    ( spl250_1351
  <=> ! [X2: fun_nat_bool,X0: fun_pname_nat,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK191(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_pname_nat(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1351])]) ).

tff(f5984,plain,
    ! [X2: fun_nat_bool,X0: fun_pname_nat,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK191(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_pname_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f4277]) ).

tff(f4277,plain,
    ! [X0: fun_pname_nat,X1: fun_pname_bool,X2: fun_nat_bool] :
      ( ( ( image_pname_nat(X0,sK191(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK191(X0,X1,X2)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK191(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_pname_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK191])],[f3266,f4276]) ).

tff(f4276,plain,
    ! [X0: fun_pname_nat,X1: fun_pname_bool,X2: fun_nat_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_pname_nat(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
     => ( ( image_pname_nat(X0,sK191(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK191(X0,X1,X2)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK191(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3266,plain,
    ! [X0: fun_pname_nat,X1: fun_pname_bool,X2: fun_nat_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_pname_nat(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_pname_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(flattening,[],[f3265]) ).

tff(f3265,plain,
    ! [X0: fun_pname_nat,X1: fun_pname_bool,X2: fun_nat_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_pname_nat(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_pname_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(ennf_transformation,[],[f2255]) ).

tff(f2255,plain,
    ! [X0: fun_pname_nat,X1: fun_pname_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_pname_nat(X0,X1)))
       => ? [X3: fun_pname_bool] :
            ( ( image_pname_nat(X0,X3) = X2 )
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f239]) ).

tff(f239,axiom,
    ! [X6: fun_pname_nat,X2: fun_pname_bool,X7: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7),image_pname_nat(X6,X2)))
       => ? [X24: fun_pname_bool] :
            ( ( image_pname_nat(X6,X24) = X7 )
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X24))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_finite__subset__image) ).

tff(f27740,plain,
    spl250_1350,
    inference(avatar_split_clause,[],[f5976,f27738]) ).

tff(f27738,plain,
    ( spl250_1350
  <=> ! [X2: fun_nat_bool,X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(X0,X2))
        | sP11(X0,X1)
        | ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1350])]) ).

tff(f5976,plain,
    ! [X2: fun_nat_bool,X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,X2))
      | sP11(X0,X1)
      | ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f3706]) ).

tff(f3706,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,X2))
      | sP11(X0,X1)
      | ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(definition_folding,[],[f3250,f3705]) ).

tff(f3705,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( ? [X3: nat,X4: fun_nat_bool] :
          ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4)))
          & hBOOL(hAPP_f54304608l_bool(X0,X4))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X1))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4)) )
      | ~ sP11(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).

tff(f3250,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,X2))
      | ? [X3: nat,X4: fun_nat_bool] :
          ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4)))
          & hBOOL(hAPP_f54304608l_bool(X0,X4))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X1))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4)) )
      | ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(flattening,[],[f3249]) ).

tff(f3249,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,X2))
      | ? [X3: nat,X4: fun_nat_bool] :
          ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4)))
          & hBOOL(hAPP_f54304608l_bool(X0,X4))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X1))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4)) )
      | ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(ennf_transformation,[],[f2247]) ).

tff(f2247,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
       => ( hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
         => ( ! [X3: nat,X4: fun_nat_bool] :
                ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
               => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X1))
                 => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
                   => ( hBOOL(hAPP_f54304608l_bool(X0,X4))
                     => hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4))) ) ) ) )
           => hBOOL(hAPP_f54304608l_bool(X0,X2)) ) ) ) ),
    inference(rectify,[],[f681]) ).

tff(f681,axiom,
    ! [X10: fun_fu425979586l_bool,X2: fun_nat_bool,X4: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X2))
       => ( hBOOL(hAPP_f54304608l_bool(X10,bot_bot_fun_nat_bool))
         => ( ! [X75: nat,X76: fun_nat_bool] :
                ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X76))
               => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X75),X2))
                 => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X75),X76))
                   => ( hBOOL(hAPP_f54304608l_bool(X10,X76))
                     => hBOOL(hAPP_f54304608l_bool(X10,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X75),X76))) ) ) ) )
           => hBOOL(hAPP_f54304608l_bool(X10,X4)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_680_finite__subset__induct) ).

tff(f27736,plain,
    spl250_1349,
    inference(avatar_split_clause,[],[f5967,f27734]) ).

tff(f27734,plain,
    ( spl250_1349
  <=> ! [X2: fun_int_bool,X0: fun_nat_int,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK188(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_nat_int(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1349])]) ).

tff(f5967,plain,
    ! [X2: fun_int_bool,X0: fun_nat_int,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK188(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_nat_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f4271]) ).

tff(f4271,plain,
    ! [X0: fun_nat_int,X1: fun_nat_bool,X2: fun_int_bool] :
      ( ( ( image_nat_int(X0,sK188(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK188(X0,X1,X2)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK188(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_nat_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK188])],[f3246,f4270]) ).

tff(f4270,plain,
    ! [X0: fun_nat_int,X1: fun_nat_bool,X2: fun_int_bool] :
      ( ? [X3: fun_nat_bool] :
          ( ( image_nat_int(X0,X3) = X2 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
     => ( ( image_nat_int(X0,sK188(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK188(X0,X1,X2)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK188(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3246,plain,
    ! [X0: fun_nat_int,X1: fun_nat_bool,X2: fun_int_bool] :
      ( ? [X3: fun_nat_bool] :
          ( ( image_nat_int(X0,X3) = X2 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_nat_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(flattening,[],[f3245]) ).

tff(f3245,plain,
    ! [X0: fun_nat_int,X1: fun_nat_bool,X2: fun_int_bool] :
      ( ? [X3: fun_nat_bool] :
          ( ( image_nat_int(X0,X3) = X2 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_nat_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(ennf_transformation,[],[f2245]) ).

tff(f2245,plain,
    ! [X0: fun_nat_int,X1: fun_nat_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_nat_int(X0,X1)))
       => ? [X3: fun_nat_bool] :
            ( ( image_nat_int(X0,X3) = X2 )
            & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f264]) ).

tff(f264,axiom,
    ! [X6: fun_nat_int,X2: fun_nat_bool,X7: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X7),image_nat_int(X6,X2)))
       => ? [X24: fun_nat_bool] :
            ( ( image_nat_int(X6,X24) = X7 )
            & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X24))
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_finite__subset__image) ).

tff(f27732,plain,
    spl250_1348,
    inference(avatar_split_clause,[],[f5964,f27730]) ).

tff(f27730,plain,
    ( spl250_1348
  <=> ! [X2: fun_int_bool,X0: fun_a_int,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK187(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_a_int(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1348])]) ).

tff(f5964,plain,
    ! [X2: fun_int_bool,X0: fun_a_int,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK187(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_a_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f4269]) ).

tff(f4269,plain,
    ! [X0: fun_a_int,X1: fun_a_bool,X2: fun_int_bool] :
      ( ( ( image_a_int(X0,sK187(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK187(X0,X1,X2)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK187(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_a_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK187])],[f3244,f4268]) ).

tff(f4268,plain,
    ! [X0: fun_a_int,X1: fun_a_bool,X2: fun_int_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_a_int(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
     => ( ( image_a_int(X0,sK187(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK187(X0,X1,X2)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK187(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3244,plain,
    ! [X0: fun_a_int,X1: fun_a_bool,X2: fun_int_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_a_int(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_a_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(flattening,[],[f3243]) ).

tff(f3243,plain,
    ! [X0: fun_a_int,X1: fun_a_bool,X2: fun_int_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_a_int(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_a_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(ennf_transformation,[],[f2244]) ).

tff(f2244,plain,
    ! [X0: fun_a_int,X1: fun_a_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_a_int(X0,X1)))
       => ? [X3: fun_a_bool] :
            ( ( image_a_int(X0,X3) = X2 )
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f240]) ).

tff(f240,axiom,
    ! [X6: fun_a_int,X2: fun_a_bool,X7: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X7),image_a_int(X6,X2)))
       => ? [X24: fun_a_bool] :
            ( ( image_a_int(X6,X24) = X7 )
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X24))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_finite__subset__image) ).

tff(f27728,plain,
    spl250_1347,
    inference(avatar_split_clause,[],[f5961,f27726]) ).

tff(f27726,plain,
    ( spl250_1347
  <=> ! [X2: fun_int_bool,X0: fun_fun_a_bool_int,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK186(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_fun_a_bool_int(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1347])]) ).

tff(f5961,plain,
    ! [X2: fun_int_bool,X0: fun_fun_a_bool_int,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK186(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_fun_a_bool_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f4267]) ).

tff(f4267,plain,
    ! [X0: fun_fun_a_bool_int,X1: fun_fun_a_bool_bool,X2: fun_int_bool] :
      ( ( ( image_fun_a_bool_int(X0,sK186(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK186(X0,X1,X2)))
        & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK186(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_fun_a_bool_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK186])],[f3242,f4266]) ).

tff(f4266,plain,
    ! [X0: fun_fun_a_bool_int,X1: fun_fun_a_bool_bool,X2: fun_int_bool] :
      ( ? [X3: fun_fun_a_bool_bool] :
          ( ( image_fun_a_bool_int(X0,X3) = X2 )
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1)) )
     => ( ( image_fun_a_bool_int(X0,sK186(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK186(X0,X1,X2)))
        & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK186(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3242,plain,
    ! [X0: fun_fun_a_bool_int,X1: fun_fun_a_bool_bool,X2: fun_int_bool] :
      ( ? [X3: fun_fun_a_bool_bool] :
          ( ( image_fun_a_bool_int(X0,X3) = X2 )
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_fun_a_bool_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(flattening,[],[f3241]) ).

tff(f3241,plain,
    ! [X0: fun_fun_a_bool_int,X1: fun_fun_a_bool_bool,X2: fun_int_bool] :
      ( ? [X3: fun_fun_a_bool_bool] :
          ( ( image_fun_a_bool_int(X0,X3) = X2 )
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_fun_a_bool_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(ennf_transformation,[],[f2243]) ).

tff(f2243,plain,
    ! [X0: fun_fun_a_bool_int,X1: fun_fun_a_bool_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_fun_a_bool_int(X0,X1)))
       => ? [X3: fun_fun_a_bool_bool] :
            ( ( image_fun_a_bool_int(X0,X3) = X2 )
            & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
            & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f244]) ).

tff(f244,axiom,
    ! [X6: fun_fun_a_bool_int,X2: fun_fun_a_bool_bool,X7: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X7),image_fun_a_bool_int(X6,X2)))
       => ? [X24: fun_fun_a_bool_bool] :
            ( ( image_fun_a_bool_int(X6,X24) = X7 )
            & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X24))
            & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_finite__subset__image) ).

tff(f27724,plain,
    spl250_1346,
    inference(avatar_split_clause,[],[f5958,f27722]) ).

tff(f27722,plain,
    ( spl250_1346
  <=> ! [X2: fun_int_bool,X0: fun_fu1830380701ol_int,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK185(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_41399353ol_int(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1346])]) ).

tff(f5958,plain,
    ! [X2: fun_int_bool,X0: fun_fu1830380701ol_int,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK185(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_41399353ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f4265]) ).

tff(f4265,plain,
    ! [X0: fun_fu1830380701ol_int,X1: fun_fu1430349052l_bool,X2: fun_int_bool] :
      ( ( ( image_41399353ol_int(X0,sK185(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK185(X0,X1,X2)))
        & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK185(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_41399353ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK185])],[f3240,f4264]) ).

tff(f4264,plain,
    ! [X0: fun_fu1830380701ol_int,X1: fun_fu1430349052l_bool,X2: fun_int_bool] :
      ( ? [X3: fun_fu1430349052l_bool] :
          ( ( image_41399353ol_int(X0,X3) = X2 )
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1)) )
     => ( ( image_41399353ol_int(X0,sK185(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK185(X0,X1,X2)))
        & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK185(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3240,plain,
    ! [X0: fun_fu1830380701ol_int,X1: fun_fu1430349052l_bool,X2: fun_int_bool] :
      ( ? [X3: fun_fu1430349052l_bool] :
          ( ( image_41399353ol_int(X0,X3) = X2 )
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_41399353ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(flattening,[],[f3239]) ).

tff(f3239,plain,
    ! [X0: fun_fu1830380701ol_int,X1: fun_fu1430349052l_bool,X2: fun_int_bool] :
      ( ? [X3: fun_fu1430349052l_bool] :
          ( ( image_41399353ol_int(X0,X3) = X2 )
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_41399353ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(ennf_transformation,[],[f2242]) ).

tff(f2242,plain,
    ! [X0: fun_fu1830380701ol_int,X1: fun_fu1430349052l_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_41399353ol_int(X0,X1)))
       => ? [X3: fun_fu1430349052l_bool] :
            ( ( image_41399353ol_int(X0,X3) = X2 )
            & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
            & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f243]) ).

tff(f243,axiom,
    ! [X6: fun_fu1830380701ol_int,X2: fun_fu1430349052l_bool,X7: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X7),image_41399353ol_int(X6,X2)))
       => ? [X24: fun_fu1430349052l_bool] :
            ( ( image_41399353ol_int(X6,X24) = X7 )
            & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X24))
            & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_finite__subset__image) ).

tff(f27720,plain,
    spl250_1345,
    inference(avatar_split_clause,[],[f5955,f27718]) ).

tff(f27718,plain,
    ( spl250_1345
  <=> ! [X2: fun_int_bool,X0: fun_fun_nat_bool_int,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK184(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_1133522419ol_int(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1345])]) ).

tff(f5955,plain,
    ! [X2: fun_int_bool,X0: fun_fun_nat_bool_int,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK184(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_1133522419ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f4263]) ).

tff(f4263,plain,
    ! [X0: fun_fun_nat_bool_int,X1: fun_fu425979586l_bool,X2: fun_int_bool] :
      ( ( ( image_1133522419ol_int(X0,sK184(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK184(X0,X1,X2)))
        & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK184(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_1133522419ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK184])],[f3238,f4262]) ).

tff(f4262,plain,
    ! [X0: fun_fun_nat_bool_int,X1: fun_fu425979586l_bool,X2: fun_int_bool] :
      ( ? [X3: fun_fu425979586l_bool] :
          ( ( image_1133522419ol_int(X0,X3) = X2 )
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
     => ( ( image_1133522419ol_int(X0,sK184(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK184(X0,X1,X2)))
        & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK184(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3238,plain,
    ! [X0: fun_fun_nat_bool_int,X1: fun_fu425979586l_bool,X2: fun_int_bool] :
      ( ? [X3: fun_fu425979586l_bool] :
          ( ( image_1133522419ol_int(X0,X3) = X2 )
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_1133522419ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(flattening,[],[f3237]) ).

tff(f3237,plain,
    ! [X0: fun_fun_nat_bool_int,X1: fun_fu425979586l_bool,X2: fun_int_bool] :
      ( ? [X3: fun_fu425979586l_bool] :
          ( ( image_1133522419ol_int(X0,X3) = X2 )
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_1133522419ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(ennf_transformation,[],[f2241]) ).

tff(f2241,plain,
    ! [X0: fun_fun_nat_bool_int,X1: fun_fu425979586l_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_1133522419ol_int(X0,X1)))
       => ? [X3: fun_fu425979586l_bool] :
            ( ( image_1133522419ol_int(X0,X3) = X2 )
            & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
            & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f242]) ).

tff(f242,axiom,
    ! [X6: fun_fun_nat_bool_int,X2: fun_fu425979586l_bool,X7: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X7),image_1133522419ol_int(X6,X2)))
       => ? [X24: fun_fu425979586l_bool] :
            ( ( image_1133522419ol_int(X6,X24) = X7 )
            & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X24))
            & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_finite__subset__image) ).

tff(f27716,plain,
    spl250_1344,
    inference(avatar_split_clause,[],[f5952,f27714]) ).

tff(f27714,plain,
    ( spl250_1344
  <=> ! [X2: fun_int_bool,X0: fun_fun_int_bool_int,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK183(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_2069007511ol_int(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1344])]) ).

tff(f5952,plain,
    ! [X2: fun_int_bool,X0: fun_fun_int_bool_int,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK183(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_2069007511ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f4261]) ).

tff(f4261,plain,
    ! [X0: fun_fun_int_bool_int,X1: fun_fu819804446l_bool,X2: fun_int_bool] :
      ( ( ( image_2069007511ol_int(X0,sK183(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK183(X0,X1,X2)))
        & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK183(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_2069007511ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK183])],[f3236,f4260]) ).

tff(f4260,plain,
    ! [X0: fun_fun_int_bool_int,X1: fun_fu819804446l_bool,X2: fun_int_bool] :
      ( ? [X3: fun_fu819804446l_bool] :
          ( ( image_2069007511ol_int(X0,X3) = X2 )
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
          & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
     => ( ( image_2069007511ol_int(X0,sK183(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK183(X0,X1,X2)))
        & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK183(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3236,plain,
    ! [X0: fun_fun_int_bool_int,X1: fun_fu819804446l_bool,X2: fun_int_bool] :
      ( ? [X3: fun_fu819804446l_bool] :
          ( ( image_2069007511ol_int(X0,X3) = X2 )
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
          & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_2069007511ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(flattening,[],[f3235]) ).

tff(f3235,plain,
    ! [X0: fun_fun_int_bool_int,X1: fun_fu819804446l_bool,X2: fun_int_bool] :
      ( ? [X3: fun_fu819804446l_bool] :
          ( ( image_2069007511ol_int(X0,X3) = X2 )
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
          & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_2069007511ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(ennf_transformation,[],[f2240]) ).

tff(f2240,plain,
    ! [X0: fun_fun_int_bool_int,X1: fun_fu819804446l_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_2069007511ol_int(X0,X1)))
       => ? [X3: fun_fu819804446l_bool] :
            ( ( image_2069007511ol_int(X0,X3) = X2 )
            & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
            & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f241]) ).

tff(f241,axiom,
    ! [X6: fun_fun_int_bool_int,X2: fun_fu819804446l_bool,X7: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X7),image_2069007511ol_int(X6,X2)))
       => ? [X24: fun_fu819804446l_bool] :
            ( ( image_2069007511ol_int(X6,X24) = X7 )
            & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X24))
            & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_finite__subset__image) ).

tff(f27712,plain,
    ( spl250_1343
    | ~ spl250_66
    | ~ spl250_152
    | ~ spl250_1162 ),
    inference(avatar_split_clause,[],[f27667,f23768,f8093,f7608,f27709]) ).

tff(f27709,plain,
    ( spl250_1343
  <=> ( fFalse = hAPP_int_bool(nat_neg,one_one_int) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1343])]) ).

tff(f23768,plain,
    ( spl250_1162
  <=> ( bot_bot_fun_int_bool = cOMBK_bool_int(hAPP_int_bool(nat_neg,one_one_int)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1162])]) ).

tff(f27667,plain,
    ( ( fFalse = hAPP_int_bool(nat_neg,one_one_int) )
    | ~ spl250_66
    | ~ spl250_152
    | ~ spl250_1162 ),
    inference(forward_demodulation,[],[f27666,f8094]) ).

tff(f27666,plain,
    ( ! [X0: int] : ( hAPP_int_bool(nat_neg,one_one_int) = hAPP_int_bool(bot_bot_fun_int_bool,X0) )
    | ~ spl250_66
    | ~ spl250_1162 ),
    inference(superposition,[],[f7609,f23770]) ).

tff(f23770,plain,
    ( ( bot_bot_fun_int_bool = cOMBK_bool_int(hAPP_int_bool(nat_neg,one_one_int)) )
    | ~ spl250_1162 ),
    inference(avatar_component_clause,[],[f23768]) ).

tff(f27707,plain,
    spl250_1342,
    inference(avatar_split_clause,[],[f5949,f27705]) ).

tff(f27705,plain,
    ( spl250_1342
  <=> ! [X2: fun_int_bool,X0: fun_pname_int,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK182(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_pname_int(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1342])]) ).

tff(f5949,plain,
    ! [X2: fun_int_bool,X0: fun_pname_int,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK182(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_pname_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f4259]) ).

tff(f4259,plain,
    ! [X0: fun_pname_int,X1: fun_pname_bool,X2: fun_int_bool] :
      ( ( ( image_pname_int(X0,sK182(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK182(X0,X1,X2)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK182(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_pname_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK182])],[f3234,f4258]) ).

tff(f4258,plain,
    ! [X0: fun_pname_int,X1: fun_pname_bool,X2: fun_int_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_pname_int(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
     => ( ( image_pname_int(X0,sK182(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK182(X0,X1,X2)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK182(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3234,plain,
    ! [X0: fun_pname_int,X1: fun_pname_bool,X2: fun_int_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_pname_int(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_pname_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(flattening,[],[f3233]) ).

tff(f3233,plain,
    ! [X0: fun_pname_int,X1: fun_pname_bool,X2: fun_int_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_pname_int(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_pname_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(ennf_transformation,[],[f2239]) ).

tff(f2239,plain,
    ! [X0: fun_pname_int,X1: fun_pname_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_pname_int(X0,X1)))
       => ? [X3: fun_pname_bool] :
            ( ( image_pname_int(X0,X3) = X2 )
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f245]) ).

tff(f245,axiom,
    ! [X6: fun_pname_int,X2: fun_pname_bool,X7: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X7),image_pname_int(X6,X2)))
       => ? [X24: fun_pname_bool] :
            ( ( image_pname_int(X6,X24) = X7 )
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X24))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_finite__subset__image) ).

tff(f27703,plain,
    spl250_1341,
    inference(avatar_split_clause,[],[f5942,f27701]) ).

tff(f27701,plain,
    ( spl250_1341
  <=> ! [X2: fun_int_bool,X0: fun_fu819804446l_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(X0,X2))
        | sP10(X0,X1)
        | ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1341])]) ).

tff(f5942,plain,
    ! [X2: fun_int_bool,X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,X2))
      | sP10(X0,X1)
      | ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f3704]) ).

tff(f3704,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,X2))
      | sP10(X0,X1)
      | ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(definition_folding,[],[f3220,f3703]) ).

tff(f3703,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( ? [X3: int,X4: fun_int_bool] :
          ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4)))
          & hBOOL(hAPP_f448129468l_bool(X0,X4))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X1))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4)) )
      | ~ sP10(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).

tff(f3220,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,X2))
      | ? [X3: int,X4: fun_int_bool] :
          ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4)))
          & hBOOL(hAPP_f448129468l_bool(X0,X4))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X1))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4)) )
      | ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(flattening,[],[f3219]) ).

tff(f3219,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,X2))
      | ? [X3: int,X4: fun_int_bool] :
          ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4)))
          & hBOOL(hAPP_f448129468l_bool(X0,X4))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X1))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4)) )
      | ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(ennf_transformation,[],[f2232]) ).

tff(f2232,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1))
       => ( hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
         => ( ! [X3: int,X4: fun_int_bool] :
                ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
               => ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X1))
                 => ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
                   => ( hBOOL(hAPP_f448129468l_bool(X0,X4))
                     => hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4))) ) ) ) )
           => hBOOL(hAPP_f448129468l_bool(X0,X2)) ) ) ) ),
    inference(rectify,[],[f680]) ).

tff(f680,axiom,
    ! [X10: fun_fu819804446l_bool,X2: fun_int_bool,X4: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4),X2))
       => ( hBOOL(hAPP_f448129468l_bool(X10,bot_bot_fun_int_bool))
         => ( ! [X75: int,X76: fun_int_bool] :
                ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X76))
               => ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X75),X2))
                 => ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X75),X76))
                   => ( hBOOL(hAPP_f448129468l_bool(X10,X76))
                     => hBOOL(hAPP_f448129468l_bool(X10,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X75),X76))) ) ) ) )
           => hBOOL(hAPP_f448129468l_bool(X10,X4)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_679_finite__subset__induct) ).

tff(f27699,plain,
    spl250_1340,
    inference(avatar_split_clause,[],[f5931,f27697]) ).

tff(f27697,plain,
    ( spl250_1340
  <=> ! [X2: fun_a_bool,X0: fun_pname_a,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK179(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1340])]) ).

tff(f5931,plain,
    ! [X2: fun_a_bool,X0: fun_pname_a,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK179(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4253]) ).

tff(f4253,plain,
    ! [X0: fun_pname_a,X1: fun_pname_bool,X2: fun_a_bool] :
      ( ( ( image_pname_a(X0,sK179(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK179(X0,X1,X2)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK179(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK179])],[f3212,f4252]) ).

tff(f4252,plain,
    ! [X0: fun_pname_a,X1: fun_pname_bool,X2: fun_a_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_pname_a(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
     => ( ( image_pname_a(X0,sK179(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK179(X0,X1,X2)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK179(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3212,plain,
    ! [X0: fun_pname_a,X1: fun_pname_bool,X2: fun_a_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_pname_a(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(flattening,[],[f3211]) ).

tff(f3211,plain,
    ! [X0: fun_pname_a,X1: fun_pname_bool,X2: fun_a_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_pname_a(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(ennf_transformation,[],[f2228]) ).

tff(f2228,plain,
    ! [X0: fun_pname_a,X1: fun_pname_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
       => ? [X3: fun_pname_bool] :
            ( ( image_pname_a(X0,X3) = X2 )
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f263]) ).

tff(f263,axiom,
    ! [X6: fun_pname_a,X2: fun_pname_bool,X7: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),image_pname_a(X6,X2)))
       => ? [X24: fun_pname_bool] :
            ( ( image_pname_a(X6,X24) = X7 )
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X24))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_finite__subset__image) ).

tff(f27695,plain,
    spl250_1339,
    inference(avatar_split_clause,[],[f5928,f27693]) ).

tff(f27693,plain,
    ( spl250_1339
  <=> ! [X2: fun_a_bool,X0: fun_int_a,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK178(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_int_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1339])]) ).

tff(f5928,plain,
    ! [X2: fun_a_bool,X0: fun_int_a,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK178(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_int_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4251]) ).

tff(f4251,plain,
    ! [X0: fun_int_a,X1: fun_int_bool,X2: fun_a_bool] :
      ( ( ( image_int_a(X0,sK178(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK178(X0,X1,X2)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK178(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_int_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK178])],[f3210,f4250]) ).

tff(f4250,plain,
    ! [X0: fun_int_a,X1: fun_int_bool,X2: fun_a_bool] :
      ( ? [X3: fun_int_bool] :
          ( ( image_int_a(X0,X3) = X2 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
     => ( ( image_int_a(X0,sK178(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK178(X0,X1,X2)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK178(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3210,plain,
    ! [X0: fun_int_a,X1: fun_int_bool,X2: fun_a_bool] :
      ( ? [X3: fun_int_bool] :
          ( ( image_int_a(X0,X3) = X2 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_int_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(flattening,[],[f3209]) ).

tff(f3209,plain,
    ! [X0: fun_int_a,X1: fun_int_bool,X2: fun_a_bool] :
      ( ? [X3: fun_int_bool] :
          ( ( image_int_a(X0,X3) = X2 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_int_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(ennf_transformation,[],[f2227]) ).

tff(f2227,plain,
    ! [X0: fun_int_a,X1: fun_int_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_int_a(X0,X1)))
       => ? [X3: fun_int_bool] :
            ( ( image_int_a(X0,X3) = X2 )
            & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
            & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f257]) ).

tff(f257,axiom,
    ! [X6: fun_int_a,X2: fun_int_bool,X7: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),image_int_a(X6,X2)))
       => ? [X24: fun_int_bool] :
            ( ( image_int_a(X6,X24) = X7 )
            & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X24))
            & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_finite__subset__image) ).

tff(f27691,plain,
    spl250_1338,
    inference(avatar_split_clause,[],[f5925,f27689]) ).

tff(f27689,plain,
    ( spl250_1338
  <=> ! [X2: fun_a_bool,X0: fun_nat_a,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK177(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_nat_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1338])]) ).

tff(f5925,plain,
    ! [X2: fun_a_bool,X0: fun_nat_a,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK177(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_nat_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4249]) ).

tff(f4249,plain,
    ! [X0: fun_nat_a,X1: fun_nat_bool,X2: fun_a_bool] :
      ( ( ( image_nat_a(X0,sK177(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK177(X0,X1,X2)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK177(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_nat_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK177])],[f3208,f4248]) ).

tff(f4248,plain,
    ! [X0: fun_nat_a,X1: fun_nat_bool,X2: fun_a_bool] :
      ( ? [X3: fun_nat_bool] :
          ( ( image_nat_a(X0,X3) = X2 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
     => ( ( image_nat_a(X0,sK177(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK177(X0,X1,X2)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK177(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3208,plain,
    ! [X0: fun_nat_a,X1: fun_nat_bool,X2: fun_a_bool] :
      ( ? [X3: fun_nat_bool] :
          ( ( image_nat_a(X0,X3) = X2 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_nat_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(flattening,[],[f3207]) ).

tff(f3207,plain,
    ! [X0: fun_nat_a,X1: fun_nat_bool,X2: fun_a_bool] :
      ( ? [X3: fun_nat_bool] :
          ( ( image_nat_a(X0,X3) = X2 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_nat_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(ennf_transformation,[],[f2226]) ).

tff(f2226,plain,
    ! [X0: fun_nat_a,X1: fun_nat_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_nat_a(X0,X1)))
       => ? [X3: fun_nat_bool] :
            ( ( image_nat_a(X0,X3) = X2 )
            & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f251]) ).

tff(f251,axiom,
    ! [X6: fun_nat_a,X2: fun_nat_bool,X7: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),image_nat_a(X6,X2)))
       => ? [X24: fun_nat_bool] :
            ( ( image_nat_a(X6,X24) = X7 )
            & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X24))
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_finite__subset__image) ).

tff(f27687,plain,
    spl250_1337,
    inference(avatar_split_clause,[],[f5922,f27685]) ).

tff(f27685,plain,
    ( spl250_1337
  <=> ! [X2: fun_a_bool,X0: fun_a_a,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK176(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_a_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1337])]) ).

tff(f5922,plain,
    ! [X2: fun_a_bool,X0: fun_a_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK176(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_a_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4247]) ).

tff(f4247,plain,
    ! [X0: fun_a_a,X1: fun_a_bool,X2: fun_a_bool] :
      ( ( ( image_a_a(X0,sK176(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK176(X0,X1,X2)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK176(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_a_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK176])],[f3206,f4246]) ).

tff(f4246,plain,
    ! [X0: fun_a_a,X1: fun_a_bool,X2: fun_a_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_a_a(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
     => ( ( image_a_a(X0,sK176(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK176(X0,X1,X2)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK176(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3206,plain,
    ! [X0: fun_a_a,X1: fun_a_bool,X2: fun_a_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_a_a(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_a_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(flattening,[],[f3205]) ).

tff(f3205,plain,
    ! [X0: fun_a_a,X1: fun_a_bool,X2: fun_a_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_a_a(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_a_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(ennf_transformation,[],[f2225]) ).

tff(f2225,plain,
    ! [X0: fun_a_a,X1: fun_a_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_a_a(X0,X1)))
       => ? [X3: fun_a_bool] :
            ( ( image_a_a(X0,X3) = X2 )
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f224]) ).

tff(f224,axiom,
    ! [X6: fun_a_a,X2: fun_a_bool,X7: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),image_a_a(X6,X2)))
       => ? [X24: fun_a_bool] :
            ( ( image_a_a(X6,X24) = X7 )
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X24))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_finite__subset__image) ).

tff(f27683,plain,
    spl250_1336,
    inference(avatar_split_clause,[],[f5919,f27681]) ).

tff(f27681,plain,
    ( spl250_1336
  <=> ! [X2: fun_a_bool,X0: fun_fun_nat_bool_a,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK175(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_nat_bool_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1336])]) ).

tff(f5919,plain,
    ! [X2: fun_a_bool,X0: fun_fun_nat_bool_a,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK175(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_nat_bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4245]) ).

tff(f4245,plain,
    ! [X0: fun_fun_nat_bool_a,X1: fun_fu425979586l_bool,X2: fun_a_bool] :
      ( ( ( image_fun_nat_bool_a(X0,sK175(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK175(X0,X1,X2)))
        & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK175(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_nat_bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK175])],[f3204,f4244]) ).

tff(f4244,plain,
    ! [X0: fun_fun_nat_bool_a,X1: fun_fu425979586l_bool,X2: fun_a_bool] :
      ( ? [X3: fun_fu425979586l_bool] :
          ( ( image_fun_nat_bool_a(X0,X3) = X2 )
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
     => ( ( image_fun_nat_bool_a(X0,sK175(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK175(X0,X1,X2)))
        & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK175(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3204,plain,
    ! [X0: fun_fun_nat_bool_a,X1: fun_fu425979586l_bool,X2: fun_a_bool] :
      ( ? [X3: fun_fu425979586l_bool] :
          ( ( image_fun_nat_bool_a(X0,X3) = X2 )
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_nat_bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(flattening,[],[f3203]) ).

tff(f3203,plain,
    ! [X0: fun_fun_nat_bool_a,X1: fun_fu425979586l_bool,X2: fun_a_bool] :
      ( ? [X3: fun_fu425979586l_bool] :
          ( ( image_fun_nat_bool_a(X0,X3) = X2 )
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_nat_bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(ennf_transformation,[],[f2224]) ).

tff(f2224,plain,
    ! [X0: fun_fun_nat_bool_a,X1: fun_fu425979586l_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_nat_bool_a(X0,X1)))
       => ? [X3: fun_fu425979586l_bool] :
            ( ( image_fun_nat_bool_a(X0,X3) = X2 )
            & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
            & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f221]) ).

tff(f221,axiom,
    ! [X6: fun_fun_nat_bool_a,X2: fun_fu425979586l_bool,X7: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),image_fun_nat_bool_a(X6,X2)))
       => ? [X24: fun_fu425979586l_bool] :
            ( ( image_fun_nat_bool_a(X6,X24) = X7 )
            & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X24))
            & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_finite__subset__image) ).

tff(f27679,plain,
    spl250_1335,
    inference(avatar_split_clause,[],[f5916,f27677]) ).

tff(f27677,plain,
    ( spl250_1335
  <=> ! [X2: fun_a_bool,X0: fun_fun_int_bool_a,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK174(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_int_bool_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1335])]) ).

tff(f5916,plain,
    ! [X2: fun_a_bool,X0: fun_fun_int_bool_a,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK174(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_int_bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4243]) ).

tff(f4243,plain,
    ! [X0: fun_fun_int_bool_a,X1: fun_fu819804446l_bool,X2: fun_a_bool] :
      ( ( ( image_fun_int_bool_a(X0,sK174(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK174(X0,X1,X2)))
        & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK174(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_int_bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK174])],[f3202,f4242]) ).

tff(f4242,plain,
    ! [X0: fun_fun_int_bool_a,X1: fun_fu819804446l_bool,X2: fun_a_bool] :
      ( ? [X3: fun_fu819804446l_bool] :
          ( ( image_fun_int_bool_a(X0,X3) = X2 )
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
          & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
     => ( ( image_fun_int_bool_a(X0,sK174(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK174(X0,X1,X2)))
        & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK174(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3202,plain,
    ! [X0: fun_fun_int_bool_a,X1: fun_fu819804446l_bool,X2: fun_a_bool] :
      ( ? [X3: fun_fu819804446l_bool] :
          ( ( image_fun_int_bool_a(X0,X3) = X2 )
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
          & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_int_bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(flattening,[],[f3201]) ).

tff(f3201,plain,
    ! [X0: fun_fun_int_bool_a,X1: fun_fu819804446l_bool,X2: fun_a_bool] :
      ( ? [X3: fun_fu819804446l_bool] :
          ( ( image_fun_int_bool_a(X0,X3) = X2 )
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
          & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_int_bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(ennf_transformation,[],[f2223]) ).

tff(f2223,plain,
    ! [X0: fun_fun_int_bool_a,X1: fun_fu819804446l_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_int_bool_a(X0,X1)))
       => ? [X3: fun_fu819804446l_bool] :
            ( ( image_fun_int_bool_a(X0,X3) = X2 )
            & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
            & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f220]) ).

tff(f220,axiom,
    ! [X6: fun_fun_int_bool_a,X2: fun_fu819804446l_bool,X7: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),image_fun_int_bool_a(X6,X2)))
       => ? [X24: fun_fu819804446l_bool] :
            ( ( image_fun_int_bool_a(X6,X24) = X7 )
            & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X24))
            & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_finite__subset__image) ).

tff(f27675,plain,
    spl250_1334,
    inference(avatar_split_clause,[],[f5913,f27673]) ).

tff(f27673,plain,
    ( spl250_1334
  <=> ! [X2: fun_a_bool,X0: fun_fun_pname_bool_a,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK173(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_876012084bool_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1334])]) ).

tff(f5913,plain,
    ! [X2: fun_a_bool,X0: fun_fun_pname_bool_a,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK173(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_876012084bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4241]) ).

tff(f4241,plain,
    ! [X0: fun_fun_pname_bool_a,X1: fun_fu1430349052l_bool,X2: fun_a_bool] :
      ( ( ( image_876012084bool_a(X0,sK173(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK173(X0,X1,X2)))
        & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK173(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_876012084bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK173])],[f3200,f4240]) ).

tff(f4240,plain,
    ! [X0: fun_fun_pname_bool_a,X1: fun_fu1430349052l_bool,X2: fun_a_bool] :
      ( ? [X3: fun_fu1430349052l_bool] :
          ( ( image_876012084bool_a(X0,X3) = X2 )
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1)) )
     => ( ( image_876012084bool_a(X0,sK173(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK173(X0,X1,X2)))
        & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK173(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3200,plain,
    ! [X0: fun_fun_pname_bool_a,X1: fun_fu1430349052l_bool,X2: fun_a_bool] :
      ( ? [X3: fun_fu1430349052l_bool] :
          ( ( image_876012084bool_a(X0,X3) = X2 )
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_876012084bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(flattening,[],[f3199]) ).

tff(f3199,plain,
    ! [X0: fun_fun_pname_bool_a,X1: fun_fu1430349052l_bool,X2: fun_a_bool] :
      ( ? [X3: fun_fu1430349052l_bool] :
          ( ( image_876012084bool_a(X0,X3) = X2 )
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_876012084bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(ennf_transformation,[],[f2222]) ).

tff(f2222,plain,
    ! [X0: fun_fun_pname_bool_a,X1: fun_fu1430349052l_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_876012084bool_a(X0,X1)))
       => ? [X3: fun_fu1430349052l_bool] :
            ( ( image_876012084bool_a(X0,X3) = X2 )
            & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
            & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f222]) ).

tff(f222,axiom,
    ! [X6: fun_fun_pname_bool_a,X2: fun_fu1430349052l_bool,X7: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),image_876012084bool_a(X6,X2)))
       => ? [X24: fun_fu1430349052l_bool] :
            ( ( image_876012084bool_a(X6,X24) = X7 )
            & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X24))
            & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_finite__subset__image) ).

tff(f27671,plain,
    spl250_1333,
    inference(avatar_split_clause,[],[f5910,f27669]) ).

tff(f27669,plain,
    ( spl250_1333
  <=> ! [X2: fun_a_bool,X0: fun_fun_a_bool_a,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK172(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_a_bool_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1333])]) ).

tff(f5910,plain,
    ! [X2: fun_a_bool,X0: fun_fun_a_bool_a,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK172(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_a_bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4239]) ).

tff(f4239,plain,
    ! [X0: fun_fun_a_bool_a,X1: fun_fun_a_bool_bool,X2: fun_a_bool] :
      ( ( ( image_fun_a_bool_a(X0,sK172(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK172(X0,X1,X2)))
        & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK172(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_a_bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK172])],[f3198,f4238]) ).

tff(f4238,plain,
    ! [X0: fun_fun_a_bool_a,X1: fun_fun_a_bool_bool,X2: fun_a_bool] :
      ( ? [X3: fun_fun_a_bool_bool] :
          ( ( image_fun_a_bool_a(X0,X3) = X2 )
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1)) )
     => ( ( image_fun_a_bool_a(X0,sK172(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK172(X0,X1,X2)))
        & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK172(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3198,plain,
    ! [X0: fun_fun_a_bool_a,X1: fun_fun_a_bool_bool,X2: fun_a_bool] :
      ( ? [X3: fun_fun_a_bool_bool] :
          ( ( image_fun_a_bool_a(X0,X3) = X2 )
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_a_bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(flattening,[],[f3197]) ).

tff(f3197,plain,
    ! [X0: fun_fun_a_bool_a,X1: fun_fun_a_bool_bool,X2: fun_a_bool] :
      ( ? [X3: fun_fun_a_bool_bool] :
          ( ( image_fun_a_bool_a(X0,X3) = X2 )
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_a_bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(ennf_transformation,[],[f2221]) ).

tff(f2221,plain,
    ! [X0: fun_fun_a_bool_a,X1: fun_fun_a_bool_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_a_bool_a(X0,X1)))
       => ? [X3: fun_fun_a_bool_bool] :
            ( ( image_fun_a_bool_a(X0,X3) = X2 )
            & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
            & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f223]) ).

tff(f223,axiom,
    ! [X6: fun_fun_a_bool_a,X2: fun_fun_a_bool_bool,X7: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),image_fun_a_bool_a(X6,X2)))
       => ? [X24: fun_fun_a_bool_bool] :
            ( ( image_fun_a_bool_a(X6,X24) = X7 )
            & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X24))
            & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_finite__subset__image) ).

tff(f27662,plain,
    spl250_1332,
    inference(avatar_split_clause,[],[f5907,f27660]) ).

tff(f27660,plain,
    ( spl250_1332
  <=> ! [X2: fun_a_bool,X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(X0,X2))
        | sP9(X0,X1)
        | ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1332])]) ).

tff(f5907,plain,
    ! [X2: fun_a_bool,X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,X2))
      | sP9(X0,X1)
      | ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f3702]) ).

tff(f3702,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,X2))
      | sP9(X0,X1)
      | ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(definition_folding,[],[f3192,f3701]) ).

tff(f3701,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( ? [X3: x_a,X4: fun_a_bool] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4)))
          & hBOOL(hAPP_fun_a_bool_bool(X0,X4))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4)) )
      | ~ sP9(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).

tff(f3192,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,X2))
      | ? [X3: x_a,X4: fun_a_bool] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4)))
          & hBOOL(hAPP_fun_a_bool_bool(X0,X4))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(flattening,[],[f3191]) ).

tff(f3191,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,X2))
      | ? [X3: x_a,X4: fun_a_bool] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4)))
          & hBOOL(hAPP_fun_a_bool_bool(X0,X4))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(ennf_transformation,[],[f2218]) ).

tff(f2218,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
       => ( hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
         => ( ! [X3: x_a,X4: fun_a_bool] :
                ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
               => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
                 => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
                   => ( hBOOL(hAPP_fun_a_bool_bool(X0,X4))
                     => hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4))) ) ) ) )
           => hBOOL(hAPP_fun_a_bool_bool(X0,X2)) ) ) ) ),
    inference(rectify,[],[f679]) ).

tff(f679,axiom,
    ! [X10: fun_fun_a_bool_bool,X2: fun_a_bool,X4: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4),X2))
       => ( hBOOL(hAPP_fun_a_bool_bool(X10,bot_bot_fun_a_bool))
         => ( ! [X75: x_a,X76: fun_a_bool] :
                ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X76))
               => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X75),X2))
                 => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X75),X76))
                   => ( hBOOL(hAPP_fun_a_bool_bool(X10,X76))
                     => hBOOL(hAPP_fun_a_bool_bool(X10,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X75),X76))) ) ) ) )
           => hBOOL(hAPP_fun_a_bool_bool(X10,X4)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_678_finite__subset__induct) ).

tff(f27658,plain,
    spl250_1331,
    inference(avatar_split_clause,[],[f5897,f27656]) ).

tff(f27656,plain,
    ( spl250_1331
  <=> ! [X2: fun_pname_bool,X0: fun_a_pname,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK169(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_a_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1331])]) ).

tff(f5897,plain,
    ! [X2: fun_pname_bool,X0: fun_a_pname,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK169(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_a_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4233]) ).

tff(f4233,plain,
    ! [X0: fun_a_pname,X1: fun_a_bool,X2: fun_pname_bool] :
      ( ( ( image_a_pname(X0,sK169(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK169(X0,X1,X2)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK169(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_a_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK169])],[f3186,f4232]) ).

tff(f4232,plain,
    ! [X0: fun_a_pname,X1: fun_a_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_a_pname(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
     => ( ( image_a_pname(X0,sK169(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK169(X0,X1,X2)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK169(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3186,plain,
    ! [X0: fun_a_pname,X1: fun_a_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_a_pname(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_a_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(flattening,[],[f3185]) ).

tff(f3185,plain,
    ! [X0: fun_a_pname,X1: fun_a_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_a_pname(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_a_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(ennf_transformation,[],[f2215]) ).

tff(f2215,plain,
    ! [X0: fun_a_pname,X1: fun_a_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_a_pname(X0,X1)))
       => ? [X3: fun_a_bool] :
            ( ( image_a_pname(X0,X3) = X2 )
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f229]) ).

tff(f229,axiom,
    ! [X6: fun_a_pname,X2: fun_a_bool,X7: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X7),image_a_pname(X6,X2)))
       => ? [X24: fun_a_bool] :
            ( ( image_a_pname(X6,X24) = X7 )
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X24))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_finite__subset__image) ).

tff(f27654,plain,
    spl250_1330,
    inference(avatar_split_clause,[],[f5894,f27652]) ).

tff(f27652,plain,
    ( spl250_1330
  <=> ! [X2: fun_pname_bool,X0: fun_nat_pname,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK168(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_nat_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1330])]) ).

tff(f5894,plain,
    ! [X2: fun_pname_bool,X0: fun_nat_pname,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK168(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_nat_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4231]) ).

tff(f4231,plain,
    ! [X0: fun_nat_pname,X1: fun_nat_bool,X2: fun_pname_bool] :
      ( ( ( image_nat_pname(X0,sK168(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK168(X0,X1,X2)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK168(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_nat_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK168])],[f3184,f4230]) ).

tff(f4230,plain,
    ! [X0: fun_nat_pname,X1: fun_nat_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_nat_bool] :
          ( ( image_nat_pname(X0,X3) = X2 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
     => ( ( image_nat_pname(X0,sK168(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK168(X0,X1,X2)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK168(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3184,plain,
    ! [X0: fun_nat_pname,X1: fun_nat_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_nat_bool] :
          ( ( image_nat_pname(X0,X3) = X2 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_nat_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(flattening,[],[f3183]) ).

tff(f3183,plain,
    ! [X0: fun_nat_pname,X1: fun_nat_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_nat_bool] :
          ( ( image_nat_pname(X0,X3) = X2 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_nat_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(ennf_transformation,[],[f2214]) ).

tff(f2214,plain,
    ! [X0: fun_nat_pname,X1: fun_nat_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_nat_pname(X0,X1)))
       => ? [X3: fun_nat_bool] :
            ( ( image_nat_pname(X0,X3) = X2 )
            & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f256]) ).

tff(f256,axiom,
    ! [X6: fun_nat_pname,X2: fun_nat_bool,X7: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X7),image_nat_pname(X6,X2)))
       => ? [X24: fun_nat_bool] :
            ( ( image_nat_pname(X6,X24) = X7 )
            & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X24))
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_finite__subset__image) ).

tff(f27650,plain,
    spl250_1329,
    inference(avatar_split_clause,[],[f5891,f27648]) ).

tff(f27648,plain,
    ( spl250_1329
  <=> ! [X2: fun_pname_bool,X0: fun_int_pname,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK167(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_int_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1329])]) ).

tff(f5891,plain,
    ! [X2: fun_pname_bool,X0: fun_int_pname,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK167(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_int_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4229]) ).

tff(f4229,plain,
    ! [X0: fun_int_pname,X1: fun_int_bool,X2: fun_pname_bool] :
      ( ( ( image_int_pname(X0,sK167(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK167(X0,X1,X2)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK167(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_int_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK167])],[f3182,f4228]) ).

tff(f4228,plain,
    ! [X0: fun_int_pname,X1: fun_int_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_int_bool] :
          ( ( image_int_pname(X0,X3) = X2 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
     => ( ( image_int_pname(X0,sK167(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK167(X0,X1,X2)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK167(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3182,plain,
    ! [X0: fun_int_pname,X1: fun_int_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_int_bool] :
          ( ( image_int_pname(X0,X3) = X2 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_int_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(flattening,[],[f3181]) ).

tff(f3181,plain,
    ! [X0: fun_int_pname,X1: fun_int_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_int_bool] :
          ( ( image_int_pname(X0,X3) = X2 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_int_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(ennf_transformation,[],[f2213]) ).

tff(f2213,plain,
    ! [X0: fun_int_pname,X1: fun_int_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_int_pname(X0,X1)))
       => ? [X3: fun_int_bool] :
            ( ( image_int_pname(X0,X3) = X2 )
            & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
            & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f262]) ).

tff(f262,axiom,
    ! [X6: fun_int_pname,X2: fun_int_bool,X7: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X7),image_int_pname(X6,X2)))
       => ? [X24: fun_int_bool] :
            ( ( image_int_pname(X6,X24) = X7 )
            & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X24))
            & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_finite__subset__image) ).

tff(f27646,plain,
    spl250_1328,
    inference(avatar_split_clause,[],[f5888,f27644]) ).

tff(f27644,plain,
    ( spl250_1328
  <=> ! [X2: fun_pname_bool,X0: fun_pname_pname,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK166(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_pname_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1328])]) ).

tff(f5888,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK166(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_pname_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4227]) ).

tff(f4227,plain,
    ! [X0: fun_pname_pname,X1: fun_pname_bool,X2: fun_pname_bool] :
      ( ( ( image_pname_pname(X0,sK166(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK166(X0,X1,X2)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK166(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_pname_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK166])],[f3180,f4226]) ).

tff(f4226,plain,
    ! [X0: fun_pname_pname,X1: fun_pname_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_pname_pname(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
     => ( ( image_pname_pname(X0,sK166(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK166(X0,X1,X2)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK166(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3180,plain,
    ! [X0: fun_pname_pname,X1: fun_pname_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_pname_pname(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_pname_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(flattening,[],[f3179]) ).

tff(f3179,plain,
    ! [X0: fun_pname_pname,X1: fun_pname_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_pname_pname(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_pname_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(ennf_transformation,[],[f2212]) ).

tff(f2212,plain,
    ! [X0: fun_pname_pname,X1: fun_pname_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_pname_pname(X0,X1)))
       => ? [X3: fun_pname_bool] :
            ( ( image_pname_pname(X0,X3) = X2 )
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f250]) ).

tff(f250,axiom,
    ! [X6: fun_pname_pname,X2: fun_pname_bool,X7: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X7),image_pname_pname(X6,X2)))
       => ? [X24: fun_pname_bool] :
            ( ( image_pname_pname(X6,X24) = X7 )
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X24))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_finite__subset__image) ).

tff(f27642,plain,
    spl250_1327,
    inference(avatar_split_clause,[],[f5885,f27640]) ).

tff(f27640,plain,
    ( spl250_1327
  <=> ! [X2: fun_pname_bool,X0: fun_fu1499449723_pname,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK165(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1283814551_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1327])]) ).

tff(f5885,plain,
    ! [X2: fun_pname_bool,X0: fun_fu1499449723_pname,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK165(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1283814551_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4225]) ).

tff(f4225,plain,
    ! [X0: fun_fu1499449723_pname,X1: fun_fu1430349052l_bool,X2: fun_pname_bool] :
      ( ( ( image_1283814551_pname(X0,sK165(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK165(X0,X1,X2)))
        & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK165(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1283814551_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK165])],[f3178,f4224]) ).

tff(f4224,plain,
    ! [X0: fun_fu1499449723_pname,X1: fun_fu1430349052l_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_fu1430349052l_bool] :
          ( ( image_1283814551_pname(X0,X3) = X2 )
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1)) )
     => ( ( image_1283814551_pname(X0,sK165(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK165(X0,X1,X2)))
        & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK165(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3178,plain,
    ! [X0: fun_fu1499449723_pname,X1: fun_fu1430349052l_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_fu1430349052l_bool] :
          ( ( image_1283814551_pname(X0,X3) = X2 )
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1283814551_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(flattening,[],[f3177]) ).

tff(f3177,plain,
    ! [X0: fun_fu1499449723_pname,X1: fun_fu1430349052l_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_fu1430349052l_bool] :
          ( ( image_1283814551_pname(X0,X3) = X2 )
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1283814551_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(ennf_transformation,[],[f2211]) ).

tff(f2211,plain,
    ! [X0: fun_fu1499449723_pname,X1: fun_fu1430349052l_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1283814551_pname(X0,X1)))
       => ? [X3: fun_fu1430349052l_bool] :
            ( ( image_1283814551_pname(X0,X3) = X2 )
            & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
            & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f232]) ).

tff(f232,axiom,
    ! [X6: fun_fu1499449723_pname,X2: fun_fu1430349052l_bool,X7: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X7),image_1283814551_pname(X6,X2)))
       => ? [X24: fun_fu1430349052l_bool] :
            ( ( image_1283814551_pname(X6,X24) = X7 )
            & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X24))
            & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_finite__subset__image) ).

tff(f27638,plain,
    spl250_1326,
    inference(avatar_split_clause,[],[f5882,f27636]) ).

tff(f27636,plain,
    ( spl250_1326
  <=> ! [X2: fun_pname_bool,X0: fun_fu953875929_pname,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK164(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_62782965_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1326])]) ).

tff(f5882,plain,
    ! [X2: fun_pname_bool,X0: fun_fu953875929_pname,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK164(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_62782965_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4223]) ).

tff(f4223,plain,
    ! [X0: fun_fu953875929_pname,X1: fun_fu819804446l_bool,X2: fun_pname_bool] :
      ( ( ( image_62782965_pname(X0,sK164(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK164(X0,X1,X2)))
        & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK164(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_62782965_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK164])],[f3176,f4222]) ).

tff(f4222,plain,
    ! [X0: fun_fu953875929_pname,X1: fun_fu819804446l_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_fu819804446l_bool] :
          ( ( image_62782965_pname(X0,X3) = X2 )
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
          & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
     => ( ( image_62782965_pname(X0,sK164(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK164(X0,X1,X2)))
        & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK164(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3176,plain,
    ! [X0: fun_fu953875929_pname,X1: fun_fu819804446l_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_fu819804446l_bool] :
          ( ( image_62782965_pname(X0,X3) = X2 )
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
          & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_62782965_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(flattening,[],[f3175]) ).

tff(f3175,plain,
    ! [X0: fun_fu953875929_pname,X1: fun_fu819804446l_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_fu819804446l_bool] :
          ( ( image_62782965_pname(X0,X3) = X2 )
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
          & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_62782965_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(ennf_transformation,[],[f2210]) ).

tff(f2210,plain,
    ! [X0: fun_fu953875929_pname,X1: fun_fu819804446l_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_62782965_pname(X0,X1)))
       => ? [X3: fun_fu819804446l_bool] :
            ( ( image_62782965_pname(X0,X3) = X2 )
            & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3))
            & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f230]) ).

tff(f230,axiom,
    ! [X6: fun_fu953875929_pname,X2: fun_fu819804446l_bool,X7: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X7),image_62782965_pname(X6,X2)))
       => ? [X24: fun_fu819804446l_bool] :
            ( ( image_62782965_pname(X6,X24) = X7 )
            & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X24))
            & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_finite__subset__image) ).

tff(f27634,plain,
    spl250_1325,
    inference(avatar_split_clause,[],[f5879,f27632]) ).

tff(f27632,plain,
    ( spl250_1325
  <=> ! [X2: fun_pname_bool,X0: fun_fu665170229_pname,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK163(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1921560913_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1325])]) ).

tff(f5879,plain,
    ! [X2: fun_pname_bool,X0: fun_fu665170229_pname,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK163(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1921560913_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4221]) ).

tff(f4221,plain,
    ! [X0: fun_fu665170229_pname,X1: fun_fu425979586l_bool,X2: fun_pname_bool] :
      ( ( ( image_1921560913_pname(X0,sK163(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK163(X0,X1,X2)))
        & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK163(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1921560913_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK163])],[f3174,f4220]) ).

tff(f4220,plain,
    ! [X0: fun_fu665170229_pname,X1: fun_fu425979586l_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_fu425979586l_bool] :
          ( ( image_1921560913_pname(X0,X3) = X2 )
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
     => ( ( image_1921560913_pname(X0,sK163(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK163(X0,X1,X2)))
        & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK163(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3174,plain,
    ! [X0: fun_fu665170229_pname,X1: fun_fu425979586l_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_fu425979586l_bool] :
          ( ( image_1921560913_pname(X0,X3) = X2 )
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1921560913_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(flattening,[],[f3173]) ).

tff(f3173,plain,
    ! [X0: fun_fu665170229_pname,X1: fun_fu425979586l_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_fu425979586l_bool] :
          ( ( image_1921560913_pname(X0,X3) = X2 )
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1921560913_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(ennf_transformation,[],[f2209]) ).

tff(f2209,plain,
    ! [X0: fun_fu665170229_pname,X1: fun_fu425979586l_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1921560913_pname(X0,X1)))
       => ? [X3: fun_fu425979586l_bool] :
            ( ( image_1921560913_pname(X0,X3) = X2 )
            & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
            & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f231]) ).

tff(f231,axiom,
    ! [X6: fun_fu665170229_pname,X2: fun_fu425979586l_bool,X7: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X7),image_1921560913_pname(X6,X2)))
       => ? [X24: fun_fu425979586l_bool] :
            ( ( image_1921560913_pname(X6,X24) = X7 )
            & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X24))
            & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_finite__subset__image) ).

tff(f27630,plain,
    spl250_1324,
    inference(avatar_split_clause,[],[f5876,f27628]) ).

tff(f27628,plain,
    ( spl250_1324
  <=> ! [X2: fun_pname_bool,X0: fun_fun_a_bool_pname,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK162(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1854862208_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1324])]) ).

tff(f5876,plain,
    ! [X2: fun_pname_bool,X0: fun_fun_a_bool_pname,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK162(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1854862208_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4219]) ).

tff(f4219,plain,
    ! [X0: fun_fun_a_bool_pname,X1: fun_fun_a_bool_bool,X2: fun_pname_bool] :
      ( ( ( image_1854862208_pname(X0,sK162(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK162(X0,X1,X2)))
        & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK162(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1854862208_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK162])],[f3172,f4218]) ).

tff(f4218,plain,
    ! [X0: fun_fun_a_bool_pname,X1: fun_fun_a_bool_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_fun_a_bool_bool] :
          ( ( image_1854862208_pname(X0,X3) = X2 )
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1)) )
     => ( ( image_1854862208_pname(X0,sK162(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK162(X0,X1,X2)))
        & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK162(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3172,plain,
    ! [X0: fun_fun_a_bool_pname,X1: fun_fun_a_bool_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_fun_a_bool_bool] :
          ( ( image_1854862208_pname(X0,X3) = X2 )
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1854862208_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(flattening,[],[f3171]) ).

tff(f3171,plain,
    ! [X0: fun_fun_a_bool_pname,X1: fun_fun_a_bool_bool,X2: fun_pname_bool] :
      ( ? [X3: fun_fun_a_bool_bool] :
          ( ( image_1854862208_pname(X0,X3) = X2 )
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1854862208_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(ennf_transformation,[],[f2208]) ).

tff(f2208,plain,
    ! [X0: fun_fun_a_bool_pname,X1: fun_fun_a_bool_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1854862208_pname(X0,X1)))
       => ? [X3: fun_fun_a_bool_bool] :
            ( ( image_1854862208_pname(X0,X3) = X2 )
            & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
            & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f233]) ).

tff(f233,axiom,
    ! [X6: fun_fun_a_bool_pname,X2: fun_fun_a_bool_bool,X7: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X7),image_1854862208_pname(X6,X2)))
       => ? [X24: fun_fun_a_bool_bool] :
            ( ( image_1854862208_pname(X6,X24) = X7 )
            & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X24))
            & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_finite__subset__image) ).

tff(f27626,plain,
    spl250_1323,
    inference(avatar_split_clause,[],[f5869,f27624]) ).

tff(f27624,plain,
    ( spl250_1323
  <=> ! [X2: fun_pname_bool,X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(X0,X2))
        | sP8(X0,X1)
        | ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1323])]) ).

tff(f5869,plain,
    ! [X2: fun_pname_bool,X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,X2))
      | sP8(X0,X1)
      | ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f3700]) ).

tff(f3700,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,X2))
      | sP8(X0,X1)
      | ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(definition_folding,[],[f3158,f3699]) ).

tff(f3699,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( ? [X3: pname,X4: fun_pname_bool] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4)))
          & hBOOL(hAPP_f1664156314l_bool(X0,X4))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4)) )
      | ~ sP8(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).

tff(f3158,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,X2))
      | ? [X3: pname,X4: fun_pname_bool] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4)))
          & hBOOL(hAPP_f1664156314l_bool(X0,X4))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(flattening,[],[f3157]) ).

tff(f3157,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,X2))
      | ? [X3: pname,X4: fun_pname_bool] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4)))
          & hBOOL(hAPP_f1664156314l_bool(X0,X4))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(ennf_transformation,[],[f2201]) ).

tff(f2201,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
       => ( hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
         => ( ! [X3: pname,X4: fun_pname_bool] :
                ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
               => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
                 => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
                   => ( hBOOL(hAPP_f1664156314l_bool(X0,X4))
                     => hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4))) ) ) ) )
           => hBOOL(hAPP_f1664156314l_bool(X0,X2)) ) ) ) ),
    inference(rectify,[],[f682]) ).

tff(f682,axiom,
    ! [X10: fun_fu1430349052l_bool,X2: fun_pname_bool,X4: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X2))
       => ( hBOOL(hAPP_f1664156314l_bool(X10,bot_bo844097828e_bool))
         => ( ! [X75: pname,X76: fun_pname_bool] :
                ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X76))
               => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X75),X2))
                 => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X75),X76))
                   => ( hBOOL(hAPP_f1664156314l_bool(X10,X76))
                     => hBOOL(hAPP_f1664156314l_bool(X10,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X75),X76))) ) ) ) )
           => hBOOL(hAPP_f1664156314l_bool(X10,X4)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_681_finite__subset__induct) ).

tff(f27617,plain,
    spl250_1322,
    inference(avatar_split_clause,[],[f5845,f27615]) ).

tff(f27615,plain,
    ( spl250_1322
  <=> ! [X2: fun_fu425979586l_bool,X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK159(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_26036933t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1322])]) ).

tff(f5845,plain,
    ! [X2: fun_fu425979586l_bool,X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK159(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_26036933t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(cnf_transformation,[],[f4213]) ).

tff(f4213,plain,
    ! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool,X2: fun_fu425979586l_bool] :
      ( ( ( image_26036933t_bool(X0,sK159(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK159(X0,X1,X2)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK159(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_26036933t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK159])],[f3124,f4212]) ).

tff(f4212,plain,
    ! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool,X2: fun_fu425979586l_bool] :
      ( ? [X3: fun_nat_bool] :
          ( ( image_26036933t_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
     => ( ( image_26036933t_bool(X0,sK159(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK159(X0,X1,X2)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK159(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3124,plain,
    ! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool,X2: fun_fu425979586l_bool] :
      ( ? [X3: fun_nat_bool] :
          ( ( image_26036933t_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_26036933t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(flattening,[],[f3123]) ).

tff(f3123,plain,
    ! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool,X2: fun_fu425979586l_bool] :
      ( ? [X3: fun_nat_bool] :
          ( ( image_26036933t_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_26036933t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(ennf_transformation,[],[f2184]) ).

tff(f2184,plain,
    ! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_26036933t_bool(X0,X1)))
       => ? [X3: fun_nat_bool] :
            ( ( image_26036933t_bool(X0,X3) = X2 )
            & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f253]) ).

tff(f253,axiom,
    ! [X6: fun_nat_fun_nat_bool,X2: fun_nat_bool,X7: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X7),image_26036933t_bool(X6,X2)))
       => ? [X24: fun_nat_bool] :
            ( ( image_26036933t_bool(X6,X24) = X7 )
            & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X24))
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_finite__subset__image) ).

tff(f27613,plain,
    spl250_1321,
    inference(avatar_split_clause,[],[f5842,f27611]) ).

tff(f27611,plain,
    ( spl250_1321
  <=> ! [X2: fun_fu1430349052l_bool,X0: fun_na936072029e_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK158(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_1655916159e_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1321])]) ).

tff(f5842,plain,
    ! [X2: fun_fu1430349052l_bool,X0: fun_na936072029e_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK158(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_1655916159e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(cnf_transformation,[],[f4211]) ).

tff(f4211,plain,
    ! [X0: fun_na936072029e_bool,X1: fun_nat_bool,X2: fun_fu1430349052l_bool] :
      ( ( ( image_1655916159e_bool(X0,sK158(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK158(X0,X1,X2)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK158(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_1655916159e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK158])],[f3122,f4210]) ).

tff(f4210,plain,
    ! [X0: fun_na936072029e_bool,X1: fun_nat_bool,X2: fun_fu1430349052l_bool] :
      ( ? [X3: fun_nat_bool] :
          ( ( image_1655916159e_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
     => ( ( image_1655916159e_bool(X0,sK158(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK158(X0,X1,X2)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK158(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3122,plain,
    ! [X0: fun_na936072029e_bool,X1: fun_nat_bool,X2: fun_fu1430349052l_bool] :
      ( ? [X3: fun_nat_bool] :
          ( ( image_1655916159e_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_1655916159e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(flattening,[],[f3121]) ).

tff(f3121,plain,
    ! [X0: fun_na936072029e_bool,X1: fun_nat_bool,X2: fun_fu1430349052l_bool] :
      ( ? [X3: fun_nat_bool] :
          ( ( image_1655916159e_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_1655916159e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(ennf_transformation,[],[f2183]) ).

tff(f2183,plain,
    ! [X0: fun_na936072029e_bool,X1: fun_nat_bool,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_1655916159e_bool(X0,X1)))
       => ? [X3: fun_nat_bool] :
            ( ( image_1655916159e_bool(X0,X3) = X2 )
            & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f254]) ).

tff(f254,axiom,
    ! [X6: fun_na936072029e_bool,X2: fun_nat_bool,X7: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X7),image_1655916159e_bool(X6,X2)))
       => ? [X24: fun_nat_bool] :
            ( ( image_1655916159e_bool(X6,X24) = X7 )
            & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X24))
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_finite__subset__image) ).

tff(f27609,plain,
    spl250_1320,
    inference(avatar_split_clause,[],[f5839,f27607]) ).

tff(f27607,plain,
    ( spl250_1320
  <=> ! [X2: fun_fu819804446l_bool,X0: fun_nat_fun_int_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK157(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1556378401t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1320])]) ).

tff(f5839,plain,
    ! [X2: fun_fu819804446l_bool,X0: fun_nat_fun_int_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK157(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1556378401t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(cnf_transformation,[],[f4209]) ).

tff(f4209,plain,
    ! [X0: fun_nat_fun_int_bool,X1: fun_nat_bool,X2: fun_fu819804446l_bool] :
      ( ( ( image_1556378401t_bool(X0,sK157(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK157(X0,X1,X2)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK157(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1556378401t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK157])],[f3120,f4208]) ).

tff(f4208,plain,
    ! [X0: fun_nat_fun_int_bool,X1: fun_nat_bool,X2: fun_fu819804446l_bool] :
      ( ? [X3: fun_nat_bool] :
          ( ( image_1556378401t_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
     => ( ( image_1556378401t_bool(X0,sK157(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK157(X0,X1,X2)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK157(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3120,plain,
    ! [X0: fun_nat_fun_int_bool,X1: fun_nat_bool,X2: fun_fu819804446l_bool] :
      ( ? [X3: fun_nat_bool] :
          ( ( image_1556378401t_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1556378401t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(flattening,[],[f3119]) ).

tff(f3119,plain,
    ! [X0: fun_nat_fun_int_bool,X1: fun_nat_bool,X2: fun_fu819804446l_bool] :
      ( ? [X3: fun_nat_bool] :
          ( ( image_1556378401t_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1556378401t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(ennf_transformation,[],[f2182]) ).

tff(f2182,plain,
    ! [X0: fun_nat_fun_int_bool,X1: fun_nat_bool,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1556378401t_bool(X0,X1)))
       => ? [X3: fun_nat_bool] :
            ( ( image_1556378401t_bool(X0,X3) = X2 )
            & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f252]) ).

tff(f252,axiom,
    ! [X6: fun_nat_fun_int_bool,X2: fun_nat_bool,X7: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X7))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X7),image_1556378401t_bool(X6,X2)))
       => ? [X24: fun_nat_bool] :
            ( ( image_1556378401t_bool(X6,X24) = X7 )
            & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X24))
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_finite__subset__image) ).

tff(f27605,plain,
    spl250_1319,
    inference(avatar_split_clause,[],[f5836,f27603]) ).

tff(f27603,plain,
    ( spl250_1319
  <=> ! [X2: fun_fun_a_bool_bool,X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK156(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_nat_fun_a_bool(X0,X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1319])]) ).

tff(f5836,plain,
    ! [X2: fun_fun_a_bool_bool,X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK156(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_nat_fun_a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(cnf_transformation,[],[f4207]) ).

tff(f4207,plain,
    ! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool,X2: fun_fun_a_bool_bool] :
      ( ( ( image_nat_fun_a_bool(X0,sK156(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK156(X0,X1,X2)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK156(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_nat_fun_a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK156])],[f3118,f4206]) ).

tff(f4206,plain,
    ! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool,X2: fun_fun_a_bool_bool] :
      ( ? [X3: fun_nat_bool] :
          ( ( image_nat_fun_a_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
     => ( ( image_nat_fun_a_bool(X0,sK156(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK156(X0,X1,X2)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK156(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3118,plain,
    ! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool,X2: fun_fun_a_bool_bool] :
      ( ? [X3: fun_nat_bool] :
          ( ( image_nat_fun_a_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_nat_fun_a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(flattening,[],[f3117]) ).

tff(f3117,plain,
    ! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool,X2: fun_fun_a_bool_bool] :
      ( ? [X3: fun_nat_bool] :
          ( ( image_nat_fun_a_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_nat_fun_a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(ennf_transformation,[],[f2181]) ).

tff(f2181,plain,
    ! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_nat_fun_a_bool(X0,X1)))
       => ? [X3: fun_nat_bool] :
            ( ( image_nat_fun_a_bool(X0,X3) = X2 )
            & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f255]) ).

tff(f255,axiom,
    ! [X6: fun_nat_fun_a_bool,X2: fun_nat_bool,X7: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X7),image_nat_fun_a_bool(X6,X2)))
       => ? [X24: fun_nat_bool] :
            ( ( image_nat_fun_a_bool(X6,X24) = X7 )
            & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X24))
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_finite__subset__image) ).

tff(f27601,plain,
    spl250_1318,
    inference(avatar_split_clause,[],[f5833,f27599]) ).

tff(f27599,plain,
    ( spl250_1318
  <=> ! [X2: fun_fu1430349052l_bool,X0: fun_in2065004473e_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK155(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_637364955e_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1318])]) ).

tff(f5833,plain,
    ! [X2: fun_fu1430349052l_bool,X0: fun_in2065004473e_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK155(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_637364955e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(cnf_transformation,[],[f4205]) ).

tff(f4205,plain,
    ! [X0: fun_in2065004473e_bool,X1: fun_int_bool,X2: fun_fu1430349052l_bool] :
      ( ( ( image_637364955e_bool(X0,sK155(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK155(X0,X1,X2)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK155(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_637364955e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK155])],[f3116,f4204]) ).

tff(f4204,plain,
    ! [X0: fun_in2065004473e_bool,X1: fun_int_bool,X2: fun_fu1430349052l_bool] :
      ( ? [X3: fun_int_bool] :
          ( ( image_637364955e_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
     => ( ( image_637364955e_bool(X0,sK155(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK155(X0,X1,X2)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK155(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3116,plain,
    ! [X0: fun_in2065004473e_bool,X1: fun_int_bool,X2: fun_fu1430349052l_bool] :
      ( ? [X3: fun_int_bool] :
          ( ( image_637364955e_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_637364955e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(flattening,[],[f3115]) ).

tff(f3115,plain,
    ! [X0: fun_in2065004473e_bool,X1: fun_int_bool,X2: fun_fu1430349052l_bool] :
      ( ? [X3: fun_int_bool] :
          ( ( image_637364955e_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_637364955e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(ennf_transformation,[],[f2180]) ).

tff(f2180,plain,
    ! [X0: fun_in2065004473e_bool,X1: fun_int_bool,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_637364955e_bool(X0,X1)))
       => ? [X3: fun_int_bool] :
            ( ( image_637364955e_bool(X0,X3) = X2 )
            & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
            & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f260]) ).

tff(f260,axiom,
    ! [X6: fun_in2065004473e_bool,X2: fun_int_bool,X7: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X7),image_637364955e_bool(X6,X2)))
       => ? [X24: fun_int_bool] :
            ( ( image_637364955e_bool(X6,X24) = X7 )
            & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X24))
            & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_finite__subset__image) ).

tff(f27597,plain,
    spl250_1317,
    inference(avatar_split_clause,[],[f5830,f27595]) ).

tff(f27595,plain,
    ( spl250_1317
  <=> ! [X2: fun_fun_a_bool_bool,X0: fun_int_fun_a_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK154(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_int_fun_a_bool(X0,X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1317])]) ).

tff(f5830,plain,
    ! [X2: fun_fun_a_bool_bool,X0: fun_int_fun_a_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK154(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_int_fun_a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(cnf_transformation,[],[f4203]) ).

tff(f4203,plain,
    ! [X0: fun_int_fun_a_bool,X1: fun_int_bool,X2: fun_fun_a_bool_bool] :
      ( ( ( image_int_fun_a_bool(X0,sK154(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK154(X0,X1,X2)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK154(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_int_fun_a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK154])],[f3114,f4202]) ).

tff(f4202,plain,
    ! [X0: fun_int_fun_a_bool,X1: fun_int_bool,X2: fun_fun_a_bool_bool] :
      ( ? [X3: fun_int_bool] :
          ( ( image_int_fun_a_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
     => ( ( image_int_fun_a_bool(X0,sK154(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK154(X0,X1,X2)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK154(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3114,plain,
    ! [X0: fun_int_fun_a_bool,X1: fun_int_bool,X2: fun_fun_a_bool_bool] :
      ( ? [X3: fun_int_bool] :
          ( ( image_int_fun_a_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_int_fun_a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(flattening,[],[f3113]) ).

tff(f3113,plain,
    ! [X0: fun_int_fun_a_bool,X1: fun_int_bool,X2: fun_fun_a_bool_bool] :
      ( ? [X3: fun_int_bool] :
          ( ( image_int_fun_a_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_int_fun_a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(ennf_transformation,[],[f2179]) ).

tff(f2179,plain,
    ! [X0: fun_int_fun_a_bool,X1: fun_int_bool,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_int_fun_a_bool(X0,X1)))
       => ? [X3: fun_int_bool] :
            ( ( image_int_fun_a_bool(X0,X3) = X2 )
            & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
            & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f261]) ).

tff(f261,axiom,
    ! [X6: fun_int_fun_a_bool,X2: fun_int_bool,X7: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X7),image_int_fun_a_bool(X6,X2)))
       => ? [X24: fun_int_bool] :
            ( ( image_int_fun_a_bool(X6,X24) = X7 )
            & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X24))
            & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_finite__subset__image) ).

tff(f27593,plain,
    spl250_1316,
    inference(avatar_split_clause,[],[f5827,f27591]) ).

tff(f27591,plain,
    ( spl250_1316
  <=> ! [X2: fun_fu819804446l_bool,X0: fun_int_fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK153(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_275383677t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1316])]) ).

tff(f5827,plain,
    ! [X2: fun_fu819804446l_bool,X0: fun_int_fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK153(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_275383677t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(cnf_transformation,[],[f4201]) ).

tff(f4201,plain,
    ! [X0: fun_int_fun_int_bool,X1: fun_int_bool,X2: fun_fu819804446l_bool] :
      ( ( ( image_275383677t_bool(X0,sK153(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK153(X0,X1,X2)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK153(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_275383677t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK153])],[f3112,f4200]) ).

tff(f4200,plain,
    ! [X0: fun_int_fun_int_bool,X1: fun_int_bool,X2: fun_fu819804446l_bool] :
      ( ? [X3: fun_int_bool] :
          ( ( image_275383677t_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
     => ( ( image_275383677t_bool(X0,sK153(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK153(X0,X1,X2)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK153(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3112,plain,
    ! [X0: fun_int_fun_int_bool,X1: fun_int_bool,X2: fun_fu819804446l_bool] :
      ( ? [X3: fun_int_bool] :
          ( ( image_275383677t_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_275383677t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(flattening,[],[f3111]) ).

tff(f3111,plain,
    ! [X0: fun_int_fun_int_bool,X1: fun_int_bool,X2: fun_fu819804446l_bool] :
      ( ? [X3: fun_int_bool] :
          ( ( image_275383677t_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_275383677t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(ennf_transformation,[],[f2178]) ).

tff(f2178,plain,
    ! [X0: fun_int_fun_int_bool,X1: fun_int_bool,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_275383677t_bool(X0,X1)))
       => ? [X3: fun_int_bool] :
            ( ( image_275383677t_bool(X0,X3) = X2 )
            & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
            & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f258]) ).

tff(f258,axiom,
    ! [X6: fun_int_fun_int_bool,X2: fun_int_bool,X7: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X7))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X7),image_275383677t_bool(X6,X2)))
       => ? [X24: fun_int_bool] :
            ( ( image_275383677t_bool(X6,X24) = X7 )
            & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X24))
            & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_finite__subset__image) ).

tff(f27589,plain,
    spl250_1315,
    inference(avatar_split_clause,[],[f5824,f27587]) ).

tff(f27587,plain,
    ( spl250_1315
  <=> ! [X2: fun_fu425979586l_bool,X0: fun_int_fun_nat_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK152(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_892525857t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1315])]) ).

tff(f5824,plain,
    ! [X2: fun_fu425979586l_bool,X0: fun_int_fun_nat_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK152(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_892525857t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(cnf_transformation,[],[f4199]) ).

tff(f4199,plain,
    ! [X0: fun_int_fun_nat_bool,X1: fun_int_bool,X2: fun_fu425979586l_bool] :
      ( ( ( image_892525857t_bool(X0,sK152(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK152(X0,X1,X2)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK152(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_892525857t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK152])],[f3110,f4198]) ).

tff(f4198,plain,
    ! [X0: fun_int_fun_nat_bool,X1: fun_int_bool,X2: fun_fu425979586l_bool] :
      ( ? [X3: fun_int_bool] :
          ( ( image_892525857t_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
     => ( ( image_892525857t_bool(X0,sK152(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK152(X0,X1,X2)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK152(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3110,plain,
    ! [X0: fun_int_fun_nat_bool,X1: fun_int_bool,X2: fun_fu425979586l_bool] :
      ( ? [X3: fun_int_bool] :
          ( ( image_892525857t_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_892525857t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(flattening,[],[f3109]) ).

tff(f3109,plain,
    ! [X0: fun_int_fun_nat_bool,X1: fun_int_bool,X2: fun_fu425979586l_bool] :
      ( ? [X3: fun_int_bool] :
          ( ( image_892525857t_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_892525857t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(ennf_transformation,[],[f2177]) ).

tff(f2177,plain,
    ! [X0: fun_int_fun_nat_bool,X1: fun_int_bool,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_892525857t_bool(X0,X1)))
       => ? [X3: fun_int_bool] :
            ( ( image_892525857t_bool(X0,X3) = X2 )
            & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
            & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f259]) ).

tff(f259,axiom,
    ! [X6: fun_int_fun_nat_bool,X2: fun_int_bool,X7: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X7),image_892525857t_bool(X6,X2)))
       => ? [X24: fun_int_bool] :
            ( ( image_892525857t_bool(X6,X24) = X7 )
            & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X24))
            & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_finite__subset__image) ).

tff(f27585,plain,
    spl250_1314,
    inference(avatar_split_clause,[],[f5821,f27583]) ).

tff(f27583,plain,
    ( spl250_1314
  <=> ! [X2: fun_fu1430349052l_bool,X0: fun_pn800050071e_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK151(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_47868345e_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1314])]) ).

tff(f5821,plain,
    ! [X2: fun_fu1430349052l_bool,X0: fun_pn800050071e_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK151(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_47868345e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(cnf_transformation,[],[f4197]) ).

tff(f4197,plain,
    ! [X0: fun_pn800050071e_bool,X1: fun_pname_bool,X2: fun_fu1430349052l_bool] :
      ( ( ( image_47868345e_bool(X0,sK151(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK151(X0,X1,X2)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK151(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_47868345e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK151])],[f3108,f4196]) ).

tff(f4196,plain,
    ! [X0: fun_pn800050071e_bool,X1: fun_pname_bool,X2: fun_fu1430349052l_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_47868345e_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
     => ( ( image_47868345e_bool(X0,sK151(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK151(X0,X1,X2)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK151(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3108,plain,
    ! [X0: fun_pn800050071e_bool,X1: fun_pname_bool,X2: fun_fu1430349052l_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_47868345e_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_47868345e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(flattening,[],[f3107]) ).

tff(f3107,plain,
    ! [X0: fun_pn800050071e_bool,X1: fun_pname_bool,X2: fun_fu1430349052l_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_47868345e_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_47868345e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(ennf_transformation,[],[f2176]) ).

tff(f2176,plain,
    ! [X0: fun_pn800050071e_bool,X1: fun_pname_bool,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_47868345e_bool(X0,X1)))
       => ? [X3: fun_pname_bool] :
            ( ( image_47868345e_bool(X0,X3) = X2 )
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f248]) ).

tff(f248,axiom,
    ! [X6: fun_pn800050071e_bool,X2: fun_pname_bool,X7: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X7),image_47868345e_bool(X6,X2)))
       => ? [X24: fun_pname_bool] :
            ( ( image_47868345e_bool(X6,X24) = X7 )
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X24))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_finite__subset__image) ).

tff(f27581,plain,
    spl250_1313,
    inference(avatar_split_clause,[],[f5818,f27579]) ).

tff(f27579,plain,
    ( spl250_1313
  <=> ! [X2: fun_fu819804446l_bool,X0: fun_pn665169337t_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK150(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1512837979t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1313])]) ).

tff(f5818,plain,
    ! [X2: fun_fu819804446l_bool,X0: fun_pn665169337t_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK150(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1512837979t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(cnf_transformation,[],[f4195]) ).

tff(f4195,plain,
    ! [X0: fun_pn665169337t_bool,X1: fun_pname_bool,X2: fun_fu819804446l_bool] :
      ( ( ( image_1512837979t_bool(X0,sK150(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK150(X0,X1,X2)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK150(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1512837979t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK150])],[f3106,f4194]) ).

tff(f4194,plain,
    ! [X0: fun_pn665169337t_bool,X1: fun_pname_bool,X2: fun_fu819804446l_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_1512837979t_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
     => ( ( image_1512837979t_bool(X0,sK150(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK150(X0,X1,X2)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK150(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3106,plain,
    ! [X0: fun_pn665169337t_bool,X1: fun_pname_bool,X2: fun_fu819804446l_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_1512837979t_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1512837979t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(flattening,[],[f3105]) ).

tff(f3105,plain,
    ! [X0: fun_pn665169337t_bool,X1: fun_pname_bool,X2: fun_fu819804446l_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_1512837979t_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1512837979t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(ennf_transformation,[],[f2175]) ).

tff(f2175,plain,
    ! [X0: fun_pn665169337t_bool,X1: fun_pname_bool,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1512837979t_bool(X0,X1)))
       => ? [X3: fun_pname_bool] :
            ( ( image_1512837979t_bool(X0,X3) = X2 )
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f246]) ).

tff(f246,axiom,
    ! [X6: fun_pn665169337t_bool,X2: fun_pname_bool,X7: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X7))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X7),image_1512837979t_bool(X6,X2)))
       => ? [X24: fun_pname_bool] :
            ( ( image_1512837979t_bool(X6,X24) = X7 )
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X24))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_finite__subset__image) ).

tff(f27577,plain,
    ( spl250_1312
    | ~ spl250_66
    | ~ spl250_152
    | ~ spl250_1154 ),
    inference(avatar_split_clause,[],[f27533,f23713,f8093,f7608,f27575]) ).

tff(f27575,plain,
    ( spl250_1312
  <=> ! [X0: pname] : ( fFalse = hAPP_pname_bool(bot_bo844097828e_bool,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1312])]) ).

tff(f23713,plain,
    ( spl250_1154
  <=> ! [X0: pname] : ( bot_bot_fun_int_bool = cOMBK_bool_int(hAPP_pname_bool(bot_bo844097828e_bool,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1154])]) ).

tff(f27533,plain,
    ( ! [X0: pname] : ( fFalse = hAPP_pname_bool(bot_bo844097828e_bool,X0) )
    | ~ spl250_66
    | ~ spl250_152
    | ~ spl250_1154 ),
    inference(forward_demodulation,[],[f27532,f8094]) ).

tff(f27532,plain,
    ( ! [X0: pname,X1: int] : ( hAPP_pname_bool(bot_bo844097828e_bool,X0) = hAPP_int_bool(bot_bot_fun_int_bool,X1) )
    | ~ spl250_66
    | ~ spl250_1154 ),
    inference(superposition,[],[f7609,f23714]) ).

tff(f23714,plain,
    ( ! [X0: pname] : ( bot_bot_fun_int_bool = cOMBK_bool_int(hAPP_pname_bool(bot_bo844097828e_bool,X0)) )
    | ~ spl250_1154 ),
    inference(avatar_component_clause,[],[f23713]) ).

tff(f27573,plain,
    spl250_1311,
    inference(avatar_split_clause,[],[f5815,f27571]) ).

tff(f27571,plain,
    ( spl250_1311
  <=> ! [X2: fun_fu425979586l_bool,X0: fun_pn406123357t_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK149(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_2129980159t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1311])]) ).

tff(f5815,plain,
    ! [X2: fun_fu425979586l_bool,X0: fun_pn406123357t_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK149(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_2129980159t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(cnf_transformation,[],[f4193]) ).

tff(f4193,plain,
    ! [X0: fun_pn406123357t_bool,X1: fun_pname_bool,X2: fun_fu425979586l_bool] :
      ( ( ( image_2129980159t_bool(X0,sK149(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK149(X0,X1,X2)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK149(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_2129980159t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK149])],[f3104,f4192]) ).

tff(f4192,plain,
    ! [X0: fun_pn406123357t_bool,X1: fun_pname_bool,X2: fun_fu425979586l_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_2129980159t_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
     => ( ( image_2129980159t_bool(X0,sK149(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK149(X0,X1,X2)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK149(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3104,plain,
    ! [X0: fun_pn406123357t_bool,X1: fun_pname_bool,X2: fun_fu425979586l_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_2129980159t_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_2129980159t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(flattening,[],[f3103]) ).

tff(f3103,plain,
    ! [X0: fun_pn406123357t_bool,X1: fun_pname_bool,X2: fun_fu425979586l_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_2129980159t_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_2129980159t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(ennf_transformation,[],[f2174]) ).

tff(f2174,plain,
    ! [X0: fun_pn406123357t_bool,X1: fun_pname_bool,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_2129980159t_bool(X0,X1)))
       => ? [X3: fun_pname_bool] :
            ( ( image_2129980159t_bool(X0,X3) = X2 )
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f247]) ).

tff(f247,axiom,
    ! [X6: fun_pn406123357t_bool,X2: fun_pname_bool,X7: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X7),image_2129980159t_bool(X6,X2)))
       => ? [X24: fun_pname_bool] :
            ( ( image_2129980159t_bool(X6,X24) = X7 )
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X24))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_finite__subset__image) ).

tff(f27569,plain,
    spl250_1310,
    inference(avatar_split_clause,[],[f5812,f27567]) ).

tff(f27567,plain,
    ( spl250_1310
  <=> ! [X2: fun_fun_a_bool_bool,X0: fun_pname_fun_a_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK148(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_112932426a_bool(X0,X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1310])]) ).

tff(f5812,plain,
    ! [X2: fun_fun_a_bool_bool,X0: fun_pname_fun_a_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK148(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_112932426a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(cnf_transformation,[],[f4191]) ).

tff(f4191,plain,
    ! [X0: fun_pname_fun_a_bool,X1: fun_pname_bool,X2: fun_fun_a_bool_bool] :
      ( ( ( image_112932426a_bool(X0,sK148(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK148(X0,X1,X2)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK148(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_112932426a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK148])],[f3102,f4190]) ).

tff(f4190,plain,
    ! [X0: fun_pname_fun_a_bool,X1: fun_pname_bool,X2: fun_fun_a_bool_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_112932426a_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
     => ( ( image_112932426a_bool(X0,sK148(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK148(X0,X1,X2)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK148(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3102,plain,
    ! [X0: fun_pname_fun_a_bool,X1: fun_pname_bool,X2: fun_fun_a_bool_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_112932426a_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_112932426a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(flattening,[],[f3101]) ).

tff(f3101,plain,
    ! [X0: fun_pname_fun_a_bool,X1: fun_pname_bool,X2: fun_fun_a_bool_bool] :
      ( ? [X3: fun_pname_bool] :
          ( ( image_112932426a_bool(X0,X3) = X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_112932426a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(ennf_transformation,[],[f2173]) ).

tff(f2173,plain,
    ! [X0: fun_pname_fun_a_bool,X1: fun_pname_bool,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_112932426a_bool(X0,X1)))
       => ? [X3: fun_pname_bool] :
            ( ( image_112932426a_bool(X0,X3) = X2 )
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f249]) ).

tff(f249,axiom,
    ! [X6: fun_pname_fun_a_bool,X2: fun_pname_bool,X7: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X7),image_112932426a_bool(X6,X2)))
       => ? [X24: fun_pname_bool] :
            ( ( image_112932426a_bool(X6,X24) = X7 )
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X24))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_finite__subset__image) ).

tff(f27565,plain,
    spl250_1309,
    inference(avatar_split_clause,[],[f5809,f27563]) ).

tff(f27563,plain,
    ( spl250_1309
  <=> ! [X2: fun_fu819804446l_bool,X0: fun_a_fun_int_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK147(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_a_fun_int_bool(X0,X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1309])]) ).

tff(f5809,plain,
    ! [X2: fun_fu819804446l_bool,X0: fun_a_fun_int_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK147(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_a_fun_int_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(cnf_transformation,[],[f4189]) ).

tff(f4189,plain,
    ! [X0: fun_a_fun_int_bool,X1: fun_a_bool,X2: fun_fu819804446l_bool] :
      ( ( ( image_a_fun_int_bool(X0,sK147(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK147(X0,X1,X2)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK147(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_a_fun_int_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK147])],[f3100,f4188]) ).

tff(f4188,plain,
    ! [X0: fun_a_fun_int_bool,X1: fun_a_bool,X2: fun_fu819804446l_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_a_fun_int_bool(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
     => ( ( image_a_fun_int_bool(X0,sK147(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK147(X0,X1,X2)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK147(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3100,plain,
    ! [X0: fun_a_fun_int_bool,X1: fun_a_bool,X2: fun_fu819804446l_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_a_fun_int_bool(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_a_fun_int_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(flattening,[],[f3099]) ).

tff(f3099,plain,
    ! [X0: fun_a_fun_int_bool,X1: fun_a_bool,X2: fun_fu819804446l_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_a_fun_int_bool(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_a_fun_int_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(ennf_transformation,[],[f2172]) ).

tff(f2172,plain,
    ! [X0: fun_a_fun_int_bool,X1: fun_a_bool,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_a_fun_int_bool(X0,X1)))
       => ? [X3: fun_a_bool] :
            ( ( image_a_fun_int_bool(X0,X3) = X2 )
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f225]) ).

tff(f225,axiom,
    ! [X6: fun_a_fun_int_bool,X2: fun_a_bool,X7: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X7))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X7),image_a_fun_int_bool(X6,X2)))
       => ? [X24: fun_a_bool] :
            ( ( image_a_fun_int_bool(X6,X24) = X7 )
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X24))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_finite__subset__image) ).

tff(f27561,plain,
    spl250_1308,
    inference(avatar_split_clause,[],[f5806,f27559]) ).

tff(f27559,plain,
    ( spl250_1308
  <=> ! [X2: fun_fu425979586l_bool,X0: fun_a_fun_nat_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK146(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_a_fun_nat_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1308])]) ).

tff(f5806,plain,
    ! [X2: fun_fu425979586l_bool,X0: fun_a_fun_nat_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK146(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_a_fun_nat_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(cnf_transformation,[],[f4187]) ).

tff(f4187,plain,
    ! [X0: fun_a_fun_nat_bool,X1: fun_a_bool,X2: fun_fu425979586l_bool] :
      ( ( ( image_a_fun_nat_bool(X0,sK146(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK146(X0,X1,X2)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK146(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_a_fun_nat_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK146])],[f3098,f4186]) ).

tff(f4186,plain,
    ! [X0: fun_a_fun_nat_bool,X1: fun_a_bool,X2: fun_fu425979586l_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_a_fun_nat_bool(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
     => ( ( image_a_fun_nat_bool(X0,sK146(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK146(X0,X1,X2)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK146(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3098,plain,
    ! [X0: fun_a_fun_nat_bool,X1: fun_a_bool,X2: fun_fu425979586l_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_a_fun_nat_bool(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_a_fun_nat_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(flattening,[],[f3097]) ).

tff(f3097,plain,
    ! [X0: fun_a_fun_nat_bool,X1: fun_a_bool,X2: fun_fu425979586l_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_a_fun_nat_bool(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_a_fun_nat_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(ennf_transformation,[],[f2171]) ).

tff(f2171,plain,
    ! [X0: fun_a_fun_nat_bool,X1: fun_a_bool,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_a_fun_nat_bool(X0,X1)))
       => ? [X3: fun_a_bool] :
            ( ( image_a_fun_nat_bool(X0,X3) = X2 )
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f226]) ).

tff(f226,axiom,
    ! [X6: fun_a_fun_nat_bool,X2: fun_a_bool,X7: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X7),image_a_fun_nat_bool(X6,X2)))
       => ? [X24: fun_a_bool] :
            ( ( image_a_fun_nat_bool(X6,X24) = X7 )
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X24))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_finite__subset__image) ).

tff(f27557,plain,
    spl250_1307,
    inference(avatar_split_clause,[],[f5803,f27555]) ).

tff(f27555,plain,
    ( spl250_1307
  <=> ! [X2: fun_fu1430349052l_bool,X0: fun_a_fun_pname_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK145(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_819518260e_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1307])]) ).

tff(f5803,plain,
    ! [X2: fun_fu1430349052l_bool,X0: fun_a_fun_pname_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK145(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_819518260e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(cnf_transformation,[],[f4185]) ).

tff(f4185,plain,
    ! [X0: fun_a_fun_pname_bool,X1: fun_a_bool,X2: fun_fu1430349052l_bool] :
      ( ( ( image_819518260e_bool(X0,sK145(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK145(X0,X1,X2)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK145(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_819518260e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK145])],[f3096,f4184]) ).

tff(f4184,plain,
    ! [X0: fun_a_fun_pname_bool,X1: fun_a_bool,X2: fun_fu1430349052l_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_819518260e_bool(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
     => ( ( image_819518260e_bool(X0,sK145(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK145(X0,X1,X2)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK145(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3096,plain,
    ! [X0: fun_a_fun_pname_bool,X1: fun_a_bool,X2: fun_fu1430349052l_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_819518260e_bool(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_819518260e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(flattening,[],[f3095]) ).

tff(f3095,plain,
    ! [X0: fun_a_fun_pname_bool,X1: fun_a_bool,X2: fun_fu1430349052l_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_819518260e_bool(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_819518260e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(ennf_transformation,[],[f2170]) ).

tff(f2170,plain,
    ! [X0: fun_a_fun_pname_bool,X1: fun_a_bool,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_819518260e_bool(X0,X1)))
       => ? [X3: fun_a_bool] :
            ( ( image_819518260e_bool(X0,X3) = X2 )
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f227]) ).

tff(f227,axiom,
    ! [X6: fun_a_fun_pname_bool,X2: fun_a_bool,X7: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X7),image_819518260e_bool(X6,X2)))
       => ? [X24: fun_a_bool] :
            ( ( image_819518260e_bool(X6,X24) = X7 )
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X24))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_finite__subset__image) ).

tff(f27553,plain,
    spl250_1306,
    inference(avatar_split_clause,[],[f5800,f27551]) ).

tff(f27551,plain,
    ( spl250_1306
  <=> ! [X2: fun_fun_a_bool_bool,X0: fun_a_fun_a_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK144(X0,X1,X2)),X1))
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_a_fun_a_bool(X0,X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1306])]) ).

tff(f5800,plain,
    ! [X2: fun_fun_a_bool_bool,X0: fun_a_fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK144(X0,X1,X2)),X1))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_a_fun_a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(cnf_transformation,[],[f4183]) ).

tff(f4183,plain,
    ! [X0: fun_a_fun_a_bool,X1: fun_a_bool,X2: fun_fun_a_bool_bool] :
      ( ( ( image_a_fun_a_bool(X0,sK144(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK144(X0,X1,X2)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK144(X0,X1,X2)),X1)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_a_fun_a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK144])],[f3094,f4182]) ).

tff(f4182,plain,
    ! [X0: fun_a_fun_a_bool,X1: fun_a_bool,X2: fun_fun_a_bool_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_a_fun_a_bool(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
     => ( ( image_a_fun_a_bool(X0,sK144(X0,X1,X2)) = X2 )
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK144(X0,X1,X2)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK144(X0,X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3094,plain,
    ! [X0: fun_a_fun_a_bool,X1: fun_a_bool,X2: fun_fun_a_bool_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_a_fun_a_bool(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_a_fun_a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(flattening,[],[f3093]) ).

tff(f3093,plain,
    ! [X0: fun_a_fun_a_bool,X1: fun_a_bool,X2: fun_fun_a_bool_bool] :
      ( ? [X3: fun_a_bool] :
          ( ( image_a_fun_a_bool(X0,X3) = X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_a_fun_a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(ennf_transformation,[],[f2169]) ).

tff(f2169,plain,
    ! [X0: fun_a_fun_a_bool,X1: fun_a_bool,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_a_fun_a_bool(X0,X1)))
       => ? [X3: fun_a_bool] :
            ( ( image_a_fun_a_bool(X0,X3) = X2 )
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) ) ) ),
    inference(rectify,[],[f228]) ).

tff(f228,axiom,
    ! [X6: fun_a_fun_a_bool,X2: fun_a_bool,X7: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X7),image_a_fun_a_bool(X6,X2)))
       => ? [X24: fun_a_bool] :
            ( ( image_a_fun_a_bool(X6,X24) = X7 )
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X24))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X24),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_finite__subset__image) ).

tff(f27549,plain,
    spl250_1305,
    inference(avatar_split_clause,[],[f5788,f27547]) ).

tff(f27547,plain,
    ( spl250_1305
  <=> ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
        ( ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)),X2) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1305])]) ).

tff(f5788,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
      ( ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)),X2) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f3072]) ).

tff(f3072,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
      ( ( ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)),X2) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2)) )
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) )
      & ( ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)),X2) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
    inference(ennf_transformation,[],[f2158]) ).

tff(f2158,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
       => ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)),X2) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2)) ) )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
       => ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)),X2) ) ) ),
    inference(rectify,[],[f579]) ).

tff(f579,axiom,
    ! [X2: fun_nat_bool,X8: nat,X7: fun_nat_bool] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X7))
       => ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X2)),X7) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X7)) ) )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X7))
       => ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X7) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X2)),X7) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_578_insert__Diff__if) ).

tff(f27545,plain,
    spl250_1304,
    inference(avatar_split_clause,[],[f5786,f27543]) ).

tff(f27543,plain,
    ( spl250_1304
  <=> ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] :
        ( ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)),X2) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1304])]) ).

tff(f5786,plain,
    ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] :
      ( ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)),X2) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
    inference(cnf_transformation,[],[f3071]) ).

tff(f3071,plain,
    ! [X0: fun_int_bool,X1: int,X2: fun_int_bool] :
      ( ( ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)),X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2)) )
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) )
      & ( ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)),X2) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ) ),
    inference(ennf_transformation,[],[f2157]) ).

tff(f2157,plain,
    ! [X0: fun_int_bool,X1: int,X2: fun_int_bool] :
      ( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
       => ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)),X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2)) ) )
      & ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
       => ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)),X2) ) ) ),
    inference(rectify,[],[f578]) ).

tff(f578,axiom,
    ! [X2: fun_int_bool,X8: int,X7: fun_int_bool] :
      ( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X7))
       => ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X2)),X7) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X7)) ) )
      & ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X7))
       => ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X7) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X2)),X7) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_577_insert__Diff__if) ).

tff(f27541,plain,
    spl250_1303,
    inference(avatar_split_clause,[],[f5784,f27539]) ).

tff(f27539,plain,
    ( spl250_1303
  <=> ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
        ( ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)),X2) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1303])]) ).

tff(f5784,plain,
    ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
      ( ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)),X2) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
    inference(cnf_transformation,[],[f3070]) ).

tff(f3070,plain,
    ! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
      ( ( ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)),X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2)) )
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) )
      & ( ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)),X2) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ) ),
    inference(ennf_transformation,[],[f2156]) ).

tff(f2156,plain,
    ! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
      ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
       => ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)),X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2)) ) )
      & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
       => ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)),X2) ) ) ),
    inference(rectify,[],[f577]) ).

tff(f577,axiom,
    ! [X2: fun_a_bool,X8: x_a,X7: fun_a_bool] :
      ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X7))
       => ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X2)),X7) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X7)) ) )
      & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X7))
       => ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X7) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X2)),X7) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_576_insert__Diff__if) ).

tff(f27537,plain,
    spl250_1302,
    inference(avatar_split_clause,[],[f5782,f27535]) ).

tff(f27535,plain,
    ( spl250_1302
  <=> ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
        ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)),X2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1302])]) ).

tff(f5782,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
      ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)),X2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
    inference(cnf_transformation,[],[f3069]) ).

tff(f3069,plain,
    ! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
      ( ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)),X2) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2)) )
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) )
      & ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)),X2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
    inference(ennf_transformation,[],[f2155]) ).

tff(f2155,plain,
    ! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
      ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
       => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)),X2) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2)) ) )
      & ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
       => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X0)),X2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2) ) ) ),
    inference(rectify,[],[f580]) ).

tff(f580,axiom,
    ! [X2: fun_pname_bool,X8: pname,X7: fun_pname_bool] :
      ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X7))
       => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),X2)),X7) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X7)) ) )
      & ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X7))
       => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X7) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),X2)),X7) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_579_insert__Diff__if) ).

tff(f27528,plain,
    spl250_1301,
    inference(avatar_split_clause,[],[f5360,f27526]) ).

tff(f27526,plain,
    ( spl250_1301
  <=> ! [X0: nat,X1: nat] :
        ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X1)),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1301])]) ).

tff(f5360,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X1)),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2998]) ).

tff(f2998,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X1)),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1906]) ).

tff(f1906,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
     => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X1)),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)) ) ),
    inference(rectify,[],[f120]) ).

tff(f120,axiom,
    ! [X11: nat,X12: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X11),X12))
     => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X12)),X11) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X12),X11)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_Suc__diff__le) ).

tff(f27524,plain,
    spl250_1300,
    inference(avatar_split_clause,[],[f5307,f27522]) ).

tff(f27522,plain,
    ( spl250_1300
  <=> ! [X0: pname,X1: fun_pname_bool] :
        ( ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool))) = X1 )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1300])]) ).

tff(f5307,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool))) = X1 )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ),
    inference(cnf_transformation,[],[f2934]) ).

tff(f2934,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool))) = X1 )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ),
    inference(ennf_transformation,[],[f1860]) ).

tff(f1860,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
     => ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool))) = X1 ) ),
    inference(rectify,[],[f548]) ).

tff(f548,axiom,
    ! [X5: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5),X2))
     => ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5),bot_bo844097828e_bool))) = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_547_insert__Diff) ).

tff(f27520,plain,
    spl250_1299,
    inference(avatar_split_clause,[],[f5281,f27518]) ).

tff(f27518,plain,
    ( spl250_1299
  <=> ! [X0: pname,X1: fun_pname_bool] :
        ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool)) = X1 )
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1299])]) ).

tff(f5281,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool)) = X1 )
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ),
    inference(cnf_transformation,[],[f2901]) ).

tff(f2901,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool)) = X1 )
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ),
    inference(ennf_transformation,[],[f1837]) ).

tff(f1837,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),bot_bo844097828e_bool)) = X1 ) ),
    inference(rectify,[],[f552]) ).

tff(f552,axiom,
    ! [X8: pname,X2: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X2))
     => ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),X2)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),bot_bo844097828e_bool)) = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_551_Diff__insert__absorb) ).

tff(f27516,plain,
    spl250_1298,
    inference(avatar_split_clause,[],[f5248,f27514]) ).

tff(f27514,plain,
    ( spl250_1298
  <=> ! [X0: nat,X1: fun_nat_bool] :
        ( ( hAPP_f22106695ol_nat(finite_card_nat,X1) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1298])]) ).

tff(f5248,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( ( hAPP_f22106695ol_nat(finite_card_nat,X1) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f2871]) ).

tff(f2871,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( ( ( ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1)) )
          | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) )
        & ( ( hAPP_f22106695ol_nat(finite_card_nat,X1) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)) )
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(ennf_transformation,[],[f1820]) ).

tff(f1820,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
     => ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
         => ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1)) ) )
        & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
         => ( hAPP_f22106695ol_nat(finite_card_nat,X1) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)) ) ) ) ),
    inference(rectify,[],[f101]) ).

tff(f101,axiom,
    ! [X8: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X2))
         => ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X2)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X2)) ) )
        & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X2))
         => ( hAPP_f22106695ol_nat(finite_card_nat,X2) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X2)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_card__insert__if) ).

tff(f27512,plain,
    spl250_1297,
    inference(avatar_split_clause,[],[f5205,f27510]) ).

tff(f27510,plain,
    ( spl250_1297
  <=> ! [X0: int,X1: fun_int_bool] :
        ( ( hAPP_f957591787ol_nat(finite_card_int,X1) = hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1297])]) ).

tff(f5205,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( ( hAPP_f957591787ol_nat(finite_card_int,X1) = hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f2831]) ).

tff(f2831,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( ( ( ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,X1)) )
          | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) )
        & ( ( hAPP_f957591787ol_nat(finite_card_int,X1) = hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)) )
          | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ) )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(ennf_transformation,[],[f1791]) ).

tff(f1791,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
     => ( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
         => ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,X1)) ) )
        & ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
         => ( hAPP_f957591787ol_nat(finite_card_int,X1) = hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)) ) ) ) ),
    inference(rectify,[],[f102]) ).

tff(f102,axiom,
    ! [X8: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X2))
         => ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X2)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,X2)) ) )
        & ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X2))
         => ( hAPP_f957591787ol_nat(finite_card_int,X2) = hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X2)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_card__insert__if) ).

tff(f27508,plain,
    spl250_1296,
    inference(avatar_split_clause,[],[f5166,f27506]) ).

tff(f27506,plain,
    ( spl250_1296
  <=> ! [X0: x_a,X1: fun_a_bool] :
        ( ( hAPP_fun_a_bool_nat(finite_card_a,X1) = hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1296])]) ).

tff(f5166,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( ( hAPP_fun_a_bool_nat(finite_card_a,X1) = hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(cnf_transformation,[],[f2794]) ).

tff(f2794,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( ( ( ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X1)) )
          | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) )
        & ( ( hAPP_fun_a_bool_nat(finite_card_a,X1) = hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(ennf_transformation,[],[f1765]) ).

tff(f1765,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
     => ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
         => ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X1)) ) )
        & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
         => ( hAPP_fun_a_bool_nat(finite_card_a,X1) = hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)) ) ) ) ),
    inference(rectify,[],[f103]) ).

tff(f103,axiom,
    ! [X8: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X2))
         => ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X2)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X2)) ) )
        & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X2))
         => ( hAPP_fun_a_bool_nat(finite_card_a,X2) = hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X2)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_card__insert__if) ).

tff(f27504,plain,
    spl250_1295,
    inference(avatar_split_clause,[],[f5125,f27502]) ).

tff(f27502,plain,
    ( spl250_1295
  <=> ! [X0: pname,X1: fun_pname_bool] :
        ( ( hAPP_f921600141ol_nat(finite_card_pname,X1) = hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1295])]) ).

tff(f5125,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( ( hAPP_f921600141ol_nat(finite_card_pname,X1) = hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f2756]) ).

tff(f2756,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( ( ( ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X1)) )
          | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) )
        & ( ( hAPP_f921600141ol_nat(finite_card_pname,X1) = hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)) )
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(ennf_transformation,[],[f1738]) ).

tff(f1738,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
     => ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
         => ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X1)) ) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
         => ( hAPP_f921600141ol_nat(finite_card_pname,X1) = hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)) ) ) ) ),
    inference(rectify,[],[f100]) ).

tff(f100,axiom,
    ! [X8: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X2))
         => ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),X2)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X2)) ) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X2))
         => ( hAPP_f921600141ol_nat(finite_card_pname,X2) = hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),X2)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_card__insert__if) ).

tff(f27500,plain,
    spl250_1294,
    inference(avatar_split_clause,[],[f5091,f27498]) ).

tff(f27498,plain,
    ( spl250_1294
  <=> ! [X0: fun_int_bool,X1: fun_fu819804446l_bool] :
        ( ( hAPP_f521865025ol_nat(finite1876863882t_bool,X1) = hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1)) )
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X0),X1))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1294])]) ).

tff(f5091,plain,
    ! [X0: fun_int_bool,X1: fun_fu819804446l_bool] :
      ( ( hAPP_f521865025ol_nat(finite1876863882t_bool,X1) = hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1)) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X0),X1))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(cnf_transformation,[],[f2707]) ).

tff(f27496,plain,
    spl250_1293,
    inference(avatar_split_clause,[],[f5089,f27494]) ).

tff(f27494,plain,
    ( spl250_1293
  <=> ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
        ( ( hAPP_f696928925ol_nat(finite346522414t_bool,X1) = hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1)) )
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1293])]) ).

tff(f5089,plain,
    ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
      ( ( hAPP_f696928925ol_nat(finite346522414t_bool,X1) = hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X0),X1))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(cnf_transformation,[],[f2706]) ).

tff(f27492,plain,
    spl250_1292,
    inference(avatar_split_clause,[],[f5087,f27490]) ).

tff(f27490,plain,
    ( spl250_1292
  <=> ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
        ( ( hAPP_f55526627ol_nat(finite1340463720e_bool,X1) = hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1)) )
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1292])]) ).

tff(f5087,plain,
    ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
      ( ( hAPP_f55526627ol_nat(finite1340463720e_bool,X1) = hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X0),X1))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(cnf_transformation,[],[f2705]) ).

tff(f27478,plain,
    spl250_1291,
    inference(avatar_split_clause,[],[f5085,f27476]) ).

tff(f27476,plain,
    ( spl250_1291
  <=> ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
        ( ( hAPP_f2009550088ol_nat(finite1306199131a_bool,X1) = hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1)) )
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1291])]) ).

tff(f5085,plain,
    ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
      ( ( hAPP_f2009550088ol_nat(finite1306199131a_bool,X1) = hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X0),X1))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(cnf_transformation,[],[f2704]) ).

tff(f27208,plain,
    ( spl250_1290
    | ~ spl250_66
    | ~ spl250_152
    | ~ spl250_1146 ),
    inference(avatar_split_clause,[],[f27039,f23656,f8093,f7608,f27206]) ).

tff(f27206,plain,
    ( spl250_1290
  <=> ! [X0: x_a] : ( fFalse = hAPP_a_bool(bot_bot_fun_a_bool,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1290])]) ).

tff(f23656,plain,
    ( spl250_1146
  <=> ! [X0: x_a] : ( bot_bot_fun_int_bool = cOMBK_bool_int(hAPP_a_bool(bot_bot_fun_a_bool,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1146])]) ).

tff(f27039,plain,
    ( ! [X0: x_a] : ( fFalse = hAPP_a_bool(bot_bot_fun_a_bool,X0) )
    | ~ spl250_66
    | ~ spl250_152
    | ~ spl250_1146 ),
    inference(forward_demodulation,[],[f27038,f8094]) ).

tff(f27038,plain,
    ( ! [X0: x_a,X1: int] : ( hAPP_a_bool(bot_bot_fun_a_bool,X0) = hAPP_int_bool(bot_bot_fun_int_bool,X1) )
    | ~ spl250_66
    | ~ spl250_1146 ),
    inference(superposition,[],[f7609,f23657]) ).

tff(f23657,plain,
    ( ! [X0: x_a] : ( bot_bot_fun_int_bool = cOMBK_bool_int(hAPP_a_bool(bot_bot_fun_a_bool,X0)) )
    | ~ spl250_1146 ),
    inference(avatar_component_clause,[],[f23656]) ).

tff(f27034,plain,
    ( spl250_1289
    | ~ spl250_1049
    | ~ spl250_1265 ),
    inference(avatar_split_clause,[],[f24284,f24281,f21382,f27032]) ).

tff(f27032,plain,
    ( spl250_1289
  <=> ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))),pls))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1289])]) ).

tff(f21382,plain,
    ( spl250_1049
  <=> ! [X2: int,X0: int,X1: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1049])]) ).

tff(f24281,plain,
    ( spl250_1265
  <=> ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1265])]) ).

tff(f24284,plain,
    ( ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))),pls))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
    | ~ spl250_1049
    | ~ spl250_1265 ),
    inference(forward_demodulation,[],[f24282,f21383]) ).

tff(f21383,plain,
    ( ! [X2: int,X0: int,X1: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),X2) )
    | ~ spl250_1049 ),
    inference(avatar_component_clause,[],[f21382]) ).

tff(f24282,plain,
    ( ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls)) )
    | ~ spl250_1265 ),
    inference(avatar_component_clause,[],[f24281]) ).

tff(f27030,plain,
    ( spl250_1288
    | ~ spl250_1049
    | ~ spl250_1264 ),
    inference(avatar_split_clause,[],[f24279,f24276,f21382,f27028]) ).

tff(f27028,plain,
    ( spl250_1288
  <=> ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1288])]) ).

tff(f24276,plain,
    ( spl250_1264
  <=> ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1264])]) ).

tff(f24279,plain,
    ( ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
    | ~ spl250_1049
    | ~ spl250_1264 ),
    inference(forward_demodulation,[],[f24277,f21383]) ).

tff(f24277,plain,
    ( ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
    | ~ spl250_1264 ),
    inference(avatar_component_clause,[],[f24276]) ).

tff(f27026,plain,
    ( spl250_1287
    | ~ spl250_1049
    | ~ spl250_1263 ),
    inference(avatar_split_clause,[],[f24274,f24271,f21382,f27024]) ).

tff(f27024,plain,
    ( spl250_1287
  <=> ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))),pls))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1287])]) ).

tff(f24271,plain,
    ( spl250_1263
  <=> ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1263])]) ).

tff(f24274,plain,
    ( ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))),pls))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
    | ~ spl250_1049
    | ~ spl250_1263 ),
    inference(forward_demodulation,[],[f24272,f21383]) ).

tff(f24272,plain,
    ( ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls)) )
    | ~ spl250_1263 ),
    inference(avatar_component_clause,[],[f24271]) ).

tff(f27022,plain,
    ( spl250_1286
    | ~ spl250_1049
    | ~ spl250_1262 ),
    inference(avatar_split_clause,[],[f24269,f24266,f21382,f27020]) ).

tff(f27020,plain,
    ( spl250_1286
  <=> ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1286])]) ).

tff(f24266,plain,
    ( spl250_1262
  <=> ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1262])]) ).

tff(f24269,plain,
    ( ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
    | ~ spl250_1049
    | ~ spl250_1262 ),
    inference(forward_demodulation,[],[f24267,f21383]) ).

tff(f24267,plain,
    ( ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
    | ~ spl250_1262 ),
    inference(avatar_component_clause,[],[f24266]) ).

tff(f27018,plain,
    ( spl250_1285
    | ~ spl250_1049
    | ~ spl250_1261 ),
    inference(avatar_split_clause,[],[f24264,f24261,f21382,f27016]) ).

tff(f27016,plain,
    ( spl250_1285
  <=> ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1285])]) ).

tff(f24261,plain,
    ( spl250_1261
  <=> ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1261])]) ).

tff(f24264,plain,
    ( ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) )
    | ~ spl250_1049
    | ~ spl250_1261 ),
    inference(forward_demodulation,[],[f24262,f21383]) ).

tff(f24262,plain,
    ( ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0))) )
    | ~ spl250_1261 ),
    inference(avatar_component_clause,[],[f24261]) ).

tff(f27014,plain,
    ( spl250_1284
    | ~ spl250_1049
    | ~ spl250_1260 ),
    inference(avatar_split_clause,[],[f24259,f24256,f21382,f27012]) ).

tff(f27012,plain,
    ( spl250_1284
  <=> ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1284])]) ).

tff(f24256,plain,
    ( spl250_1260
  <=> ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1260])]) ).

tff(f24259,plain,
    ( ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) )
    | ~ spl250_1049
    | ~ spl250_1260 ),
    inference(forward_demodulation,[],[f24257,f21383]) ).

tff(f24257,plain,
    ( ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) )
    | ~ spl250_1260 ),
    inference(avatar_component_clause,[],[f24256]) ).

tff(f27010,plain,
    ( spl250_1283
    | ~ spl250_1049
    | ~ spl250_1259 ),
    inference(avatar_split_clause,[],[f24254,f24251,f21382,f27008]) ).

tff(f27008,plain,
    ( spl250_1283
  <=> ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1283])]) ).

tff(f24251,plain,
    ( spl250_1259
  <=> ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1259])]) ).

tff(f24254,plain,
    ( ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) )
    | ~ spl250_1049
    | ~ spl250_1259 ),
    inference(forward_demodulation,[],[f24252,f21383]) ).

tff(f24252,plain,
    ( ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0))) )
    | ~ spl250_1259 ),
    inference(avatar_component_clause,[],[f24251]) ).

tff(f27006,plain,
    ( spl250_1282
    | ~ spl250_1049
    | ~ spl250_1257 ),
    inference(avatar_split_clause,[],[f24244,f24241,f21382,f27004]) ).

tff(f27004,plain,
    ( spl250_1282
  <=> ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1282])]) ).

tff(f24241,plain,
    ( spl250_1257
  <=> ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1257])]) ).

tff(f24244,plain,
    ( ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) )
    | ~ spl250_1049
    | ~ spl250_1257 ),
    inference(forward_demodulation,[],[f24242,f21383]) ).

tff(f24242,plain,
    ( ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) )
    | ~ spl250_1257 ),
    inference(avatar_component_clause,[],[f24241]) ).

tff(f26216,plain,
    ( spl250_1281
    | ~ spl250_97
    | ~ spl250_183
    | ~ spl250_1135 ),
    inference(avatar_split_clause,[],[f25222,f23609,f8279,f7800,f26213]) ).

tff(f26213,plain,
    ( spl250_1281
  <=> ( zero_zero_nat = sK125(one_one_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1281])]) ).

tff(f7800,plain,
    ( spl250_97
  <=> ! [X0: nat] : ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_97])]) ).

tff(f8279,plain,
    ( spl250_183
  <=> ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X0)),one_one_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_183])]) ).

tff(f23609,plain,
    ( spl250_1135
  <=> ( one_one_nat = hAPP_nat_nat(suc,sK125(one_one_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1135])]) ).

tff(f25222,plain,
    ( ( zero_zero_nat = sK125(one_one_nat) )
    | ~ spl250_97
    | ~ spl250_183
    | ~ spl250_1135 ),
    inference(forward_demodulation,[],[f25186,f7801]) ).

tff(f7801,plain,
    ( ! [X0: nat] : ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X0) )
    | ~ spl250_97 ),
    inference(avatar_component_clause,[],[f7800]) ).

tff(f25186,plain,
    ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,one_one_nat),one_one_nat) = sK125(one_one_nat) )
    | ~ spl250_183
    | ~ spl250_1135 ),
    inference(superposition,[],[f8280,f23611]) ).

tff(f23611,plain,
    ( ( one_one_nat = hAPP_nat_nat(suc,sK125(one_one_nat)) )
    | ~ spl250_1135 ),
    inference(avatar_component_clause,[],[f23609]) ).

tff(f8280,plain,
    ( ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X0)),one_one_nat) = X0 )
    | ~ spl250_183 ),
    inference(avatar_component_clause,[],[f8279]) ).

tff(f25644,plain,
    ( ~ spl250_1280
    | ~ spl250_25
    | ~ spl250_1135 ),
    inference(avatar_split_clause,[],[f25182,f23609,f7430,f25641]) ).

tff(f25641,plain,
    ( spl250_1280
  <=> ( one_one_nat = sK125(one_one_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1280])]) ).

tff(f7430,plain,
    ( spl250_25
  <=> ! [X0: nat] : ( hAPP_nat_nat(suc,X0) != X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_25])]) ).

tff(f25182,plain,
    ( ( one_one_nat != sK125(one_one_nat) )
    | ~ spl250_25
    | ~ spl250_1135 ),
    inference(superposition,[],[f7431,f23611]) ).

tff(f7431,plain,
    ( ! [X0: nat] : ( hAPP_nat_nat(suc,X0) != X0 )
    | ~ spl250_25 ),
    inference(avatar_component_clause,[],[f7430]) ).

tff(f24826,plain,
    ( spl250_1279
    | ~ spl250_97
    | ~ spl250_183
    | ~ spl250_1124 ),
    inference(avatar_split_clause,[],[f24655,f23563,f8279,f7800,f24823]) ).

tff(f24823,plain,
    ( spl250_1279
  <=> ( zero_zero_nat = sK35(one_one_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1279])]) ).

tff(f23563,plain,
    ( spl250_1124
  <=> ( one_one_nat = hAPP_nat_nat(suc,sK35(one_one_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1124])]) ).

tff(f24655,plain,
    ( ( zero_zero_nat = sK35(one_one_nat) )
    | ~ spl250_97
    | ~ spl250_183
    | ~ spl250_1124 ),
    inference(forward_demodulation,[],[f24619,f7801]) ).

tff(f24619,plain,
    ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,one_one_nat),one_one_nat) = sK35(one_one_nat) )
    | ~ spl250_183
    | ~ spl250_1124 ),
    inference(superposition,[],[f8280,f23565]) ).

tff(f23565,plain,
    ( ( one_one_nat = hAPP_nat_nat(suc,sK35(one_one_nat)) )
    | ~ spl250_1124 ),
    inference(avatar_component_clause,[],[f23563]) ).

tff(f24769,plain,
    ( ~ spl250_1278
    | ~ spl250_25
    | ~ spl250_1124 ),
    inference(avatar_split_clause,[],[f24615,f23563,f7430,f24766]) ).

tff(f24766,plain,
    ( spl250_1278
  <=> ( one_one_nat = sK35(one_one_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1278])]) ).

tff(f24615,plain,
    ( ( one_one_nat != sK35(one_one_nat) )
    | ~ spl250_25
    | ~ spl250_1124 ),
    inference(superposition,[],[f7431,f23565]) ).

tff(f24342,plain,
    ( spl250_1277
    | ~ spl250_20
    | ~ spl250_110
    | ~ spl250_922
    | ~ spl250_1125 ),
    inference(avatar_split_clause,[],[f23571,f23568,f18006,f7853,f7406,f24340]) ).

tff(f24340,plain,
    ( spl250_1277
  <=> ! [X0: nat,X1: nat] :
        ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),X1)),X0)) )
        | ( zero_zero_nat = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1277])]) ).

tff(f23568,plain,
    ( spl250_1125
  <=> ! [X0: nat,X1: nat] :
        ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)),X0)) )
        | ( zero_zero_nat = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1125])]) ).

tff(f23571,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),X1)),X0)) )
        | ( zero_zero_nat = X1 ) )
    | ~ spl250_20
    | ~ spl250_110
    | ~ spl250_922
    | ~ spl250_1125 ),
    inference(forward_demodulation,[],[f23569,f18373]) ).

tff(f23569,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)),X0)) )
        | ( zero_zero_nat = X1 ) )
    | ~ spl250_1125 ),
    inference(avatar_component_clause,[],[f23568]) ).

tff(f24329,plain,
    spl250_1276,
    inference(avatar_split_clause,[],[f7306,f24327]) ).

tff(f24327,plain,
    ( spl250_1276
  <=> ! [X0: nat,X3: nat,X2: nat,X1: nat] :
        ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_n1699378549t_bool(fequal_nat,X3)) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_n1699378549t_bool(fequal_nat,X1)) )
        | sP27(X2,X1,X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1276])]) ).

tff(f7306,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_n1699378549t_bool(fequal_nat,X3)) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_n1699378549t_bool(fequal_nat,X1)) )
      | sP27(X2,X1,X3,X0) ),
    inference(forward_demodulation,[],[f7305,f6931]) ).

tff(f7305,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_n1699378549t_bool(fequal_nat,X3)) )
      | sP27(X2,X1,X3,X0) ),
    inference(forward_demodulation,[],[f6530,f6931]) ).

tff(f6530,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( sP27(X2,X1,X3,X0)
      | ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),bot_bot_fun_nat_bool)) ) ),
    inference(cnf_transformation,[],[f4529]) ).

tff(f4529,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),bot_bot_fun_nat_bool)) )
        | ~ sP27(X2,X1,X3,X0) )
      & ( sP27(X2,X1,X3,X0)
        | ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),bot_bot_fun_nat_bool)) ) ) ),
    inference(nnf_transformation,[],[f3738]) ).

tff(f3738,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),bot_bot_fun_nat_bool)) )
    <=> sP27(X2,X1,X3,X0) ),
    inference(definition_folding,[],[f2562,f3737]) ).

tff(f3737,plain,
    ! [X2: nat,X1: nat,X3: nat,X0: nat] :
      ( sP27(X2,X1,X3,X0)
    <=> ( ( ( X1 = X2 )
          & ( X0 = X3 ) )
        | ( ( X1 = X3 )
          & ( X0 = X2 ) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP27])]) ).

tff(f2562,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),bot_bot_fun_nat_bool)) )
    <=> ( ( ( X1 = X2 )
          & ( X0 = X3 ) )
        | ( ( X1 = X3 )
          & ( X0 = X2 ) ) ) ),
    inference(rectify,[],[f598]) ).

tff(f598,axiom,
    ! [X5: nat,X28: nat,X29: nat,X70: nat] :
      ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X28),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X29),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X70),bot_bot_fun_nat_bool)) )
    <=> ( ( ( X28 = X29 )
          & ( X5 = X70 ) )
        | ( ( X28 = X70 )
          & ( X5 = X29 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_597_doubleton__eq__iff) ).

tff(f24325,plain,
    spl250_1275,
    inference(avatar_split_clause,[],[f7304,f24323]) ).

tff(f24323,plain,
    ( spl250_1275
  <=> ! [X0: nat,X3: nat,X2: nat,X1: nat] :
        ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_n1699378549t_bool(fequal_nat,X3)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_n1699378549t_bool(fequal_nat,X1)) )
        | ~ sP27(X2,X1,X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1275])]) ).

tff(f7304,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_n1699378549t_bool(fequal_nat,X3)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_n1699378549t_bool(fequal_nat,X1)) )
      | ~ sP27(X2,X1,X3,X0) ),
    inference(forward_demodulation,[],[f7303,f6931]) ).

tff(f7303,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_n1699378549t_bool(fequal_nat,X3)) )
      | ~ sP27(X2,X1,X3,X0) ),
    inference(forward_demodulation,[],[f6531,f6931]) ).

tff(f6531,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),bot_bot_fun_nat_bool)) )
      | ~ sP27(X2,X1,X3,X0) ),
    inference(cnf_transformation,[],[f4529]) ).

tff(f24321,plain,
    spl250_1274,
    inference(avatar_split_clause,[],[f7302,f24319]) ).

tff(f24319,plain,
    ( spl250_1274
  <=> ! [X0: int,X3: int,X2: int,X1: int] :
        ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_i1948725293t_bool(fequal_int,X3)) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_i1948725293t_bool(fequal_int,X1)) )
        | sP26(X2,X1,X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1274])]) ).

tff(f7302,plain,
    ! [X2: int,X3: int,X0: int,X1: int] :
      ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_i1948725293t_bool(fequal_int,X3)) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_i1948725293t_bool(fequal_int,X1)) )
      | sP26(X2,X1,X3,X0) ),
    inference(forward_demodulation,[],[f7301,f6930]) ).

tff(f7301,plain,
    ! [X2: int,X3: int,X0: int,X1: int] :
      ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_i1948725293t_bool(fequal_int,X3)) )
      | sP26(X2,X1,X3,X0) ),
    inference(forward_demodulation,[],[f6522,f6930]) ).

tff(f6522,plain,
    ! [X2: int,X3: int,X0: int,X1: int] :
      ( sP26(X2,X1,X3,X0)
      | ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),bot_bot_fun_int_bool)) ) ),
    inference(cnf_transformation,[],[f4525]) ).

tff(f4525,plain,
    ! [X0: int,X1: int,X2: int,X3: int] :
      ( ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),bot_bot_fun_int_bool)) )
        | ~ sP26(X2,X1,X3,X0) )
      & ( sP26(X2,X1,X3,X0)
        | ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),bot_bot_fun_int_bool)) ) ) ),
    inference(nnf_transformation,[],[f3736]) ).

tff(f3736,plain,
    ! [X0: int,X1: int,X2: int,X3: int] :
      ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),bot_bot_fun_int_bool)) )
    <=> sP26(X2,X1,X3,X0) ),
    inference(definition_folding,[],[f2561,f3735]) ).

tff(f3735,plain,
    ! [X2: int,X1: int,X3: int,X0: int] :
      ( sP26(X2,X1,X3,X0)
    <=> ( ( ( X1 = X2 )
          & ( X0 = X3 ) )
        | ( ( X1 = X3 )
          & ( X0 = X2 ) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP26])]) ).

tff(f2561,plain,
    ! [X0: int,X1: int,X2: int,X3: int] :
      ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),bot_bot_fun_int_bool)) )
    <=> ( ( ( X1 = X2 )
          & ( X0 = X3 ) )
        | ( ( X1 = X3 )
          & ( X0 = X2 ) ) ) ),
    inference(rectify,[],[f599]) ).

tff(f599,axiom,
    ! [X5: int,X28: int,X29: int,X70: int] :
      ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X28),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X29),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X70),bot_bot_fun_int_bool)) )
    <=> ( ( ( X28 = X29 )
          & ( X5 = X70 ) )
        | ( ( X28 = X70 )
          & ( X5 = X29 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_598_doubleton__eq__iff) ).

tff(f24317,plain,
    spl250_1273,
    inference(avatar_split_clause,[],[f7300,f24315]) ).

tff(f24315,plain,
    ( spl250_1273
  <=> ! [X0: int,X3: int,X2: int,X1: int] :
        ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_i1948725293t_bool(fequal_int,X3)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_i1948725293t_bool(fequal_int,X1)) )
        | ~ sP26(X2,X1,X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1273])]) ).

tff(f7300,plain,
    ! [X2: int,X3: int,X0: int,X1: int] :
      ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_i1948725293t_bool(fequal_int,X3)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_i1948725293t_bool(fequal_int,X1)) )
      | ~ sP26(X2,X1,X3,X0) ),
    inference(forward_demodulation,[],[f7299,f6930]) ).

tff(f7299,plain,
    ! [X2: int,X3: int,X0: int,X1: int] :
      ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_i1948725293t_bool(fequal_int,X3)) )
      | ~ sP26(X2,X1,X3,X0) ),
    inference(forward_demodulation,[],[f6523,f6930]) ).

tff(f6523,plain,
    ! [X2: int,X3: int,X0: int,X1: int] :
      ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),bot_bot_fun_int_bool)) )
      | ~ sP26(X2,X1,X3,X0) ),
    inference(cnf_transformation,[],[f4525]) ).

tff(f24313,plain,
    spl250_1272,
    inference(avatar_split_clause,[],[f7060,f24311]) ).

tff(f24311,plain,
    ( spl250_1272
  <=> ! [X0: x_a,X1: fun_a_bool] :
        ( ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),collect_a(hAPP_a_fun_a_bool(fequal_a,X0))) = X1 )
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1272])]) ).

tff(f7060,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),collect_a(hAPP_a_fun_a_bool(fequal_a,X0))) = X1 )
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ),
    inference(forward_demodulation,[],[f5282,f4680]) ).

tff(f5282,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)) = X1 )
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ),
    inference(cnf_transformation,[],[f2902]) ).

tff(f2902,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)) = X1 )
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ),
    inference(ennf_transformation,[],[f1838]) ).

tff(f1838,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
     => ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)) = X1 ) ),
    inference(rectify,[],[f549]) ).

tff(f549,axiom,
    ! [X8: x_a,X2: fun_a_bool] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X2))
     => ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X2)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),bot_bot_fun_a_bool)) = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_548_Diff__insert__absorb) ).

tff(f24309,plain,
    spl250_1271,
    inference(avatar_split_clause,[],[f7052,f24307]) ).

tff(f24307,plain,
    ( spl250_1271
  <=> ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
        ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_n1699378549t_bool(fequal_nat,sK114(X0))))
        | hBOOL(hAPP_f54304608l_bool(X0,X1))
        | sP3(X0)
        | ( bot_bot_fun_nat_bool = X1 )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1271])]) ).

tff(f7052,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_n1699378549t_bool(fequal_nat,sK114(X0))))
      | hBOOL(hAPP_f54304608l_bool(X0,X1))
      | sP3(X0)
      | ( bot_bot_fun_nat_bool = X1 )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(forward_demodulation,[],[f5257,f6931]) ).

tff(f5257,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,X1))
      | sP3(X0)
      | ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK114(X0)),bot_bot_fun_nat_bool)))
      | ( bot_bot_fun_nat_bool = X1 )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f3970]) ).

tff(f3970,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,X1))
      | sP3(X0)
      | ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK114(X0)),bot_bot_fun_nat_bool)))
      | ( bot_bot_fun_nat_bool = X1 )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK114])],[f3691,f3969]) ).

tff(f3969,plain,
    ! [X0: fun_fu425979586l_bool] :
      ( ? [X2: nat] : ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)))
     => ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK114(X0)),bot_bot_fun_nat_bool))) ),
    introduced(choice_axiom,[]) ).

tff(f3691,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,X1))
      | sP3(X0)
      | ? [X2: nat] : ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)))
      | ( bot_bot_fun_nat_bool = X1 )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(definition_folding,[],[f2874,f3690]) ).

tff(f3690,plain,
    ! [X0: fun_fu425979586l_bool] :
      ( ? [X3: nat,X4: fun_nat_bool] :
          ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4)))
          & hBOOL(hAPP_f54304608l_bool(X0,X4))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
          & ( bot_bot_fun_nat_bool != X4 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4)) )
      | ~ sP3(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

tff(f2874,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,X1))
      | ? [X3: nat,X4: fun_nat_bool] :
          ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4)))
          & hBOOL(hAPP_f54304608l_bool(X0,X4))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
          & ( bot_bot_fun_nat_bool != X4 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4)) )
      | ? [X2: nat] : ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)))
      | ( bot_bot_fun_nat_bool = X1 )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(flattening,[],[f2873]) ).

tff(f2873,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,X1))
      | ? [X3: nat,X4: fun_nat_bool] :
          ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4)))
          & hBOOL(hAPP_f54304608l_bool(X0,X4))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
          & ( bot_bot_fun_nat_bool != X4 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4)) )
      | ? [X2: nat] : ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)))
      | ( bot_bot_fun_nat_bool = X1 )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(ennf_transformation,[],[f1822]) ).

tff(f1822,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
     => ( ( bot_bot_fun_nat_bool != X1 )
       => ( ! [X2: nat] : hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)))
         => ( ! [X3: nat,X4: fun_nat_bool] :
                ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
               => ( ( bot_bot_fun_nat_bool != X4 )
                 => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
                   => ( hBOOL(hAPP_f54304608l_bool(X0,X4))
                     => hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4))) ) ) ) )
           => hBOOL(hAPP_f54304608l_bool(X0,X1)) ) ) ) ),
    inference(rectify,[],[f782]) ).

tff(f782,axiom,
    ! [X10: fun_fu425979586l_bool,X4: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
     => ( ( bot_bot_fun_nat_bool != X4 )
       => ( ! [X27: nat] : hBOOL(hAPP_f54304608l_bool(X10,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X27),bot_bot_fun_nat_bool)))
         => ( ! [X27: nat,X76: fun_nat_bool] :
                ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X76))
               => ( ( bot_bot_fun_nat_bool != X76 )
                 => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X27),X76))
                   => ( hBOOL(hAPP_f54304608l_bool(X10,X76))
                     => hBOOL(hAPP_f54304608l_bool(X10,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X27),X76))) ) ) ) )
           => hBOOL(hAPP_f54304608l_bool(X10,X4)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_781_finite__ne__induct) ).

tff(f24305,plain,
    spl250_1270,
    inference(avatar_split_clause,[],[f7046,f24303]) ).

tff(f24303,plain,
    ( spl250_1270
  <=> ! [X0: nat,X1: fun_nat_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_n1699378549t_bool(fequal_nat,X0)))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1270])]) ).

tff(f7046,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_n1699378549t_bool(fequal_nat,X0)))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(forward_demodulation,[],[f5244,f6931]) ).

tff(f5244,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f2867]) ).

tff(f2867,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(ennf_transformation,[],[f1816]) ).

tff(f1816,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)))),hAPP_f22106695ol_nat(finite_card_nat,X1))) ),
    inference(rectify,[],[f653]) ).

tff(f653,axiom,
    ! [X8: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),bot_bot_fun_nat_bool)))),hAPP_f22106695ol_nat(finite_card_nat,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_card__Diff1__le) ).

tff(f24301,plain,
    ( spl250_1269
    | ~ spl250_97
    | ~ spl250_183
    | ~ spl250_1119 ),
    inference(avatar_split_clause,[],[f24169,f23384,f8279,f7800,f24298]) ).

tff(f24298,plain,
    ( spl250_1269
  <=> ( zero_zero_nat = sK62(one_one_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1269])]) ).

tff(f23384,plain,
    ( spl250_1119
  <=> ( one_one_nat = hAPP_nat_nat(suc,sK62(one_one_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1119])]) ).

tff(f24169,plain,
    ( ( zero_zero_nat = sK62(one_one_nat) )
    | ~ spl250_97
    | ~ spl250_183
    | ~ spl250_1119 ),
    inference(forward_demodulation,[],[f24133,f7801]) ).

tff(f24133,plain,
    ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,one_one_nat),one_one_nat) = sK62(one_one_nat) )
    | ~ spl250_183
    | ~ spl250_1119 ),
    inference(superposition,[],[f8280,f23386]) ).

tff(f23386,plain,
    ( ( one_one_nat = hAPP_nat_nat(suc,sK62(one_one_nat)) )
    | ~ spl250_1119 ),
    inference(avatar_component_clause,[],[f23384]) ).

tff(f24296,plain,
    spl250_1268,
    inference(avatar_split_clause,[],[f7040,f24294]) ).

tff(f24294,plain,
    ( spl250_1268
  <=> ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
        ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_i1948725293t_bool(fequal_int,sK107(X0))))
        | hBOOL(hAPP_f448129468l_bool(X0,X1))
        | sP2(X0)
        | ( bot_bot_fun_int_bool = X1 )
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1268])]) ).

tff(f7040,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_i1948725293t_bool(fequal_int,sK107(X0))))
      | hBOOL(hAPP_f448129468l_bool(X0,X1))
      | sP2(X0)
      | ( bot_bot_fun_int_bool = X1 )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(forward_demodulation,[],[f5214,f6930]) ).

tff(f5214,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,X1))
      | sP2(X0)
      | ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK107(X0)),bot_bot_fun_int_bool)))
      | ( bot_bot_fun_int_bool = X1 )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f3959]) ).

tff(f3959,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,X1))
      | sP2(X0)
      | ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK107(X0)),bot_bot_fun_int_bool)))
      | ( bot_bot_fun_int_bool = X1 )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK107])],[f3689,f3958]) ).

tff(f3958,plain,
    ! [X0: fun_fu819804446l_bool] :
      ( ? [X2: int] : ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)))
     => ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK107(X0)),bot_bot_fun_int_bool))) ),
    introduced(choice_axiom,[]) ).

tff(f3689,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,X1))
      | sP2(X0)
      | ? [X2: int] : ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)))
      | ( bot_bot_fun_int_bool = X1 )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(definition_folding,[],[f2834,f3688]) ).

tff(f3688,plain,
    ! [X0: fun_fu819804446l_bool] :
      ( ? [X3: int,X4: fun_int_bool] :
          ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4)))
          & hBOOL(hAPP_f448129468l_bool(X0,X4))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
          & ( bot_bot_fun_int_bool != X4 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4)) )
      | ~ sP2(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

tff(f2834,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,X1))
      | ? [X3: int,X4: fun_int_bool] :
          ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4)))
          & hBOOL(hAPP_f448129468l_bool(X0,X4))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
          & ( bot_bot_fun_int_bool != X4 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4)) )
      | ? [X2: int] : ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)))
      | ( bot_bot_fun_int_bool = X1 )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(flattening,[],[f2833]) ).

tff(f2833,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,X1))
      | ? [X3: int,X4: fun_int_bool] :
          ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4)))
          & hBOOL(hAPP_f448129468l_bool(X0,X4))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
          & ( bot_bot_fun_int_bool != X4 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4)) )
      | ? [X2: int] : ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)))
      | ( bot_bot_fun_int_bool = X1 )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(ennf_transformation,[],[f1793]) ).

tff(f1793,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
     => ( ( bot_bot_fun_int_bool != X1 )
       => ( ! [X2: int] : hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)))
         => ( ! [X3: int,X4: fun_int_bool] :
                ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
               => ( ( bot_bot_fun_int_bool != X4 )
                 => ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
                   => ( hBOOL(hAPP_f448129468l_bool(X0,X4))
                     => hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4))) ) ) ) )
           => hBOOL(hAPP_f448129468l_bool(X0,X1)) ) ) ) ),
    inference(rectify,[],[f781]) ).

tff(f781,axiom,
    ! [X10: fun_fu819804446l_bool,X4: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
     => ( ( bot_bot_fun_int_bool != X4 )
       => ( ! [X27: int] : hBOOL(hAPP_f448129468l_bool(X10,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X27),bot_bot_fun_int_bool)))
         => ( ! [X27: int,X76: fun_int_bool] :
                ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X76))
               => ( ( bot_bot_fun_int_bool != X76 )
                 => ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X27),X76))
                   => ( hBOOL(hAPP_f448129468l_bool(X10,X76))
                     => hBOOL(hAPP_f448129468l_bool(X10,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X27),X76))) ) ) ) )
           => hBOOL(hAPP_f448129468l_bool(X10,X4)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_780_finite__ne__induct) ).

tff(f24292,plain,
    spl250_1267,
    inference(avatar_split_clause,[],[f7034,f24290]) ).

tff(f24290,plain,
    ( spl250_1267
  <=> ! [X0: int,X1: fun_int_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_i1948725293t_bool(fequal_int,X0)))),hAPP_f957591787ol_nat(finite_card_int,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1267])]) ).

tff(f7034,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_i1948725293t_bool(fequal_int,X0)))),hAPP_f957591787ol_nat(finite_card_int,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(forward_demodulation,[],[f5201,f6930]) ).

tff(f5201,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)))),hAPP_f957591787ol_nat(finite_card_int,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f2827]) ).

tff(f2827,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)))),hAPP_f957591787ol_nat(finite_card_int,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(ennf_transformation,[],[f1787]) ).

tff(f1787,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)))),hAPP_f957591787ol_nat(finite_card_int,X1))) ),
    inference(rectify,[],[f652]) ).

tff(f652,axiom,
    ! [X8: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),bot_bot_fun_int_bool)))),hAPP_f957591787ol_nat(finite_card_int,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_651_card__Diff1__le) ).

tff(f24288,plain,
    spl250_1266,
    inference(avatar_split_clause,[],[f6683,f24286]) ).

tff(f24286,plain,
    ( spl250_1266
  <=> ! [X2: nat,X0: fun_int_bool,X1: nat] :
        ( sP24(X0,X1,X2)
        | ~ hBOOL(hAPP_int_bool(X0,pls))
        | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X2)),hAPP_nat_int(semiri1621563631at_int,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1266])]) ).

tff(f6683,plain,
    ! [X2: nat,X0: fun_int_bool,X1: nat] :
      ( sP24(X0,X1,X2)
      | ~ hBOOL(hAPP_int_bool(X0,pls))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X2)),hAPP_nat_int(semiri1621563631at_int,X1)))) ),
    inference(definition_unfolding,[],[f6397,f4550]) ).

tff(f6397,plain,
    ! [X2: nat,X0: fun_int_bool,X1: nat] :
      ( sP24(X0,X1,X2)
      | ~ hBOOL(hAPP_int_bool(X0,zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X2)),hAPP_nat_int(semiri1621563631at_int,X1)))) ),
    inference(cnf_transformation,[],[f4476]) ).

tff(f24283,plain,
    spl250_1265,
    inference(avatar_split_clause,[],[f6618,f24281]) ).

tff(f6618,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls)) ),
    inference(definition_unfolding,[],[f4837,f4687]) ).

tff(f4837,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),pls)) ),
    inference(cnf_transformation,[],[f3856]) ).

tff(f3856,plain,
    ! [X0: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),pls)) ) ),
    inference(nnf_transformation,[],[f1502]) ).

tff(f1502,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),pls))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(rectify,[],[f1198]) ).

tff(f1198,axiom,
    ! [X13: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X13)),pls))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),pls)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1197_rel__simps_I29_J) ).

tff(f24278,plain,
    spl250_1264,
    inference(avatar_split_clause,[],[f6617,f24276]) ).

tff(f6617,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(definition_unfolding,[],[f4838,f4687]) ).

tff(f4838,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X0)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(cnf_transformation,[],[f3856]) ).

tff(f24273,plain,
    spl250_1263,
    inference(avatar_split_clause,[],[f6616,f24271]) ).

tff(f6616,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls)) ),
    inference(definition_unfolding,[],[f4835,f4687]) ).

tff(f4835,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),pls)) ),
    inference(cnf_transformation,[],[f3855]) ).

tff(f3855,plain,
    ! [X0: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),pls)) ) ),
    inference(nnf_transformation,[],[f1501]) ).

tff(f1501,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),pls))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(rectify,[],[f1195]) ).

tff(f1195,axiom,
    ! [X13: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X13)),pls))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),pls)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1194_rel__simps_I12_J) ).

tff(f24268,plain,
    spl250_1262,
    inference(avatar_split_clause,[],[f6615,f24266]) ).

tff(f6615,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(definition_unfolding,[],[f4836,f4687]) ).

tff(f4836,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X0)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(cnf_transformation,[],[f3855]) ).

tff(f24263,plain,
    spl250_1261,
    inference(avatar_split_clause,[],[f6612,f24261]) ).

tff(f6612,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0))) ),
    inference(definition_unfolding,[],[f4831,f4687]) ).

tff(f4831,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X0))) ),
    inference(cnf_transformation,[],[f3853]) ).

tff(f3853,plain,
    ! [X0: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X0)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X0))) ) ),
    inference(nnf_transformation,[],[f1499]) ).

tff(f1499,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X0)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(rectify,[],[f1191]) ).

tff(f1191,axiom,
    ! [X13: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X13)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1190_rel__simps_I22_J) ).

tff(f24258,plain,
    spl250_1260,
    inference(avatar_split_clause,[],[f6611,f24256]) ).

tff(f6611,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(definition_unfolding,[],[f4832,f4687]) ).

tff(f4832,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f3853]) ).

tff(f24253,plain,
    spl250_1259,
    inference(avatar_split_clause,[],[f6610,f24251]) ).

tff(f6610,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0))) ),
    inference(definition_unfolding,[],[f4829,f4687]) ).

tff(f4829,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X0))) ),
    inference(cnf_transformation,[],[f3852]) ).

tff(f3852,plain,
    ! [X0: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X0)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X0))) ) ),
    inference(nnf_transformation,[],[f1498]) ).

tff(f1498,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X0)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(rectify,[],[f1199]) ).

tff(f1199,axiom,
    ! [X13: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X13)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1198_rel__simps_I5_J) ).

tff(f24249,plain,
    ( ~ spl250_1258
    | ~ spl250_25
    | ~ spl250_1119 ),
    inference(avatar_split_clause,[],[f24129,f23384,f7430,f24246]) ).

tff(f24246,plain,
    ( spl250_1258
  <=> ( one_one_nat = sK62(one_one_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1258])]) ).

tff(f24129,plain,
    ( ( one_one_nat != sK62(one_one_nat) )
    | ~ spl250_25
    | ~ spl250_1119 ),
    inference(superposition,[],[f7431,f23386]) ).

tff(f24243,plain,
    spl250_1257,
    inference(avatar_split_clause,[],[f6609,f24241]) ).

tff(f6609,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(definition_unfolding,[],[f4830,f4687]) ).

tff(f4830,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(cnf_transformation,[],[f3852]) ).

tff(f24239,plain,
    spl250_1256,
    inference(avatar_split_clause,[],[f6449,f24237]) ).

tff(f24237,plain,
    ( spl250_1256
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1256])]) ).

tff(f6449,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
    inference(cnf_transformation,[],[f4506]) ).

tff(f4506,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1))) ) ),
    inference(flattening,[],[f4505]) ).

tff(f4505,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1))) ) ),
    inference(nnf_transformation,[],[f3595]) ).

tff(f3595,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ) ),
    inference(ennf_transformation,[],[f2516]) ).

tff(f2516,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2)) ) ),
    inference(rectify,[],[f1014]) ).

tff(f1014,axiom,
    ! [X22: nat,X13: nat,X14: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X22),X13)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),X13)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X13))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X14)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1013_mult__le__cancel2) ).

tff(f24235,plain,
    spl250_1255,
    inference(avatar_split_clause,[],[f6446,f24233]) ).

tff(f24233,plain,
    ( spl250_1255
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1255])]) ).

tff(f6446,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f4504]) ).

tff(f4504,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2))) ) ),
    inference(flattening,[],[f4503]) ).

tff(f4503,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2))) ) ),
    inference(nnf_transformation,[],[f3594]) ).

tff(f3594,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
    inference(ennf_transformation,[],[f2515]) ).

tff(f2515,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
    inference(rectify,[],[f1013]) ).

tff(f1013,axiom,
    ! [X13: nat,X22: nat,X14: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X13),X22)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X13),X14)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X13))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X14)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1012_mult__le__cancel1) ).

tff(f24231,plain,
    spl250_1254,
    inference(avatar_split_clause,[],[f6444,f24229]) ).

tff(f24229,plain,
    ( spl250_1254
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1254])]) ).

tff(f6444,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f4502]) ).

tff(f4502,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2))) ) ),
    inference(nnf_transformation,[],[f2514]) ).

tff(f2514,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(rectify,[],[f879]) ).

tff(f879,axiom,
    ! [X13: nat,X22: nat,X14: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X13),X22)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X13),X14)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X14)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_878_nat__add__left__cancel__less) ).

tff(f24227,plain,
    spl250_1253,
    inference(avatar_split_clause,[],[f6443,f24225]) ).

tff(f24225,plain,
    ( spl250_1253
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1253])]) ).

tff(f6443,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2))) ),
    inference(cnf_transformation,[],[f4502]) ).

tff(f24223,plain,
    spl250_1252,
    inference(avatar_split_clause,[],[f6441,f24221]) ).

tff(f24221,plain,
    ( spl250_1252
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1252])]) ).

tff(f6441,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1))) ),
    inference(cnf_transformation,[],[f4501]) ).

tff(f4501,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1))) ) ),
    inference(flattening,[],[f4500]) ).

tff(f4500,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1))) ) ),
    inference(nnf_transformation,[],[f2513]) ).

tff(f2513,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ) ),
    inference(rectify,[],[f1001]) ).

tff(f1001,axiom,
    ! [X22: nat,X13: nat,X14: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X22),X13)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),X13)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X14))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X13)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1000_mult__less__cancel2) ).

tff(f24219,plain,
    spl250_1251,
    inference(avatar_split_clause,[],[f6440,f24217]) ).

tff(f24217,plain,
    ( spl250_1251
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1251])]) ).

tff(f6440,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1))) ),
    inference(cnf_transformation,[],[f4501]) ).

tff(f24215,plain,
    spl250_1250,
    inference(avatar_split_clause,[],[f6438,f24213]) ).

tff(f24213,plain,
    ( spl250_1250
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1250])]) ).

tff(f6438,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2))) ),
    inference(cnf_transformation,[],[f4499]) ).

tff(f4499,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2))) ) ),
    inference(flattening,[],[f4498]) ).

tff(f4498,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2))) ) ),
    inference(nnf_transformation,[],[f2512]) ).

tff(f2512,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
    inference(rectify,[],[f1002]) ).

tff(f1002,axiom,
    ! [X13: nat,X22: nat,X14: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X13),X22)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X13),X14)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X14))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X13)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1001_mult__less__cancel1) ).

tff(f24211,plain,
    spl250_1249,
    inference(avatar_split_clause,[],[f6437,f24209]) ).

tff(f24209,plain,
    ( spl250_1249
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1249])]) ).

tff(f6437,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2))) ),
    inference(cnf_transformation,[],[f4499]) ).

tff(f24207,plain,
    spl250_1248,
    inference(avatar_split_clause,[],[f6432,f24205]) ).

tff(f24205,plain,
    ( spl250_1248
  <=> ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1248])]) ).

tff(f6432,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2))) ),
    inference(cnf_transformation,[],[f4495]) ).

tff(f4495,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2))) )
      & ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))) ) ),
    inference(nnf_transformation,[],[f2509]) ).

tff(f2509,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))))
    <=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2))) ),
    inference(rectify,[],[f657]) ).

tff(f657,axiom,
    ! [X2: fun_nat_bool,X5: nat,X7: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5),X7))))
    <=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_656_finite__Diff__insert) ).

tff(f24127,plain,
    spl250_1247,
    inference(avatar_split_clause,[],[f6431,f24125]) ).

tff(f24125,plain,
    ( spl250_1247
  <=> ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1247])]) ).

tff(f6431,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))) ),
    inference(cnf_transformation,[],[f4495]) ).

tff(f24123,plain,
    spl250_1246,
    inference(avatar_split_clause,[],[f6430,f24121]) ).

tff(f24121,plain,
    ( spl250_1246
  <=> ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1246])]) ).

tff(f6430,plain,
    ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2))) ),
    inference(cnf_transformation,[],[f4494]) ).

tff(f4494,plain,
    ! [X0: fun_int_bool,X1: int,X2: fun_int_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2))) )
      & ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))) ) ),
    inference(nnf_transformation,[],[f2508]) ).

tff(f2508,plain,
    ! [X0: fun_int_bool,X1: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))))
    <=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2))) ),
    inference(rectify,[],[f656]) ).

tff(f656,axiom,
    ! [X2: fun_int_bool,X5: int,X7: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5),X7))))
    <=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_655_finite__Diff__insert) ).

tff(f24119,plain,
    spl250_1245,
    inference(avatar_split_clause,[],[f6429,f24117]) ).

tff(f24117,plain,
    ( spl250_1245
  <=> ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1245])]) ).

tff(f6429,plain,
    ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))) ),
    inference(cnf_transformation,[],[f4494]) ).

tff(f24115,plain,
    spl250_1244,
    inference(avatar_split_clause,[],[f6428,f24113]) ).

tff(f24113,plain,
    ( spl250_1244
  <=> ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1244])]) ).

tff(f6428,plain,
    ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2))) ),
    inference(cnf_transformation,[],[f4493]) ).

tff(f4493,plain,
    ! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2))) )
      & ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))) ) ),
    inference(nnf_transformation,[],[f2507]) ).

tff(f2507,plain,
    ! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))))
    <=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2))) ),
    inference(rectify,[],[f655]) ).

tff(f655,axiom,
    ! [X2: fun_a_bool,X5: x_a,X7: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),X7))))
    <=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_654_finite__Diff__insert) ).

tff(f24111,plain,
    spl250_1243,
    inference(avatar_split_clause,[],[f6427,f24109]) ).

tff(f24109,plain,
    ( spl250_1243
  <=> ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1243])]) ).

tff(f6427,plain,
    ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))) ),
    inference(cnf_transformation,[],[f4493]) ).

tff(f24107,plain,
    spl250_1242,
    inference(avatar_split_clause,[],[f6426,f24105]) ).

tff(f24105,plain,
    ( spl250_1242
  <=> ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1242])]) ).

tff(f6426,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2))) ),
    inference(cnf_transformation,[],[f4492]) ).

tff(f4492,plain,
    ! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2))) )
      & ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))) ) ),
    inference(nnf_transformation,[],[f2506]) ).

tff(f2506,plain,
    ! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))))
    <=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2))) ),
    inference(rectify,[],[f658]) ).

tff(f658,axiom,
    ! [X2: fun_pname_bool,X5: pname,X7: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5),X7))))
    <=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_657_finite__Diff__insert) ).

tff(f24103,plain,
    spl250_1241,
    inference(avatar_split_clause,[],[f6425,f24101]) ).

tff(f24101,plain,
    ( spl250_1241
  <=> ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1241])]) ).

tff(f6425,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))) ),
    inference(cnf_transformation,[],[f4492]) ).

tff(f24099,plain,
    spl250_1240,
    inference(avatar_split_clause,[],[f6403,f24097]) ).

tff(f24097,plain,
    ( spl250_1240
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1240])]) ).

tff(f6403,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1))) ),
    inference(cnf_transformation,[],[f4479]) ).

tff(f4479,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2)) ) ),
    inference(nnf_transformation,[],[f2496]) ).

tff(f2496,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1))) ),
    inference(rectify,[],[f840]) ).

tff(f840,axiom,
    ! [X117: nat,X13: nat,X30: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X117),X13)),X30))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X117),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X30),X13))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_839_le__diff__conv) ).

tff(f24095,plain,
    spl250_1239,
    inference(avatar_split_clause,[],[f6402,f24093]) ).

tff(f24093,plain,
    ( spl250_1239
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1239])]) ).

tff(f6402,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f4479]) ).

tff(f24091,plain,
    spl250_1238,
    inference(avatar_split_clause,[],[f6401,f24089]) ).

tff(f24089,plain,
    ( spl250_1238
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1238])]) ).

tff(f6401,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)),X1)) ),
    inference(cnf_transformation,[],[f4478]) ).

tff(f4478,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)),X1)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ) ),
    inference(nnf_transformation,[],[f2495]) ).

tff(f2495,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)),X1)) ),
    inference(rectify,[],[f910]) ).

tff(f910,axiom,
    ! [X30: nat,X117: nat,X13: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X30),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X117),X13)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X30),X13)),X117)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_909_less__diff__conv) ).

tff(f24079,plain,
    spl250_1237,
    inference(avatar_split_clause,[],[f6400,f24077]) ).

tff(f24077,plain,
    ( spl250_1237
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1237])]) ).

tff(f6400,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ),
    inference(cnf_transformation,[],[f4478]) ).

tff(f24075,plain,
    spl250_1236,
    inference(avatar_split_clause,[],[f6316,f24073]) ).

tff(f24073,plain,
    ( spl250_1236
  <=> ! [X2: nat,X0: fun_nat_bool,X1: nat] :
        ( sP19(X0,X1,X2)
        | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK247(X0,X1,X2)) = X1 )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1236])]) ).

tff(f6316,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: nat] :
      ( sP19(X0,X1,X2)
      | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK247(X0,X1,X2)) = X1 )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f4431]) ).

tff(f4431,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( ( sP19(X0,X1,X2)
        | ( ~ hBOOL(hAPP_nat_bool(X0,sK247(X0,X1,X2)))
          & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK247(X0,X1,X2)) = X1 ) )
        | ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
      & ( ( ! [X4: nat] :
              ( hBOOL(hAPP_nat_bool(X0,X4))
              | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4) != X1 ) )
          & ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
        | ~ sP19(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK247])],[f4429,f4430]) ).

tff(f4430,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( ? [X3: nat] :
          ( ~ hBOOL(hAPP_nat_bool(X0,X3))
          & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) = X1 ) )
     => ( ~ hBOOL(hAPP_nat_bool(X0,sK247(X0,X1,X2)))
        & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK247(X0,X1,X2)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f4429,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( ( sP19(X0,X1,X2)
        | ? [X3: nat] :
            ( ~ hBOOL(hAPP_nat_bool(X0,X3))
            & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) = X1 ) )
        | ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
      & ( ( ! [X4: nat] :
              ( hBOOL(hAPP_nat_bool(X0,X4))
              | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4) != X1 ) )
          & ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
        | ~ sP19(X0,X1,X2) ) ),
    inference(rectify,[],[f4428]) ).

tff(f4428,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( ( sP19(X0,X1,X2)
        | ? [X3: nat] :
            ( ~ hBOOL(hAPP_nat_bool(X0,X3))
            & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) = X1 ) )
        | ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
      & ( ( ! [X3: nat] :
              ( hBOOL(hAPP_nat_bool(X0,X3))
              | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) != X1 ) )
          & ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
        | ~ sP19(X0,X1,X2) ) ),
    inference(flattening,[],[f4427]) ).

tff(f4427,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( ( sP19(X0,X1,X2)
        | ? [X3: nat] :
            ( ~ hBOOL(hAPP_nat_bool(X0,X3))
            & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) = X1 ) )
        | ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
      & ( ( ! [X3: nat] :
              ( hBOOL(hAPP_nat_bool(X0,X3))
              | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) != X1 ) )
          & ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
        | ~ sP19(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f3721]) ).

tff(f3721,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( sP19(X0,X1,X2)
    <=> ( ! [X3: nat] :
            ( hBOOL(hAPP_nat_bool(X0,X3))
            | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) != X1 ) )
        & ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP19])]) ).

tff(f24071,plain,
    spl250_1235,
    inference(avatar_split_clause,[],[f6308,f24069]) ).

tff(f24069,plain,
    ( spl250_1235
  <=> ! [X2: nat,X0: fun_nat_bool,X1: nat] :
        ( sP18(X0,X1,X2)
        | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK246(X0,X1,X2)) = X1 )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1235])]) ).

tff(f6308,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: nat] :
      ( sP18(X0,X1,X2)
      | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK246(X0,X1,X2)) = X1 )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f4425]) ).

tff(f4425,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( ( sP18(X0,X1,X2)
        | ( ~ hBOOL(hAPP_nat_bool(X0,sK246(X0,X1,X2)))
          & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK246(X0,X1,X2)) = X1 ) )
        | ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
      & ( ( ! [X4: nat] :
              ( hBOOL(hAPP_nat_bool(X0,X4))
              | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4) != X1 ) )
          & ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
        | ~ sP18(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK246])],[f4423,f4424]) ).

tff(f4424,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( ? [X3: nat] :
          ( ~ hBOOL(hAPP_nat_bool(X0,X3))
          & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) = X1 ) )
     => ( ~ hBOOL(hAPP_nat_bool(X0,sK246(X0,X1,X2)))
        & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK246(X0,X1,X2)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f4423,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( ( sP18(X0,X1,X2)
        | ? [X3: nat] :
            ( ~ hBOOL(hAPP_nat_bool(X0,X3))
            & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) = X1 ) )
        | ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
      & ( ( ! [X4: nat] :
              ( hBOOL(hAPP_nat_bool(X0,X4))
              | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4) != X1 ) )
          & ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
        | ~ sP18(X0,X1,X2) ) ),
    inference(rectify,[],[f4422]) ).

tff(f4422,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( ( sP18(X0,X1,X2)
        | ? [X3: nat] :
            ( ~ hBOOL(hAPP_nat_bool(X0,X3))
            & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) = X1 ) )
        | ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
      & ( ( ! [X3: nat] :
              ( hBOOL(hAPP_nat_bool(X0,X3))
              | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) != X1 ) )
          & ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
        | ~ sP18(X0,X1,X2) ) ),
    inference(flattening,[],[f4421]) ).

tff(f4421,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( ( sP18(X0,X1,X2)
        | ? [X3: nat] :
            ( ~ hBOOL(hAPP_nat_bool(X0,X3))
            & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) = X1 ) )
        | ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
      & ( ( ! [X3: nat] :
              ( hBOOL(hAPP_nat_bool(X0,X3))
              | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) != X1 ) )
          & ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
        | ~ sP18(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f3719]) ).

tff(f3719,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( sP18(X0,X1,X2)
    <=> ( ! [X3: nat] :
            ( hBOOL(hAPP_nat_bool(X0,X3))
            | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) != X1 ) )
        & ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).

tff(f24067,plain,
    spl250_1234,
    inference(avatar_split_clause,[],[f6239,f24065]) ).

tff(f24065,plain,
    ( spl250_1234
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1234])]) ).

tff(f6239,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1))) ),
    inference(cnf_transformation,[],[f3555]) ).

tff(f3555,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1))) ),
    inference(ennf_transformation,[],[f2449]) ).

tff(f2449,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2)) ),
    inference(rectify,[],[f815]) ).

tff(f815,axiom,
    ! [X106: nat,X107: nat,X108: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X106),X107)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X108),X107)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X106),X108)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_814_add__le__imp__le__right) ).

tff(f24063,plain,
    spl250_1233,
    inference(avatar_split_clause,[],[f6238,f24061]) ).

tff(f24061,plain,
    ( spl250_1233
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1233])]) ).

tff(f6238,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2))) ),
    inference(cnf_transformation,[],[f3554]) ).

tff(f3554,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2))) ),
    inference(ennf_transformation,[],[f2448]) ).

tff(f2448,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(rectify,[],[f817]) ).

tff(f817,axiom,
    ! [X109: nat,X110: nat,X111: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X109),X110)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X109),X111)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X110),X111)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_816_add__le__imp__le__left) ).

tff(f24059,plain,
    spl250_1232,
    inference(avatar_split_clause,[],[f6237,f24057]) ).

tff(f24057,plain,
    ( spl250_1232
  <=> ! [X2: int,X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X2))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1232])]) ).

tff(f6237,plain,
    ! [X2: int,X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X1))) ),
    inference(cnf_transformation,[],[f3553]) ).

tff(f3553,plain,
    ! [X0: int,X1: int,X2: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X1))) ),
    inference(ennf_transformation,[],[f2447]) ).

tff(f2447,plain,
    ! [X0: int,X1: int,X2: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X1)))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X2)) ),
    inference(rectify,[],[f814]) ).

tff(f814,axiom,
    ! [X106: int,X107: int,X108: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X106),X107)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X108),X107)))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X106),X108)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_813_add__le__imp__le__right) ).

tff(f24055,plain,
    spl250_1231,
    inference(avatar_split_clause,[],[f6236,f24053]) ).

tff(f24053,plain,
    ( spl250_1231
  <=> ! [X2: int,X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1231])]) ).

tff(f6236,plain,
    ! [X2: int,X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2))) ),
    inference(cnf_transformation,[],[f3552]) ).

tff(f3552,plain,
    ! [X0: int,X1: int,X2: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2))) ),
    inference(ennf_transformation,[],[f2446]) ).

tff(f2446,plain,
    ! [X0: int,X1: int,X2: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2)))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
    inference(rectify,[],[f816]) ).

tff(f816,axiom,
    ! [X109: int,X110: int,X111: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X109),X110)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X109),X111)))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X110),X111)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_815_add__le__imp__le__left) ).

tff(f24051,plain,
    spl250_1230,
    inference(avatar_split_clause,[],[f6180,f24049]) ).

tff(f24049,plain,
    ( spl250_1230
  <=> ! [X2: nat,X0: fun_nat_bool,X1: nat] :
        ( hBOOL(hAPP_nat_bool(X0,X1))
        | ~ hBOOL(hAPP_nat_bool(X0,sK222(X0,X2)))
        | ~ hBOOL(hAPP_nat_bool(X0,X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1230])]) ).

tff(f6180,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_nat_bool(X0,X1))
      | ~ hBOOL(hAPP_nat_bool(X0,sK222(X0,X2)))
      | ~ hBOOL(hAPP_nat_bool(X0,X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f4351]) ).

tff(f24047,plain,
    spl250_1229,
    inference(avatar_split_clause,[],[f6168,f24045]) ).

tff(f24045,plain,
    ( spl250_1229
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1229])]) ).

tff(f6168,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f3478]) ).

tff(f3478,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f2392]) ).

tff(f2392,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2))) ),
    inference(rectify,[],[f811]) ).

tff(f811,axiom,
    ! [X99: nat,X100: nat,X101: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X100),X101))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X99),X100)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X99),X101))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_810_add__left__mono) ).

tff(f24043,plain,
    spl250_1228,
    inference(avatar_split_clause,[],[f6166,f24041]) ).

tff(f24041,plain,
    ( spl250_1228
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1228])]) ).

tff(f6166,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f3476]) ).

tff(f3476,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f2390]) ).

tff(f2390,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0))) ),
    inference(rectify,[],[f809]) ).

tff(f809,axiom,
    ! [X96: nat,X97: nat,X98: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X97),X98))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X97),X96)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X98),X96))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_808_add__right__mono) ).

tff(f24034,plain,
    spl250_1227,
    inference(avatar_split_clause,[],[f6165,f24032]) ).

tff(f24032,plain,
    ( spl250_1227
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1227])]) ).

tff(f6165,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f3475]) ).

tff(f3475,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f2389]) ).

tff(f2389,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0))) ),
    inference(rectify,[],[f178]) ).

tff(f178,axiom,
    ! [X23: nat,X12: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X11))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X12),X23)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X11),X23))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_diff__le__mono) ).

tff(f24030,plain,
    spl250_1226,
    inference(avatar_split_clause,[],[f6164,f24028]) ).

tff(f24028,plain,
    ( spl250_1226
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1226])]) ).

tff(f6164,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f3474]) ).

tff(f3474,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f2388]) ).

tff(f2388,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1))) ),
    inference(rectify,[],[f179]) ).

tff(f179,axiom,
    ! [X23: nat,X12: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X11))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X23),X11)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X23),X12))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_diff__le__mono2) ).

tff(f24026,plain,
    spl250_1225,
    inference(avatar_split_clause,[],[f6163,f24024]) ).

tff(f24024,plain,
    ( spl250_1225
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X0)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1225])]) ).

tff(f6163,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f3473]) ).

tff(f3473,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f2387]) ).

tff(f2387,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X0))) ),
    inference(rectify,[],[f989]) ).

tff(f989,axiom,
    ! [X19: nat,X20: nat,X21: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X20),X21))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X20),X19)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X21),X19))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_988_mult__le__mono1) ).

tff(f24022,plain,
    spl250_1224,
    inference(avatar_split_clause,[],[f6162,f24020]) ).

tff(f24020,plain,
    ( spl250_1224
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1224])]) ).

tff(f6162,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f3472]) ).

tff(f3472,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f2386]) ).

tff(f2386,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2))) ),
    inference(rectify,[],[f988]) ).

tff(f988,axiom,
    ! [X19: nat,X20: nat,X21: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X20),X21))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X19),X20)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X19),X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_987_mult__le__mono2) ).

tff(f24018,plain,
    spl250_1223,
    inference(avatar_split_clause,[],[f6161,f24016]) ).

tff(f24016,plain,
    ( spl250_1223
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)),X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1223])]) ).

tff(f6161,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f3471]) ).

tff(f3471,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f2385]) ).

tff(f2385,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)),X1))) ),
    inference(rectify,[],[f841]) ).

tff(f841,axiom,
    ! [X12: nat,X19: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X19),X11))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X11),X12)),X19))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_840_le__add__diff) ).

tff(f24014,plain,
    spl250_1222,
    inference(avatar_split_clause,[],[f6154,f24012]) ).

tff(f24012,plain,
    ( spl250_1222
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X0))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1222])]) ).

tff(f6154,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f3462]) ).

tff(f3462,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(flattening,[],[f3461]) ).

tff(f3461,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f2378]) ).

tff(f2378,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X0)) ) ),
    inference(rectify,[],[f873]) ).

tff(f873,axiom,
    ! [X19: nat,X20: nat,X21: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X20),X21))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X21),X19))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X20)),X19)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_872_less__trans__Suc) ).

tff(f24010,plain,
    spl250_1221,
    inference(avatar_split_clause,[],[f6151,f24008]) ).

tff(f24008,plain,
    ( spl250_1221
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1221])]) ).

tff(f6151,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f3456]) ).

tff(f3456,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f2375]) ).

tff(f2375,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0))) ),
    inference(rectify,[],[f882]) ).

tff(f882,axiom,
    ! [X19: nat,X20: nat,X21: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X20),X21))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X20),X19)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X21),X19))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_881_add__less__mono1) ).

tff(f24006,plain,
    spl250_1220,
    inference(avatar_split_clause,[],[f6141,f24004]) ).

tff(f24004,plain,
    ( spl250_1220
  <=> ! [X2: int,X0: fun_int_bool,X1: int] :
        ( hBOOL(hAPP_int_bool(X0,X2))
        | hBOOL(hAPP_int_bool(X0,sK221(X0,X1)))
        | ~ hBOOL(hAPP_int_bool(X0,X1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1220])]) ).

tff(f6141,plain,
    ! [X2: int,X0: fun_int_bool,X1: int] :
      ( hBOOL(hAPP_int_bool(X0,X2))
      | hBOOL(hAPP_int_bool(X0,sK221(X0,X1)))
      | ~ hBOOL(hAPP_int_bool(X0,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
    inference(cnf_transformation,[],[f4349]) ).

tff(f24002,plain,
    spl250_1219,
    inference(avatar_split_clause,[],[f6138,f24000]) ).

tff(f24000,plain,
    ( spl250_1219
  <=> ! [X2: int,X0: fun_int_bool,X1: int] :
        ( hBOOL(hAPP_int_bool(X0,X1))
        | hBOOL(hAPP_int_bool(X0,sK220(X0,X2)))
        | ~ hBOOL(hAPP_int_bool(X0,X2))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1219])]) ).

tff(f6138,plain,
    ! [X2: int,X0: fun_int_bool,X1: int] :
      ( hBOOL(hAPP_int_bool(X0,X1))
      | hBOOL(hAPP_int_bool(X0,sK220(X0,X2)))
      | ~ hBOOL(hAPP_int_bool(X0,X2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
    inference(cnf_transformation,[],[f4347]) ).

tff(f23998,plain,
    spl250_1218,
    inference(avatar_split_clause,[],[f6134,f23996]) ).

tff(f23996,plain,
    ( spl250_1218
  <=> ! [X2: int,X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X0)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1218])]) ).

tff(f6134,plain,
    ! [X2: int,X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
    inference(cnf_transformation,[],[f3436]) ).

tff(f3436,plain,
    ! [X0: int,X1: int,X2: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
    inference(ennf_transformation,[],[f2362]) ).

tff(f2362,plain,
    ! [X0: int,X1: int,X2: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X0))) ),
    inference(rectify,[],[f808]) ).

tff(f808,axiom,
    ! [X96: int,X97: int,X98: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X97),X98))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X97),X96)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X98),X96))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_807_add__right__mono) ).

tff(f23994,plain,
    ( spl250_1217
    | spl250_18
    | ~ spl250_545 ),
    inference(avatar_split_clause,[],[f15677,f10955,f7396,f23991]) ).

tff(f23991,plain,
    ( spl250_1217
  <=> ( bot_bot_fun_nat_bool = cOMBK_bool_nat(hAPP_int_bool(nat_neg,pls)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1217])]) ).

tff(f7396,plain,
    ( spl250_18
  <=> hBOOL(hAPP_int_bool(nat_neg,pls)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_18])]) ).

tff(f10955,plain,
    ( spl250_545
  <=> ! [X0: bool] :
        ( hBOOL(X0)
        | ( bot_bot_fun_nat_bool = cOMBK_bool_nat(X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_545])]) ).

tff(f15677,plain,
    ( ( bot_bot_fun_nat_bool = cOMBK_bool_nat(hAPP_int_bool(nat_neg,pls)) )
    | spl250_18
    | ~ spl250_545 ),
    inference(resolution,[],[f10956,f7398]) ).

tff(f7398,plain,
    ( ~ hBOOL(hAPP_int_bool(nat_neg,pls))
    | spl250_18 ),
    inference(avatar_component_clause,[],[f7396]) ).

tff(f10956,plain,
    ( ! [X0: bool] :
        ( hBOOL(X0)
        | ( bot_bot_fun_nat_bool = cOMBK_bool_nat(X0) ) )
    | ~ spl250_545 ),
    inference(avatar_component_clause,[],[f10955]) ).

tff(f23989,plain,
    spl250_1216,
    inference(avatar_split_clause,[],[f6132,f23987]) ).

tff(f23987,plain,
    ( spl250_1216
  <=> ! [X2: int,X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1216])]) ).

tff(f6132,plain,
    ! [X2: int,X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
    inference(cnf_transformation,[],[f3434]) ).

tff(f3434,plain,
    ! [X0: int,X1: int,X2: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
    inference(ennf_transformation,[],[f2360]) ).

tff(f2360,plain,
    ! [X0: int,X1: int,X2: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2))) ),
    inference(rectify,[],[f1041]) ).

tff(f1041,axiom,
    ! [X19: int,X20: int,X21: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X20),X21))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X19),X20)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X19),X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1040_zadd__left__mono) ).

tff(f23985,plain,
    spl250_1215,
    inference(avatar_split_clause,[],[f6123,f23983]) ).

tff(f23983,plain,
    ( spl250_1215
  <=> ! [X2: int,X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X0)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1215])]) ).

tff(f6123,plain,
    ! [X2: int,X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
    inference(cnf_transformation,[],[f3425]) ).

tff(f3425,plain,
    ! [X0: int,X1: int,X2: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
    inference(ennf_transformation,[],[f2355]) ).

tff(f2355,plain,
    ! [X0: int,X1: int,X2: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X0))) ),
    inference(rectify,[],[f1052]) ).

tff(f1052,axiom,
    ! [X19: int,X20: int,X21: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X20),X21))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X20),X19)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X21),X19))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1051_zadd__strict__right__mono) ).

tff(f23981,plain,
    spl250_1214,
    inference(avatar_split_clause,[],[f6113,f23979]) ).

tff(f23979,plain,
    ( spl250_1214
  <=> ! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1214])]) ).

tff(f6113,plain,
    ! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
    inference(cnf_transformation,[],[f3406]) ).

tff(f3406,plain,
    ! [X0: nat,X1: fun_nat_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
    inference(ennf_transformation,[],[f2345]) ).

tff(f2345,plain,
    ! [X0: nat,X1: fun_nat_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2))) ),
    inference(rectify,[],[f467]) ).

tff(f467,axiom,
    ! [X5: nat,X64: fun_nat_bool,X67: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X64),X67))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5),X64)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5),X67))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_466_insert__mono) ).

tff(f23977,plain,
    spl250_1213,
    inference(avatar_split_clause,[],[f6092,f23975]) ).

tff(f23975,plain,
    ( spl250_1213
  <=> ! [X2: fun_int_bool,X0: int,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2)))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1213])]) ).

tff(f6092,plain,
    ! [X2: fun_int_bool,X0: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ),
    inference(cnf_transformation,[],[f3374]) ).

tff(f3374,plain,
    ! [X0: int,X1: fun_int_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ),
    inference(ennf_transformation,[],[f2324]) ).

tff(f2324,plain,
    ! [X0: int,X1: fun_int_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
     => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2))) ),
    inference(rectify,[],[f466]) ).

tff(f466,axiom,
    ! [X5: int,X64: fun_int_bool,X67: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X64),X67))
     => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5),X64)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5),X67))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_465_insert__mono) ).

tff(f23973,plain,
    spl250_1212,
    inference(avatar_split_clause,[],[f6075,f23971]) ).

tff(f23971,plain,
    ( spl250_1212
  <=> ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1212])]) ).

tff(f6075,plain,
    ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
    inference(cnf_transformation,[],[f3346]) ).

tff(f3346,plain,
    ! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
    inference(ennf_transformation,[],[f2307]) ).

tff(f2307,plain,
    ! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2))) ),
    inference(rectify,[],[f465]) ).

tff(f465,axiom,
    ! [X5: x_a,X64: fun_a_bool,X67: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X64),X67))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),X64)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),X67))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_insert__mono) ).

tff(f23969,plain,
    spl250_1211,
    inference(avatar_split_clause,[],[f6051,f23967]) ).

tff(f23967,plain,
    ( spl250_1211
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( X0 = X1 )
        | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X0) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1211])]) ).

tff(f6051,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X0) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
    inference(cnf_transformation,[],[f4339]) ).

tff(f4339,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1) )
          | ( X0 != X1 ) )
        & ( ( X0 = X1 )
          | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X0) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1) ) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
    inference(nnf_transformation,[],[f3318]) ).

tff(f3318,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1) )
      <=> ( X0 = X1 ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
    inference(ennf_transformation,[],[f2286]) ).

tff(f2286,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
     => ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1) )
      <=> ( X0 = X1 ) ) ),
    inference(rectify,[],[f1060]) ).

tff(f1060,axiom,
    ! [X22: nat,X14: nat,X13: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X13))
     => ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X13),X22) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X13),X14) )
      <=> ( X14 = X22 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1059_nat__mult__eq__cancel1) ).

tff(f23965,plain,
    spl250_1210,
    inference(avatar_split_clause,[],[f6001,f23963]) ).

tff(f23963,plain,
    ( spl250_1210
  <=> ! [X2: fun_nat_bool,X0: fun_a_nat,X1: fun_a_bool] :
        ( ( image_a_nat(X0,sK196(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_a_nat(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1210])]) ).

tff(f6001,plain,
    ! [X2: fun_nat_bool,X0: fun_a_nat,X1: fun_a_bool] :
      ( ( image_a_nat(X0,sK196(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_a_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f4287]) ).

tff(f23961,plain,
    spl250_1209,
    inference(avatar_split_clause,[],[f5998,f23959]) ).

tff(f23959,plain,
    ( spl250_1209
  <=> ! [X2: fun_nat_bool,X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool] :
        ( ( image_1551609309ol_nat(X0,sK195(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1551609309ol_nat(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1209])]) ).

tff(f5998,plain,
    ! [X2: fun_nat_bool,X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool] :
      ( ( image_1551609309ol_nat(X0,sK195(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1551609309ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f4285]) ).

tff(f23957,plain,
    spl250_1208,
    inference(avatar_split_clause,[],[f5995,f23955]) ).

tff(f23955,plain,
    ( spl250_1208
  <=> ! [X2: fun_nat_bool,X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool] :
        ( ( image_496248727ol_nat(X0,sK194(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_496248727ol_nat(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1208])]) ).

tff(f5995,plain,
    ! [X2: fun_nat_bool,X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool] :
      ( ( image_496248727ol_nat(X0,sK194(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_496248727ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f4283]) ).

tff(f23953,plain,
    spl250_1207,
    inference(avatar_split_clause,[],[f5992,f23951]) ).

tff(f23951,plain,
    ( spl250_1207
  <=> ! [X2: fun_nat_bool,X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool] :
        ( ( image_fun_a_bool_nat(X0,sK193(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_fun_a_bool_nat(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1207])]) ).

tff(f5992,plain,
    ! [X2: fun_nat_bool,X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool] :
      ( ( image_fun_a_bool_nat(X0,sK193(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_fun_a_bool_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f4281]) ).

tff(f23949,plain,
    ( spl250_1206
    | spl250_9
    | ~ spl250_545 ),
    inference(avatar_split_clause,[],[f15676,f10955,f7354,f23946]) ).

tff(f23946,plain,
    ( spl250_1206
  <=> ( bot_bot_fun_nat_bool = cOMBK_bool_nat(hAPP_int_bool(nat_neg,one_one_int)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1206])]) ).

tff(f7354,plain,
    ( spl250_9
  <=> hBOOL(hAPP_int_bool(nat_neg,one_one_int)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_9])]) ).

tff(f15676,plain,
    ( ( bot_bot_fun_nat_bool = cOMBK_bool_nat(hAPP_int_bool(nat_neg,one_one_int)) )
    | spl250_9
    | ~ spl250_545 ),
    inference(resolution,[],[f10956,f7356]) ).

tff(f7356,plain,
    ( ~ hBOOL(hAPP_int_bool(nat_neg,one_one_int))
    | spl250_9 ),
    inference(avatar_component_clause,[],[f7354]) ).

tff(f23944,plain,
    spl250_1205,
    inference(avatar_split_clause,[],[f5989,f23942]) ).

tff(f23942,plain,
    ( spl250_1205
  <=> ! [X2: fun_nat_bool,X0: fun_fun_int_bool_nat,X1: fun_fu819804446l_bool] :
        ( ( image_1431733819ol_nat(X0,sK192(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1431733819ol_nat(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1205])]) ).

tff(f5989,plain,
    ! [X2: fun_nat_bool,X0: fun_fun_int_bool_nat,X1: fun_fu819804446l_bool] :
      ( ( image_1431733819ol_nat(X0,sK192(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1431733819ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f4279]) ).

tff(f23940,plain,
    spl250_1204,
    inference(avatar_split_clause,[],[f5986,f23938]) ).

tff(f23938,plain,
    ( spl250_1204
  <=> ! [X2: fun_nat_bool,X0: fun_pname_nat,X1: fun_pname_bool] :
        ( ( image_pname_nat(X0,sK191(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_pname_nat(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1204])]) ).

tff(f5986,plain,
    ! [X2: fun_nat_bool,X0: fun_pname_nat,X1: fun_pname_bool] :
      ( ( image_pname_nat(X0,sK191(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_pname_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f4277]) ).

tff(f23936,plain,
    spl250_1203,
    inference(avatar_split_clause,[],[f5969,f23934]) ).

tff(f23934,plain,
    ( spl250_1203
  <=> ! [X2: fun_int_bool,X0: fun_nat_int,X1: fun_nat_bool] :
        ( ( image_nat_int(X0,sK188(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_nat_int(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1203])]) ).

tff(f5969,plain,
    ! [X2: fun_int_bool,X0: fun_nat_int,X1: fun_nat_bool] :
      ( ( image_nat_int(X0,sK188(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_nat_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f4271]) ).

tff(f23932,plain,
    spl250_1202,
    inference(avatar_split_clause,[],[f5966,f23930]) ).

tff(f23930,plain,
    ( spl250_1202
  <=> ! [X2: fun_int_bool,X0: fun_a_int,X1: fun_a_bool] :
        ( ( image_a_int(X0,sK187(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_a_int(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1202])]) ).

tff(f5966,plain,
    ! [X2: fun_int_bool,X0: fun_a_int,X1: fun_a_bool] :
      ( ( image_a_int(X0,sK187(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_a_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f4269]) ).

tff(f23928,plain,
    spl250_1201,
    inference(avatar_split_clause,[],[f5963,f23926]) ).

tff(f23926,plain,
    ( spl250_1201
  <=> ! [X2: fun_int_bool,X0: fun_fun_a_bool_int,X1: fun_fun_a_bool_bool] :
        ( ( image_fun_a_bool_int(X0,sK186(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_fun_a_bool_int(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1201])]) ).

tff(f5963,plain,
    ! [X2: fun_int_bool,X0: fun_fun_a_bool_int,X1: fun_fun_a_bool_bool] :
      ( ( image_fun_a_bool_int(X0,sK186(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_fun_a_bool_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f4267]) ).

tff(f23924,plain,
    spl250_1200,
    inference(avatar_split_clause,[],[f5960,f23922]) ).

tff(f23922,plain,
    ( spl250_1200
  <=> ! [X2: fun_int_bool,X0: fun_fu1830380701ol_int,X1: fun_fu1430349052l_bool] :
        ( ( image_41399353ol_int(X0,sK185(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_41399353ol_int(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1200])]) ).

tff(f5960,plain,
    ! [X2: fun_int_bool,X0: fun_fu1830380701ol_int,X1: fun_fu1430349052l_bool] :
      ( ( image_41399353ol_int(X0,sK185(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_41399353ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f4265]) ).

tff(f23920,plain,
    spl250_1199,
    inference(avatar_split_clause,[],[f5957,f23918]) ).

tff(f23918,plain,
    ( spl250_1199
  <=> ! [X2: fun_int_bool,X0: fun_fun_nat_bool_int,X1: fun_fu425979586l_bool] :
        ( ( image_1133522419ol_int(X0,sK184(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_1133522419ol_int(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1199])]) ).

tff(f5957,plain,
    ! [X2: fun_int_bool,X0: fun_fun_nat_bool_int,X1: fun_fu425979586l_bool] :
      ( ( image_1133522419ol_int(X0,sK184(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_1133522419ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f4263]) ).

tff(f23916,plain,
    spl250_1198,
    inference(avatar_split_clause,[],[f5954,f23914]) ).

tff(f23914,plain,
    ( spl250_1198
  <=> ! [X2: fun_int_bool,X0: fun_fun_int_bool_int,X1: fun_fu819804446l_bool] :
        ( ( image_2069007511ol_int(X0,sK183(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_2069007511ol_int(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1198])]) ).

tff(f5954,plain,
    ! [X2: fun_int_bool,X0: fun_fun_int_bool_int,X1: fun_fu819804446l_bool] :
      ( ( image_2069007511ol_int(X0,sK183(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_2069007511ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f4261]) ).

tff(f23912,plain,
    spl250_1197,
    inference(avatar_split_clause,[],[f5951,f23910]) ).

tff(f23910,plain,
    ( spl250_1197
  <=> ! [X2: fun_int_bool,X0: fun_pname_int,X1: fun_pname_bool] :
        ( ( image_pname_int(X0,sK182(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_pname_int(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1197])]) ).

tff(f5951,plain,
    ! [X2: fun_int_bool,X0: fun_pname_int,X1: fun_pname_bool] :
      ( ( image_pname_int(X0,sK182(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_pname_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f4259]) ).

tff(f23908,plain,
    spl250_1196,
    inference(avatar_split_clause,[],[f5933,f23906]) ).

tff(f23906,plain,
    ( spl250_1196
  <=> ! [X2: fun_a_bool,X0: fun_pname_a,X1: fun_pname_bool] :
        ( ( image_pname_a(X0,sK179(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1196])]) ).

tff(f5933,plain,
    ! [X2: fun_a_bool,X0: fun_pname_a,X1: fun_pname_bool] :
      ( ( image_pname_a(X0,sK179(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4253]) ).

tff(f23904,plain,
    ( spl250_1195
    | ~ spl250_334
    | ~ spl250_545 ),
    inference(avatar_split_clause,[],[f15658,f10955,f9512,f23902]) ).

tff(f23902,plain,
    ( spl250_1195
  <=> ! [X0: pname] : ( bot_bot_fun_nat_bool = cOMBK_bool_nat(hAPP_pname_bool(bot_bo844097828e_bool,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1195])]) ).

tff(f9512,plain,
    ( spl250_334
  <=> ! [X0: pname] : ~ hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_334])]) ).

tff(f15658,plain,
    ( ! [X0: pname] : ( bot_bot_fun_nat_bool = cOMBK_bool_nat(hAPP_pname_bool(bot_bo844097828e_bool,X0)) )
    | ~ spl250_334
    | ~ spl250_545 ),
    inference(resolution,[],[f10956,f9513]) ).

tff(f9513,plain,
    ( ! [X0: pname] : ~ hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X0))
    | ~ spl250_334 ),
    inference(avatar_component_clause,[],[f9512]) ).

tff(f23900,plain,
    spl250_1194,
    inference(avatar_split_clause,[],[f5930,f23898]) ).

tff(f23898,plain,
    ( spl250_1194
  <=> ! [X2: fun_a_bool,X0: fun_int_a,X1: fun_int_bool] :
        ( ( image_int_a(X0,sK178(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_int_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1194])]) ).

tff(f5930,plain,
    ! [X2: fun_a_bool,X0: fun_int_a,X1: fun_int_bool] :
      ( ( image_int_a(X0,sK178(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_int_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4251]) ).

tff(f23896,plain,
    spl250_1193,
    inference(avatar_split_clause,[],[f5927,f23894]) ).

tff(f23894,plain,
    ( spl250_1193
  <=> ! [X2: fun_a_bool,X0: fun_nat_a,X1: fun_nat_bool] :
        ( ( image_nat_a(X0,sK177(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_nat_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1193])]) ).

tff(f5927,plain,
    ! [X2: fun_a_bool,X0: fun_nat_a,X1: fun_nat_bool] :
      ( ( image_nat_a(X0,sK177(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_nat_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4249]) ).

tff(f23892,plain,
    spl250_1192,
    inference(avatar_split_clause,[],[f5924,f23890]) ).

tff(f23890,plain,
    ( spl250_1192
  <=> ! [X2: fun_a_bool,X0: fun_a_a,X1: fun_a_bool] :
        ( ( image_a_a(X0,sK176(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_a_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1192])]) ).

tff(f5924,plain,
    ! [X2: fun_a_bool,X0: fun_a_a,X1: fun_a_bool] :
      ( ( image_a_a(X0,sK176(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_a_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4247]) ).

tff(f23888,plain,
    spl250_1191,
    inference(avatar_split_clause,[],[f5921,f23886]) ).

tff(f23886,plain,
    ( spl250_1191
  <=> ! [X2: fun_a_bool,X0: fun_fun_nat_bool_a,X1: fun_fu425979586l_bool] :
        ( ( image_fun_nat_bool_a(X0,sK175(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_nat_bool_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1191])]) ).

tff(f5921,plain,
    ! [X2: fun_a_bool,X0: fun_fun_nat_bool_a,X1: fun_fu425979586l_bool] :
      ( ( image_fun_nat_bool_a(X0,sK175(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_nat_bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4245]) ).

tff(f23884,plain,
    spl250_1190,
    inference(avatar_split_clause,[],[f5918,f23882]) ).

tff(f23882,plain,
    ( spl250_1190
  <=> ! [X2: fun_a_bool,X0: fun_fun_int_bool_a,X1: fun_fu819804446l_bool] :
        ( ( image_fun_int_bool_a(X0,sK174(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_int_bool_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1190])]) ).

tff(f5918,plain,
    ! [X2: fun_a_bool,X0: fun_fun_int_bool_a,X1: fun_fu819804446l_bool] :
      ( ( image_fun_int_bool_a(X0,sK174(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_int_bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4243]) ).

tff(f23880,plain,
    spl250_1189,
    inference(avatar_split_clause,[],[f5915,f23878]) ).

tff(f23878,plain,
    ( spl250_1189
  <=> ! [X2: fun_a_bool,X0: fun_fun_pname_bool_a,X1: fun_fu1430349052l_bool] :
        ( ( image_876012084bool_a(X0,sK173(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_876012084bool_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1189])]) ).

tff(f5915,plain,
    ! [X2: fun_a_bool,X0: fun_fun_pname_bool_a,X1: fun_fu1430349052l_bool] :
      ( ( image_876012084bool_a(X0,sK173(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_876012084bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4241]) ).

tff(f23876,plain,
    spl250_1188,
    inference(avatar_split_clause,[],[f5912,f23874]) ).

tff(f23874,plain,
    ( spl250_1188
  <=> ! [X2: fun_a_bool,X0: fun_fun_a_bool_a,X1: fun_fun_a_bool_bool] :
        ( ( image_fun_a_bool_a(X0,sK172(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_a_bool_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1188])]) ).

tff(f5912,plain,
    ! [X2: fun_a_bool,X0: fun_fun_a_bool_a,X1: fun_fun_a_bool_bool] :
      ( ( image_fun_a_bool_a(X0,sK172(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_a_bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4239]) ).

tff(f23872,plain,
    spl250_1187,
    inference(avatar_split_clause,[],[f5899,f23870]) ).

tff(f23870,plain,
    ( spl250_1187
  <=> ! [X2: fun_pname_bool,X0: fun_a_pname,X1: fun_a_bool] :
        ( ( image_a_pname(X0,sK169(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_a_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1187])]) ).

tff(f5899,plain,
    ! [X2: fun_pname_bool,X0: fun_a_pname,X1: fun_a_bool] :
      ( ( image_a_pname(X0,sK169(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_a_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4233]) ).

tff(f23868,plain,
    spl250_1186,
    inference(avatar_split_clause,[],[f5896,f23866]) ).

tff(f23866,plain,
    ( spl250_1186
  <=> ! [X2: fun_pname_bool,X0: fun_nat_pname,X1: fun_nat_bool] :
        ( ( image_nat_pname(X0,sK168(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_nat_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1186])]) ).

tff(f5896,plain,
    ! [X2: fun_pname_bool,X0: fun_nat_pname,X1: fun_nat_bool] :
      ( ( image_nat_pname(X0,sK168(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_nat_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4231]) ).

tff(f23864,plain,
    spl250_1185,
    inference(avatar_split_clause,[],[f5893,f23862]) ).

tff(f23862,plain,
    ( spl250_1185
  <=> ! [X2: fun_pname_bool,X0: fun_int_pname,X1: fun_int_bool] :
        ( ( image_int_pname(X0,sK167(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_int_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1185])]) ).

tff(f5893,plain,
    ! [X2: fun_pname_bool,X0: fun_int_pname,X1: fun_int_bool] :
      ( ( image_int_pname(X0,sK167(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_int_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4229]) ).

tff(f23860,plain,
    ( spl250_1184
    | ~ spl250_57
    | ~ spl250_545 ),
    inference(avatar_split_clause,[],[f15653,f10955,f7569,f23858]) ).

tff(f23858,plain,
    ( spl250_1184
  <=> ! [X0: x_a] : ( bot_bot_fun_nat_bool = cOMBK_bool_nat(hAPP_a_bool(bot_bot_fun_a_bool,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1184])]) ).

tff(f7569,plain,
    ( spl250_57
  <=> ! [X0: x_a] : ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_57])]) ).

tff(f15653,plain,
    ( ! [X0: x_a] : ( bot_bot_fun_nat_bool = cOMBK_bool_nat(hAPP_a_bool(bot_bot_fun_a_bool,X0)) )
    | ~ spl250_57
    | ~ spl250_545 ),
    inference(resolution,[],[f10956,f7570]) ).

tff(f7570,plain,
    ( ! [X0: x_a] : ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X0))
    | ~ spl250_57 ),
    inference(avatar_component_clause,[],[f7569]) ).

tff(f23856,plain,
    spl250_1183,
    inference(avatar_split_clause,[],[f5890,f23854]) ).

tff(f23854,plain,
    ( spl250_1183
  <=> ! [X2: fun_pname_bool,X0: fun_pname_pname,X1: fun_pname_bool] :
        ( ( image_pname_pname(X0,sK166(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_pname_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1183])]) ).

tff(f5890,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_pname,X1: fun_pname_bool] :
      ( ( image_pname_pname(X0,sK166(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_pname_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4227]) ).

tff(f23852,plain,
    spl250_1182,
    inference(avatar_split_clause,[],[f5887,f23850]) ).

tff(f23850,plain,
    ( spl250_1182
  <=> ! [X2: fun_pname_bool,X0: fun_fu1499449723_pname,X1: fun_fu1430349052l_bool] :
        ( ( image_1283814551_pname(X0,sK165(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1283814551_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1182])]) ).

tff(f5887,plain,
    ! [X2: fun_pname_bool,X0: fun_fu1499449723_pname,X1: fun_fu1430349052l_bool] :
      ( ( image_1283814551_pname(X0,sK165(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1283814551_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4225]) ).

tff(f23848,plain,
    spl250_1181,
    inference(avatar_split_clause,[],[f5884,f23846]) ).

tff(f23846,plain,
    ( spl250_1181
  <=> ! [X2: fun_pname_bool,X0: fun_fu953875929_pname,X1: fun_fu819804446l_bool] :
        ( ( image_62782965_pname(X0,sK164(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_62782965_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1181])]) ).

tff(f5884,plain,
    ! [X2: fun_pname_bool,X0: fun_fu953875929_pname,X1: fun_fu819804446l_bool] :
      ( ( image_62782965_pname(X0,sK164(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_62782965_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4223]) ).

tff(f23844,plain,
    spl250_1180,
    inference(avatar_split_clause,[],[f5881,f23842]) ).

tff(f23842,plain,
    ( spl250_1180
  <=> ! [X2: fun_pname_bool,X0: fun_fu665170229_pname,X1: fun_fu425979586l_bool] :
        ( ( image_1921560913_pname(X0,sK163(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1921560913_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1180])]) ).

tff(f5881,plain,
    ! [X2: fun_pname_bool,X0: fun_fu665170229_pname,X1: fun_fu425979586l_bool] :
      ( ( image_1921560913_pname(X0,sK163(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1921560913_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4221]) ).

tff(f23840,plain,
    spl250_1179,
    inference(avatar_split_clause,[],[f5878,f23838]) ).

tff(f23838,plain,
    ( spl250_1179
  <=> ! [X2: fun_pname_bool,X0: fun_fun_a_bool_pname,X1: fun_fun_a_bool_bool] :
        ( ( image_1854862208_pname(X0,sK162(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1854862208_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1179])]) ).

tff(f5878,plain,
    ! [X2: fun_pname_bool,X0: fun_fun_a_bool_pname,X1: fun_fun_a_bool_bool] :
      ( ( image_1854862208_pname(X0,sK162(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1854862208_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4219]) ).

tff(f23836,plain,
    spl250_1178,
    inference(avatar_split_clause,[],[f5847,f23834]) ).

tff(f23834,plain,
    ( spl250_1178
  <=> ! [X2: fun_fu425979586l_bool,X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
        ( ( image_26036933t_bool(X0,sK159(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_26036933t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1178])]) ).

tff(f5847,plain,
    ! [X2: fun_fu425979586l_bool,X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
      ( ( image_26036933t_bool(X0,sK159(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_26036933t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(cnf_transformation,[],[f4213]) ).

tff(f23832,plain,
    spl250_1177,
    inference(avatar_split_clause,[],[f5844,f23830]) ).

tff(f23830,plain,
    ( spl250_1177
  <=> ! [X2: fun_fu1430349052l_bool,X0: fun_na936072029e_bool,X1: fun_nat_bool] :
        ( ( image_1655916159e_bool(X0,sK158(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_1655916159e_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1177])]) ).

tff(f5844,plain,
    ! [X2: fun_fu1430349052l_bool,X0: fun_na936072029e_bool,X1: fun_nat_bool] :
      ( ( image_1655916159e_bool(X0,sK158(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_1655916159e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(cnf_transformation,[],[f4211]) ).

tff(f23828,plain,
    spl250_1176,
    inference(avatar_split_clause,[],[f5841,f23826]) ).

tff(f23826,plain,
    ( spl250_1176
  <=> ! [X2: fun_fu819804446l_bool,X0: fun_nat_fun_int_bool,X1: fun_nat_bool] :
        ( ( image_1556378401t_bool(X0,sK157(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1556378401t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1176])]) ).

tff(f5841,plain,
    ! [X2: fun_fu819804446l_bool,X0: fun_nat_fun_int_bool,X1: fun_nat_bool] :
      ( ( image_1556378401t_bool(X0,sK157(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1556378401t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(cnf_transformation,[],[f4209]) ).

tff(f23824,plain,
    spl250_1175,
    inference(avatar_split_clause,[],[f5838,f23822]) ).

tff(f23822,plain,
    ( spl250_1175
  <=> ! [X2: fun_fun_a_bool_bool,X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
        ( ( image_nat_fun_a_bool(X0,sK156(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_nat_fun_a_bool(X0,X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1175])]) ).

tff(f5838,plain,
    ! [X2: fun_fun_a_bool_bool,X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
      ( ( image_nat_fun_a_bool(X0,sK156(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_nat_fun_a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(cnf_transformation,[],[f4207]) ).

tff(f23820,plain,
    spl250_1174,
    inference(avatar_split_clause,[],[f5835,f23818]) ).

tff(f23818,plain,
    ( spl250_1174
  <=> ! [X2: fun_fu1430349052l_bool,X0: fun_in2065004473e_bool,X1: fun_int_bool] :
        ( ( image_637364955e_bool(X0,sK155(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_637364955e_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1174])]) ).

tff(f5835,plain,
    ! [X2: fun_fu1430349052l_bool,X0: fun_in2065004473e_bool,X1: fun_int_bool] :
      ( ( image_637364955e_bool(X0,sK155(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_637364955e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(cnf_transformation,[],[f4205]) ).

tff(f23816,plain,
    ( spl250_1173
    | spl250_18
    | ~ spl250_544 ),
    inference(avatar_split_clause,[],[f12494,f10924,f7396,f23813]) ).

tff(f10924,plain,
    ( spl250_544
  <=> ! [X0: bool] :
        ( hBOOL(X0)
        | ( bot_bot_fun_int_bool = cOMBK_bool_int(X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_544])]) ).

tff(f12494,plain,
    ( ( bot_bot_fun_int_bool = cOMBK_bool_int(hAPP_int_bool(nat_neg,pls)) )
    | spl250_18
    | ~ spl250_544 ),
    inference(resolution,[],[f10925,f7398]) ).

tff(f10925,plain,
    ( ! [X0: bool] :
        ( hBOOL(X0)
        | ( bot_bot_fun_int_bool = cOMBK_bool_int(X0) ) )
    | ~ spl250_544 ),
    inference(avatar_component_clause,[],[f10924]) ).

tff(f23811,plain,
    spl250_1172,
    inference(avatar_split_clause,[],[f5832,f23809]) ).

tff(f23809,plain,
    ( spl250_1172
  <=> ! [X2: fun_fun_a_bool_bool,X0: fun_int_fun_a_bool,X1: fun_int_bool] :
        ( ( image_int_fun_a_bool(X0,sK154(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_int_fun_a_bool(X0,X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1172])]) ).

tff(f5832,plain,
    ! [X2: fun_fun_a_bool_bool,X0: fun_int_fun_a_bool,X1: fun_int_bool] :
      ( ( image_int_fun_a_bool(X0,sK154(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_int_fun_a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(cnf_transformation,[],[f4203]) ).

tff(f23807,plain,
    spl250_1171,
    inference(avatar_split_clause,[],[f5829,f23805]) ).

tff(f23805,plain,
    ( spl250_1171
  <=> ! [X2: fun_fu819804446l_bool,X0: fun_int_fun_int_bool,X1: fun_int_bool] :
        ( ( image_275383677t_bool(X0,sK153(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_275383677t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1171])]) ).

tff(f5829,plain,
    ! [X2: fun_fu819804446l_bool,X0: fun_int_fun_int_bool,X1: fun_int_bool] :
      ( ( image_275383677t_bool(X0,sK153(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_275383677t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(cnf_transformation,[],[f4201]) ).

tff(f23803,plain,
    spl250_1170,
    inference(avatar_split_clause,[],[f5826,f23801]) ).

tff(f23801,plain,
    ( spl250_1170
  <=> ! [X2: fun_fu425979586l_bool,X0: fun_int_fun_nat_bool,X1: fun_int_bool] :
        ( ( image_892525857t_bool(X0,sK152(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_892525857t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1170])]) ).

tff(f5826,plain,
    ! [X2: fun_fu425979586l_bool,X0: fun_int_fun_nat_bool,X1: fun_int_bool] :
      ( ( image_892525857t_bool(X0,sK152(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_892525857t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(cnf_transformation,[],[f4199]) ).

tff(f23799,plain,
    spl250_1169,
    inference(avatar_split_clause,[],[f5823,f23797]) ).

tff(f23797,plain,
    ( spl250_1169
  <=> ! [X2: fun_fu1430349052l_bool,X0: fun_pn800050071e_bool,X1: fun_pname_bool] :
        ( ( image_47868345e_bool(X0,sK151(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_47868345e_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1169])]) ).

tff(f5823,plain,
    ! [X2: fun_fu1430349052l_bool,X0: fun_pn800050071e_bool,X1: fun_pname_bool] :
      ( ( image_47868345e_bool(X0,sK151(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_47868345e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(cnf_transformation,[],[f4197]) ).

tff(f23795,plain,
    spl250_1168,
    inference(avatar_split_clause,[],[f5820,f23793]) ).

tff(f23793,plain,
    ( spl250_1168
  <=> ! [X2: fun_fu819804446l_bool,X0: fun_pn665169337t_bool,X1: fun_pname_bool] :
        ( ( image_1512837979t_bool(X0,sK150(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1512837979t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1168])]) ).

tff(f5820,plain,
    ! [X2: fun_fu819804446l_bool,X0: fun_pn665169337t_bool,X1: fun_pname_bool] :
      ( ( image_1512837979t_bool(X0,sK150(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1512837979t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(cnf_transformation,[],[f4195]) ).

tff(f23791,plain,
    spl250_1167,
    inference(avatar_split_clause,[],[f5817,f23789]) ).

tff(f23789,plain,
    ( spl250_1167
  <=> ! [X2: fun_fu425979586l_bool,X0: fun_pn406123357t_bool,X1: fun_pname_bool] :
        ( ( image_2129980159t_bool(X0,sK149(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_2129980159t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1167])]) ).

tff(f5817,plain,
    ! [X2: fun_fu425979586l_bool,X0: fun_pn406123357t_bool,X1: fun_pname_bool] :
      ( ( image_2129980159t_bool(X0,sK149(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_2129980159t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(cnf_transformation,[],[f4193]) ).

tff(f23787,plain,
    spl250_1166,
    inference(avatar_split_clause,[],[f5814,f23785]) ).

tff(f23785,plain,
    ( spl250_1166
  <=> ! [X2: fun_fun_a_bool_bool,X0: fun_pname_fun_a_bool,X1: fun_pname_bool] :
        ( ( image_112932426a_bool(X0,sK148(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_112932426a_bool(X0,X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1166])]) ).

tff(f5814,plain,
    ! [X2: fun_fun_a_bool_bool,X0: fun_pname_fun_a_bool,X1: fun_pname_bool] :
      ( ( image_112932426a_bool(X0,sK148(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_112932426a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(cnf_transformation,[],[f4191]) ).

tff(f23783,plain,
    spl250_1165,
    inference(avatar_split_clause,[],[f5811,f23781]) ).

tff(f23781,plain,
    ( spl250_1165
  <=> ! [X2: fun_fu819804446l_bool,X0: fun_a_fun_int_bool,X1: fun_a_bool] :
        ( ( image_a_fun_int_bool(X0,sK147(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_a_fun_int_bool(X0,X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1165])]) ).

tff(f5811,plain,
    ! [X2: fun_fu819804446l_bool,X0: fun_a_fun_int_bool,X1: fun_a_bool] :
      ( ( image_a_fun_int_bool(X0,sK147(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_a_fun_int_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(cnf_transformation,[],[f4189]) ).

tff(f23779,plain,
    spl250_1164,
    inference(avatar_split_clause,[],[f5808,f23777]) ).

tff(f23777,plain,
    ( spl250_1164
  <=> ! [X2: fun_fu425979586l_bool,X0: fun_a_fun_nat_bool,X1: fun_a_bool] :
        ( ( image_a_fun_nat_bool(X0,sK146(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_a_fun_nat_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1164])]) ).

tff(f5808,plain,
    ! [X2: fun_fu425979586l_bool,X0: fun_a_fun_nat_bool,X1: fun_a_bool] :
      ( ( image_a_fun_nat_bool(X0,sK146(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_a_fun_nat_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(cnf_transformation,[],[f4187]) ).

tff(f23775,plain,
    spl250_1163,
    inference(avatar_split_clause,[],[f5805,f23773]) ).

tff(f23773,plain,
    ( spl250_1163
  <=> ! [X2: fun_fu1430349052l_bool,X0: fun_a_fun_pname_bool,X1: fun_a_bool] :
        ( ( image_819518260e_bool(X0,sK145(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_819518260e_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1163])]) ).

tff(f5805,plain,
    ! [X2: fun_fu1430349052l_bool,X0: fun_a_fun_pname_bool,X1: fun_a_bool] :
      ( ( image_819518260e_bool(X0,sK145(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_819518260e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(cnf_transformation,[],[f4185]) ).

tff(f23771,plain,
    ( spl250_1162
    | spl250_9
    | ~ spl250_544 ),
    inference(avatar_split_clause,[],[f12493,f10924,f7354,f23768]) ).

tff(f12493,plain,
    ( ( bot_bot_fun_int_bool = cOMBK_bool_int(hAPP_int_bool(nat_neg,one_one_int)) )
    | spl250_9
    | ~ spl250_544 ),
    inference(resolution,[],[f10925,f7356]) ).

tff(f23766,plain,
    spl250_1161,
    inference(avatar_split_clause,[],[f5802,f23764]) ).

tff(f23764,plain,
    ( spl250_1161
  <=> ! [X2: fun_fun_a_bool_bool,X0: fun_a_fun_a_bool,X1: fun_a_bool] :
        ( ( image_a_fun_a_bool(X0,sK144(X0,X1,X2)) = X2 )
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_a_fun_a_bool(X0,X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1161])]) ).

tff(f5802,plain,
    ! [X2: fun_fun_a_bool_bool,X0: fun_a_fun_a_bool,X1: fun_a_bool] :
      ( ( image_a_fun_a_bool(X0,sK144(X0,X1,X2)) = X2 )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_a_fun_a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(cnf_transformation,[],[f4183]) ).

tff(f23762,plain,
    spl250_1160,
    inference(avatar_split_clause,[],[f5760,f23760]) ).

tff(f23760,plain,
    ( spl250_1160
  <=> ! [X2: fun_nat_bool,X0: fun_nat_int,X1: fun_nat_bool] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,image_nat_int(X0,X1)),image_nat_int(X0,X2))),image_nat_int(X0,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1160])]) ).

tff(f5760,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_int,X1: fun_nat_bool] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,image_nat_int(X0,X1)),image_nat_int(X0,X2))),image_nat_int(X0,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2)))),
    inference(cnf_transformation,[],[f2136]) ).

tff(f2136,plain,
    ! [X0: fun_nat_int,X1: fun_nat_bool,X2: fun_nat_bool] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,image_nat_int(X0,X1)),image_nat_int(X0,X2))),image_nat_int(X0,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2)))),
    inference(rectify,[],[f659]) ).

tff(f659,axiom,
    ! [X6: fun_nat_int,X2: fun_nat_bool,X7: fun_nat_bool] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,image_nat_int(X6,X2)),image_nat_int(X6,X7))),image_nat_int(X6,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X7)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_658_image__diff__subset) ).

tff(f23758,plain,
    spl250_1159,
    inference(avatar_split_clause,[],[f5759,f23756]) ).

tff(f23756,plain,
    ( spl250_1159
  <=> ! [X2: fun_pname_bool,X0: fun_pname_a,X1: fun_pname_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,image_pname_a(X0,X1)),image_pname_a(X0,X2))),image_pname_a(X0,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1159])]) ).

tff(f5759,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_a,X1: fun_pname_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,image_pname_a(X0,X1)),image_pname_a(X0,X2))),image_pname_a(X0,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2)))),
    inference(cnf_transformation,[],[f2135]) ).

tff(f2135,plain,
    ! [X0: fun_pname_a,X1: fun_pname_bool,X2: fun_pname_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,image_pname_a(X0,X1)),image_pname_a(X0,X2))),image_pname_a(X0,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2)))),
    inference(rectify,[],[f660]) ).

tff(f660,axiom,
    ! [X6: fun_pname_a,X2: fun_pname_bool,X7: fun_pname_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,image_pname_a(X6,X2)),image_pname_a(X6,X7))),image_pname_a(X6,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X7)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_659_image__diff__subset) ).

tff(f23748,plain,
    ( spl250_1158
    | ~ spl250_369
    | ~ spl250_574
    | ~ spl250_1157 ),
    inference(avatar_split_clause,[],[f23744,f23740,f11754,f9687,f23746]) ).

tff(f23746,plain,
    ( spl250_1158
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( ~ hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(ord_less_eq_bool,X0),X1),sK138(X0,X1)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1158])]) ).

tff(f9687,plain,
    ( spl250_369
  <=> ! [X2: nat,X0: fun_bo1549164019l_bool,X1: fun_nat_bool] : ( hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_nat_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_369])]) ).

tff(f11754,plain,
    ( spl250_574
  <=> ! [X2: nat,X0: fun_na1469252690l_bool,X1: fun_nat_bool] : ( hAPP_nat_bool(cOMBS_nat_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_n1006566506l_bool(X0,X2),hAPP_nat_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_574])]) ).

tff(f23740,plain,
    ( spl250_1157
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,sK138(X0,X1))),hAPP_nat_bool(X1,sK138(X0,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1157])]) ).

tff(f23744,plain,
    ( ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( ~ hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(ord_less_eq_bool,X0),X1),sK138(X0,X1)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) )
    | ~ spl250_369
    | ~ spl250_574
    | ~ spl250_1157 ),
    inference(forward_demodulation,[],[f23743,f11755]) ).

tff(f11755,plain,
    ( ! [X2: nat,X0: fun_na1469252690l_bool,X1: fun_nat_bool] : ( hAPP_nat_bool(cOMBS_nat_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_n1006566506l_bool(X0,X2),hAPP_nat_bool(X1,X2)) )
    | ~ spl250_574 ),
    inference(avatar_component_clause,[],[f11754]) ).

tff(f23743,plain,
    ( ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( ~ hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(ord_less_eq_bool,X0),sK138(X0,X1)),hAPP_nat_bool(X1,sK138(X0,X1))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) )
    | ~ spl250_369
    | ~ spl250_1157 ),
    inference(forward_demodulation,[],[f23741,f9688]) ).

tff(f9688,plain,
    ( ! [X2: nat,X0: fun_bo1549164019l_bool,X1: fun_nat_bool] : ( hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_nat_bool(X1,X2)) )
    | ~ spl250_369 ),
    inference(avatar_component_clause,[],[f9687]) ).

tff(f23741,plain,
    ( ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,sK138(X0,X1))),hAPP_nat_bool(X1,sK138(X0,X1)))) )
    | ~ spl250_1157 ),
    inference(avatar_component_clause,[],[f23740]) ).

tff(f23742,plain,
    spl250_1157,
    inference(avatar_split_clause,[],[f5509,f23740]) ).

tff(f5509,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,sK138(X0,X1))),hAPP_nat_bool(X1,sK138(X0,X1)))) ),
    inference(cnf_transformation,[],[f4071]) ).

tff(f4071,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,sK138(X0,X1))),hAPP_nat_bool(X1,sK138(X0,X1)))) )
      & ( ! [X3: nat] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X3)),hAPP_nat_bool(X1,X3)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK138])],[f4069,f4070]) ).

tff(f4070,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ? [X2: nat] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X2)),hAPP_nat_bool(X1,X2)))
     => ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,sK138(X0,X1))),hAPP_nat_bool(X1,sK138(X0,X1)))) ),
    introduced(choice_axiom,[]) ).

tff(f4069,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
        | ? [X2: nat] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X2)),hAPP_nat_bool(X1,X2))) )
      & ( ! [X3: nat] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X3)),hAPP_nat_bool(X1,X3)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ) ),
    inference(rectify,[],[f4068]) ).

tff(f4068,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
        | ? [X2: nat] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X2)),hAPP_nat_bool(X1,X2))) )
      & ( ! [X2: nat] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X2)),hAPP_nat_bool(X1,X2)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ) ),
    inference(nnf_transformation,[],[f1987]) ).

tff(f1987,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
    <=> ! [X2: nat] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X2)),hAPP_nat_bool(X1,X2))) ),
    inference(rectify,[],[f443]) ).

tff(f443,axiom,
    ! [X6: fun_nat_bool,X66: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6),X66))
    <=> ! [X27: nat] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X6,X27)),hAPP_nat_bool(X66,X27))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_442_le__fun__def) ).

tff(f23732,plain,
    ( spl250_1156
    | ~ spl250_368
    | ~ spl250_573
    | ~ spl250_1155 ),
    inference(avatar_split_clause,[],[f23728,f23724,f11750,f9683,f23730]) ).

tff(f23730,plain,
    ( spl250_1156
  <=> ! [X0: fun_int_bool,X1: fun_int_bool] :
        ( ~ hBOOL(hAPP_int_bool(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(ord_less_eq_bool,X0),X1),sK137(X0,X1)))
        | hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1156])]) ).

tff(f9683,plain,
    ( spl250_368
  <=> ! [X2: int,X0: fun_bo1549164019l_bool,X1: fun_int_bool] : ( hAPP_i68813070l_bool(cOMBB_1652995168ol_int(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_int_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_368])]) ).

tff(f11750,plain,
    ( spl250_573
  <=> ! [X2: int,X0: fun_in531499254l_bool,X1: fun_int_bool] : ( hAPP_int_bool(cOMBS_int_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_i68813070l_bool(X0,X2),hAPP_int_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_573])]) ).

tff(f23724,plain,
    ( spl250_1155
  <=> ! [X0: fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,sK137(X0,X1))),hAPP_int_bool(X1,sK137(X0,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1155])]) ).

tff(f23728,plain,
    ( ! [X0: fun_int_bool,X1: fun_int_bool] :
        ( ~ hBOOL(hAPP_int_bool(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(ord_less_eq_bool,X0),X1),sK137(X0,X1)))
        | hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) )
    | ~ spl250_368
    | ~ spl250_573
    | ~ spl250_1155 ),
    inference(forward_demodulation,[],[f23727,f11751]) ).

tff(f11751,plain,
    ( ! [X2: int,X0: fun_in531499254l_bool,X1: fun_int_bool] : ( hAPP_int_bool(cOMBS_int_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_i68813070l_bool(X0,X2),hAPP_int_bool(X1,X2)) )
    | ~ spl250_573 ),
    inference(avatar_component_clause,[],[f11750]) ).

tff(f23727,plain,
    ( ! [X0: fun_int_bool,X1: fun_int_bool] :
        ( ~ hBOOL(hAPP_bool_bool(hAPP_i68813070l_bool(cOMBB_1652995168ol_int(ord_less_eq_bool,X0),sK137(X0,X1)),hAPP_int_bool(X1,sK137(X0,X1))))
        | hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) )
    | ~ spl250_368
    | ~ spl250_1155 ),
    inference(forward_demodulation,[],[f23725,f9684]) ).

tff(f9684,plain,
    ( ! [X2: int,X0: fun_bo1549164019l_bool,X1: fun_int_bool] : ( hAPP_i68813070l_bool(cOMBB_1652995168ol_int(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_int_bool(X1,X2)) )
    | ~ spl250_368 ),
    inference(avatar_component_clause,[],[f9683]) ).

tff(f23725,plain,
    ( ! [X0: fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,sK137(X0,X1))),hAPP_int_bool(X1,sK137(X0,X1)))) )
    | ~ spl250_1155 ),
    inference(avatar_component_clause,[],[f23724]) ).

tff(f23726,plain,
    spl250_1155,
    inference(avatar_split_clause,[],[f5499,f23724]) ).

tff(f5499,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,sK137(X0,X1))),hAPP_int_bool(X1,sK137(X0,X1)))) ),
    inference(cnf_transformation,[],[f4063]) ).

tff(f4063,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,sK137(X0,X1))),hAPP_int_bool(X1,sK137(X0,X1)))) )
      & ( ! [X3: int] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X3)),hAPP_int_bool(X1,X3)))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK137])],[f4061,f4062]) ).

tff(f4062,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ? [X2: int] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X2)),hAPP_int_bool(X1,X2)))
     => ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,sK137(X0,X1))),hAPP_int_bool(X1,sK137(X0,X1)))) ),
    introduced(choice_axiom,[]) ).

tff(f4061,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
        | ? [X2: int] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X2)),hAPP_int_bool(X1,X2))) )
      & ( ! [X3: int] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X3)),hAPP_int_bool(X1,X3)))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ) ),
    inference(rectify,[],[f4060]) ).

tff(f4060,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
        | ? [X2: int] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X2)),hAPP_int_bool(X1,X2))) )
      & ( ! [X2: int] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X2)),hAPP_int_bool(X1,X2)))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ) ),
    inference(nnf_transformation,[],[f1982]) ).

tff(f1982,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
    <=> ! [X2: int] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X2)),hAPP_int_bool(X1,X2))) ),
    inference(rectify,[],[f442]) ).

tff(f442,axiom,
    ! [X6: fun_int_bool,X66: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X6),X66))
    <=> ! [X27: int] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X6,X27)),hAPP_int_bool(X66,X27))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_441_le__fun__def) ).

tff(f23715,plain,
    ( spl250_1154
    | ~ spl250_334
    | ~ spl250_544 ),
    inference(avatar_split_clause,[],[f12478,f10924,f9512,f23713]) ).

tff(f12478,plain,
    ( ! [X0: pname] : ( bot_bot_fun_int_bool = cOMBK_bool_int(hAPP_pname_bool(bot_bo844097828e_bool,X0)) )
    | ~ spl250_334
    | ~ spl250_544 ),
    inference(resolution,[],[f10925,f9513]) ).

tff(f23711,plain,
    ( spl250_1153
    | ~ spl250_367
    | ~ spl250_568
    | ~ spl250_1152 ),
    inference(avatar_split_clause,[],[f23707,f23703,f11730,f9678,f23709]) ).

tff(f23709,plain,
    ( spl250_1153
  <=> ! [X0: fun_a_bool,X1: fun_a_bool] :
        ( ~ hBOOL(hAPP_a_bool(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(ord_less_eq_bool,X0),X1),sK136(X0,X1)))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1153])]) ).

tff(f9678,plain,
    ( spl250_367
  <=> ! [X2: x_a,X0: fun_bo1549164019l_bool,X1: fun_a_bool] : ( hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_a_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_367])]) ).

tff(f11730,plain,
    ( spl250_568
  <=> ! [X2: x_a,X0: fun_a_fun_bool_bool,X1: fun_a_bool] : ( hAPP_a_bool(cOMBS_a_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X0,X2),hAPP_a_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_568])]) ).

tff(f23703,plain,
    ( spl250_1152
  <=> ! [X0: fun_a_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,sK136(X0,X1))),hAPP_a_bool(X1,sK136(X0,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1152])]) ).

tff(f23707,plain,
    ( ! [X0: fun_a_bool,X1: fun_a_bool] :
        ( ~ hBOOL(hAPP_a_bool(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(ord_less_eq_bool,X0),X1),sK136(X0,X1)))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) )
    | ~ spl250_367
    | ~ spl250_568
    | ~ spl250_1152 ),
    inference(forward_demodulation,[],[f23706,f11731]) ).

tff(f11731,plain,
    ( ! [X2: x_a,X0: fun_a_fun_bool_bool,X1: fun_a_bool] : ( hAPP_a_bool(cOMBS_a_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X0,X2),hAPP_a_bool(X1,X2)) )
    | ~ spl250_568 ),
    inference(avatar_component_clause,[],[f11730]) ).

tff(f23706,plain,
    ( ! [X0: fun_a_bool,X1: fun_a_bool] :
        ( ~ hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(ord_less_eq_bool,X0),sK136(X0,X1)),hAPP_a_bool(X1,sK136(X0,X1))))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) )
    | ~ spl250_367
    | ~ spl250_1152 ),
    inference(forward_demodulation,[],[f23704,f9679]) ).

tff(f9679,plain,
    ( ! [X2: x_a,X0: fun_bo1549164019l_bool,X1: fun_a_bool] : ( hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_a_bool(X1,X2)) )
    | ~ spl250_367 ),
    inference(avatar_component_clause,[],[f9678]) ).

tff(f23704,plain,
    ( ! [X0: fun_a_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,sK136(X0,X1))),hAPP_a_bool(X1,sK136(X0,X1)))) )
    | ~ spl250_1152 ),
    inference(avatar_component_clause,[],[f23703]) ).

tff(f23705,plain,
    spl250_1152,
    inference(avatar_split_clause,[],[f5495,f23703]) ).

tff(f5495,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,sK136(X0,X1))),hAPP_a_bool(X1,sK136(X0,X1)))) ),
    inference(cnf_transformation,[],[f4058]) ).

tff(f4058,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,sK136(X0,X1))),hAPP_a_bool(X1,sK136(X0,X1)))) )
      & ( ! [X3: x_a] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X3)),hAPP_a_bool(X1,X3)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK136])],[f4056,f4057]) ).

tff(f4057,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( ? [X2: x_a] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X2)),hAPP_a_bool(X1,X2)))
     => ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,sK136(X0,X1))),hAPP_a_bool(X1,sK136(X0,X1)))) ),
    introduced(choice_axiom,[]) ).

tff(f4056,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
        | ? [X2: x_a] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X2)),hAPP_a_bool(X1,X2))) )
      & ( ! [X3: x_a] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X3)),hAPP_a_bool(X1,X3)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ) ),
    inference(rectify,[],[f4055]) ).

tff(f4055,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
        | ? [X2: x_a] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X2)),hAPP_a_bool(X1,X2))) )
      & ( ! [X2: x_a] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X2)),hAPP_a_bool(X1,X2)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ) ),
    inference(nnf_transformation,[],[f1980]) ).

tff(f1980,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
    <=> ! [X2: x_a] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X2)),hAPP_a_bool(X1,X2))) ),
    inference(rectify,[],[f444]) ).

tff(f444,axiom,
    ! [X6: fun_a_bool,X66: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X6),X66))
    <=> ! [X27: x_a] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X6,X27)),hAPP_a_bool(X66,X27))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_443_le__fun__def) ).

tff(f23695,plain,
    ( spl250_1151
    | ~ spl250_369
    | ~ spl250_574
    | ~ spl250_1150 ),
    inference(avatar_split_clause,[],[f23691,f23687,f11754,f9687,f23693]) ).

tff(f23693,plain,
    ( spl250_1151
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( ~ hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(ord_less_eq_bool,X0),X1),sK129(X0,X1)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1151])]) ).

tff(f23687,plain,
    ( spl250_1150
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,sK129(X0,X1))),hAPP_nat_bool(X1,sK129(X0,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1150])]) ).

tff(f23691,plain,
    ( ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( ~ hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(ord_less_eq_bool,X0),X1),sK129(X0,X1)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) )
    | ~ spl250_369
    | ~ spl250_574
    | ~ spl250_1150 ),
    inference(forward_demodulation,[],[f23690,f11755]) ).

tff(f23690,plain,
    ( ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( ~ hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(ord_less_eq_bool,X0),sK129(X0,X1)),hAPP_nat_bool(X1,sK129(X0,X1))))
        | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) )
    | ~ spl250_369
    | ~ spl250_1150 ),
    inference(forward_demodulation,[],[f23688,f9688]) ).

tff(f23688,plain,
    ( ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,sK129(X0,X1))),hAPP_nat_bool(X1,sK129(X0,X1)))) )
    | ~ spl250_1150 ),
    inference(avatar_component_clause,[],[f23687]) ).

tff(f23689,plain,
    spl250_1150,
    inference(avatar_split_clause,[],[f5419,f23687]) ).

tff(f5419,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,sK129(X0,X1))),hAPP_nat_bool(X1,sK129(X0,X1)))) ),
    inference(cnf_transformation,[],[f4006]) ).

tff(f4006,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,sK129(X0,X1))),hAPP_nat_bool(X1,sK129(X0,X1)))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK129])],[f3059,f4005]) ).

tff(f4005,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ? [X2: nat] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X2)),hAPP_nat_bool(X1,X2)))
     => ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,sK129(X0,X1))),hAPP_nat_bool(X1,sK129(X0,X1)))) ),
    introduced(choice_axiom,[]) ).

tff(f3059,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
      | ? [X2: nat] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X2)),hAPP_nat_bool(X1,X2))) ),
    inference(ennf_transformation,[],[f1953]) ).

tff(f1953,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ! [X2: nat] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X2)),hAPP_nat_bool(X1,X2)))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ),
    inference(rectify,[],[f485]) ).

tff(f485,axiom,
    ! [X6: fun_nat_bool,X66: fun_nat_bool] :
      ( ! [X27: nat] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X6,X27)),hAPP_nat_bool(X66,X27)))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6),X66)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_484_le__funI) ).

tff(f23679,plain,
    ( spl250_1149
    | ~ spl250_368
    | ~ spl250_573
    | ~ spl250_1148 ),
    inference(avatar_split_clause,[],[f23675,f23671,f11750,f9683,f23677]) ).

tff(f23677,plain,
    ( spl250_1149
  <=> ! [X0: fun_int_bool,X1: fun_int_bool] :
        ( ~ hBOOL(hAPP_int_bool(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(ord_less_eq_bool,X0),X1),sK128(X0,X1)))
        | hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1149])]) ).

tff(f23671,plain,
    ( spl250_1148
  <=> ! [X0: fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,sK128(X0,X1))),hAPP_int_bool(X1,sK128(X0,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1148])]) ).

tff(f23675,plain,
    ( ! [X0: fun_int_bool,X1: fun_int_bool] :
        ( ~ hBOOL(hAPP_int_bool(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(ord_less_eq_bool,X0),X1),sK128(X0,X1)))
        | hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) )
    | ~ spl250_368
    | ~ spl250_573
    | ~ spl250_1148 ),
    inference(forward_demodulation,[],[f23674,f11751]) ).

tff(f23674,plain,
    ( ! [X0: fun_int_bool,X1: fun_int_bool] :
        ( ~ hBOOL(hAPP_bool_bool(hAPP_i68813070l_bool(cOMBB_1652995168ol_int(ord_less_eq_bool,X0),sK128(X0,X1)),hAPP_int_bool(X1,sK128(X0,X1))))
        | hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) )
    | ~ spl250_368
    | ~ spl250_1148 ),
    inference(forward_demodulation,[],[f23672,f9684]) ).

tff(f23672,plain,
    ( ! [X0: fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,sK128(X0,X1))),hAPP_int_bool(X1,sK128(X0,X1)))) )
    | ~ spl250_1148 ),
    inference(avatar_component_clause,[],[f23671]) ).

tff(f23673,plain,
    spl250_1148,
    inference(avatar_split_clause,[],[f5418,f23671]) ).

tff(f5418,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,sK128(X0,X1))),hAPP_int_bool(X1,sK128(X0,X1)))) ),
    inference(cnf_transformation,[],[f4004]) ).

tff(f4004,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,sK128(X0,X1))),hAPP_int_bool(X1,sK128(X0,X1)))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK128])],[f3058,f4003]) ).

tff(f4003,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ? [X2: int] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X2)),hAPP_int_bool(X1,X2)))
     => ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,sK128(X0,X1))),hAPP_int_bool(X1,sK128(X0,X1)))) ),
    introduced(choice_axiom,[]) ).

tff(f3058,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
      | ? [X2: int] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X2)),hAPP_int_bool(X1,X2))) ),
    inference(ennf_transformation,[],[f1952]) ).

tff(f1952,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ! [X2: int] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X2)),hAPP_int_bool(X1,X2)))
     => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ),
    inference(rectify,[],[f484]) ).

tff(f484,axiom,
    ! [X6: fun_int_bool,X66: fun_int_bool] :
      ( ! [X27: int] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X6,X27)),hAPP_int_bool(X66,X27)))
     => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X6),X66)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_483_le__funI) ).

tff(f23662,plain,
    ( spl250_1147
    | ~ spl250_367
    | ~ spl250_568
    | ~ spl250_1145 ),
    inference(avatar_split_clause,[],[f23654,f23650,f11730,f9678,f23660]) ).

tff(f23660,plain,
    ( spl250_1147
  <=> ! [X0: fun_a_bool,X1: fun_a_bool] :
        ( ~ hBOOL(hAPP_a_bool(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(ord_less_eq_bool,X0),X1),sK127(X0,X1)))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1147])]) ).

tff(f23650,plain,
    ( spl250_1145
  <=> ! [X0: fun_a_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,sK127(X0,X1))),hAPP_a_bool(X1,sK127(X0,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1145])]) ).

tff(f23654,plain,
    ( ! [X0: fun_a_bool,X1: fun_a_bool] :
        ( ~ hBOOL(hAPP_a_bool(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(ord_less_eq_bool,X0),X1),sK127(X0,X1)))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) )
    | ~ spl250_367
    | ~ spl250_568
    | ~ spl250_1145 ),
    inference(forward_demodulation,[],[f23653,f11731]) ).

tff(f23653,plain,
    ( ! [X0: fun_a_bool,X1: fun_a_bool] :
        ( ~ hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(ord_less_eq_bool,X0),sK127(X0,X1)),hAPP_a_bool(X1,sK127(X0,X1))))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) )
    | ~ spl250_367
    | ~ spl250_1145 ),
    inference(forward_demodulation,[],[f23651,f9679]) ).

tff(f23651,plain,
    ( ! [X0: fun_a_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,sK127(X0,X1))),hAPP_a_bool(X1,sK127(X0,X1)))) )
    | ~ spl250_1145 ),
    inference(avatar_component_clause,[],[f23650]) ).

tff(f23658,plain,
    ( spl250_1146
    | ~ spl250_57
    | ~ spl250_544 ),
    inference(avatar_split_clause,[],[f12474,f10924,f7569,f23656]) ).

tff(f12474,plain,
    ( ! [X0: x_a] : ( bot_bot_fun_int_bool = cOMBK_bool_int(hAPP_a_bool(bot_bot_fun_a_bool,X0)) )
    | ~ spl250_57
    | ~ spl250_544 ),
    inference(resolution,[],[f10925,f7570]) ).

tff(f23652,plain,
    spl250_1145,
    inference(avatar_split_clause,[],[f5417,f23650]) ).

tff(f5417,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,sK127(X0,X1))),hAPP_a_bool(X1,sK127(X0,X1)))) ),
    inference(cnf_transformation,[],[f4002]) ).

tff(f4002,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,sK127(X0,X1))),hAPP_a_bool(X1,sK127(X0,X1)))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK127])],[f3057,f4001]) ).

tff(f4001,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( ? [X2: x_a] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X2)),hAPP_a_bool(X1,X2)))
     => ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,sK127(X0,X1))),hAPP_a_bool(X1,sK127(X0,X1)))) ),
    introduced(choice_axiom,[]) ).

tff(f3057,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
      | ? [X2: x_a] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X2)),hAPP_a_bool(X1,X2))) ),
    inference(ennf_transformation,[],[f1951]) ).

tff(f1951,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( ! [X2: x_a] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X2)),hAPP_a_bool(X1,X2)))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ),
    inference(rectify,[],[f486]) ).

tff(f486,axiom,
    ! [X6: fun_a_bool,X66: fun_a_bool] :
      ( ! [X27: x_a] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X6,X27)),hAPP_a_bool(X66,X27)))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X6),X66)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_485_le__funI) ).

tff(f23648,plain,
    spl250_1144,
    inference(avatar_split_clause,[],[f5271,f23646]) ).

tff(f23646,plain,
    ( spl250_1144
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f22106695ol_nat(finite_card_nat,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1144])]) ).

tff(f5271,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f22106695ol_nat(finite_card_nat,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f2890]) ).

tff(f2890,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f22106695ol_nat(finite_card_nat,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(flattening,[],[f2889]) ).

tff(f2889,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f22106695ol_nat(finite_card_nat,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(ennf_transformation,[],[f1830]) ).

tff(f1830,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X0)),hAPP_f22106695ol_nat(finite_card_nat,X1))) ) ),
    inference(rectify,[],[f78]) ).

tff(f78,axiom,
    ! [X2: fun_nat_bool,X7: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X7))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X2)),hAPP_f22106695ol_nat(finite_card_nat,X7))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_card__mono) ).

tff(f23644,plain,
    spl250_1143,
    inference(avatar_split_clause,[],[f5263,f23642]) ).

tff(f23642,plain,
    ( spl250_1143
  <=> ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK117(X0)),sK118(X0)))
        | ~ hBOOL(hAPP_f54304608l_bool(X0,X1))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1143])]) ).

tff(f5263,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK117(X0)),sK118(X0)))
      | ~ hBOOL(hAPP_f54304608l_bool(X0,X1))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f3974]) ).

tff(f3974,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
      | ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,sK118(X0)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK117(X0)),bot_bot_fun_nat_bool))))
        & hBOOL(hAPP_f54304608l_bool(X0,sK118(X0)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK117(X0)),sK118(X0)))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK118(X0))) )
      | ~ hBOOL(hAPP_f54304608l_bool(X0,X1))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK117,sK118])],[f2878,f3973]) ).

tff(f3973,plain,
    ! [X0: fun_fu425979586l_bool] :
      ( ? [X2: nat,X3: fun_nat_bool] :
          ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X3),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))))
          & hBOOL(hAPP_f54304608l_bool(X0,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) )
     => ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,sK118(X0)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK117(X0)),bot_bot_fun_nat_bool))))
        & hBOOL(hAPP_f54304608l_bool(X0,sK118(X0)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK117(X0)),sK118(X0)))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK118(X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f2878,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
      | ? [X2: nat,X3: fun_nat_bool] :
          ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X3),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))))
          & hBOOL(hAPP_f54304608l_bool(X0,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) )
      | ~ hBOOL(hAPP_f54304608l_bool(X0,X1))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(flattening,[],[f2877]) ).

tff(f2877,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
      | ? [X2: nat,X3: fun_nat_bool] :
          ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X3),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))))
          & hBOOL(hAPP_f54304608l_bool(X0,X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) )
      | ~ hBOOL(hAPP_f54304608l_bool(X0,X1))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(ennf_transformation,[],[f1824]) ).

tff(f1824,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
     => ( hBOOL(hAPP_f54304608l_bool(X0,X1))
       => ( ! [X2: nat,X3: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
             => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3))
               => ( hBOOL(hAPP_f54304608l_bool(X0,X3))
                 => hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X3),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)))) ) ) )
         => hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool)) ) ) ),
    inference(rectify,[],[f686]) ).

tff(f686,axiom,
    ! [X10: fun_fu425979586l_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f54304608l_bool(X10,X2))
       => ( ! [X75: nat,X78: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X78))
             => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X75),X78))
               => ( hBOOL(hAPP_f54304608l_bool(X10,X78))
                 => hBOOL(hAPP_f54304608l_bool(X10,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X78),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X75),bot_bot_fun_nat_bool)))) ) ) )
         => hBOOL(hAPP_f54304608l_bool(X10,bot_bot_fun_nat_bool)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_685_finite__empty__induct) ).

tff(f23640,plain,
    spl250_1142,
    inference(avatar_split_clause,[],[f5259,f23638]) ).

tff(f23638,plain,
    ( spl250_1142
  <=> ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(X0,X1))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK115(X0)),sK116(X0)))
        | ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1142])]) ).

tff(f5259,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,X1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK115(X0)),sK116(X0)))
      | ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f3972]) ).

tff(f23636,plain,
    spl250_1141,
    inference(avatar_split_clause,[],[f5228,f23634]) ).

tff(f23634,plain,
    ( spl250_1141
  <=> ! [X0: fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X0)),hAPP_f957591787ol_nat(finite_card_int,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1141])]) ).

tff(f5228,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X0)),hAPP_f957591787ol_nat(finite_card_int,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f2850]) ).

tff(f2850,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X0)),hAPP_f957591787ol_nat(finite_card_int,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(flattening,[],[f2849]) ).

tff(f2849,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X0)),hAPP_f957591787ol_nat(finite_card_int,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(ennf_transformation,[],[f1801]) ).

tff(f1801,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X0)),hAPP_f957591787ol_nat(finite_card_int,X1))) ) ),
    inference(rectify,[],[f79]) ).

tff(f79,axiom,
    ! [X2: fun_int_bool,X7: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X7))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X2)),hAPP_f957591787ol_nat(finite_card_int,X7))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_card__mono) ).

tff(f23632,plain,
    spl250_1140,
    inference(avatar_split_clause,[],[f5220,f23630]) ).

tff(f23630,plain,
    ( spl250_1140
  <=> ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK110(X0)),sK111(X0)))
        | ~ hBOOL(hAPP_f448129468l_bool(X0,X1))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1140])]) ).

tff(f5220,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK110(X0)),sK111(X0)))
      | ~ hBOOL(hAPP_f448129468l_bool(X0,X1))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f3963]) ).

tff(f3963,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
      | ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,sK111(X0)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK110(X0)),bot_bot_fun_int_bool))))
        & hBOOL(hAPP_f448129468l_bool(X0,sK111(X0)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK110(X0)),sK111(X0)))
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK111(X0))) )
      | ~ hBOOL(hAPP_f448129468l_bool(X0,X1))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK110,sK111])],[f2838,f3962]) ).

tff(f3962,plain,
    ! [X0: fun_fu819804446l_bool] :
      ( ? [X2: int,X3: fun_int_bool] :
          ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X3),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))))
          & hBOOL(hAPP_f448129468l_bool(X0,X3))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X3))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) )
     => ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,sK111(X0)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK110(X0)),bot_bot_fun_int_bool))))
        & hBOOL(hAPP_f448129468l_bool(X0,sK111(X0)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK110(X0)),sK111(X0)))
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK111(X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f2838,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
      | ? [X2: int,X3: fun_int_bool] :
          ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X3),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))))
          & hBOOL(hAPP_f448129468l_bool(X0,X3))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X3))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) )
      | ~ hBOOL(hAPP_f448129468l_bool(X0,X1))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(flattening,[],[f2837]) ).

tff(f2837,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
      | ? [X2: int,X3: fun_int_bool] :
          ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X3),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))))
          & hBOOL(hAPP_f448129468l_bool(X0,X3))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X3))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) )
      | ~ hBOOL(hAPP_f448129468l_bool(X0,X1))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(ennf_transformation,[],[f1795]) ).

tff(f1795,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
     => ( hBOOL(hAPP_f448129468l_bool(X0,X1))
       => ( ! [X2: int,X3: fun_int_bool] :
              ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
             => ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X3))
               => ( hBOOL(hAPP_f448129468l_bool(X0,X3))
                 => hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X3),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)))) ) ) )
         => hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool)) ) ) ),
    inference(rectify,[],[f685]) ).

tff(f685,axiom,
    ! [X10: fun_fu819804446l_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_f448129468l_bool(X10,X2))
       => ( ! [X75: int,X78: fun_int_bool] :
              ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X78))
             => ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X75),X78))
               => ( hBOOL(hAPP_f448129468l_bool(X10,X78))
                 => hBOOL(hAPP_f448129468l_bool(X10,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X78),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X75),bot_bot_fun_int_bool)))) ) ) )
         => hBOOL(hAPP_f448129468l_bool(X10,bot_bot_fun_int_bool)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_684_finite__empty__induct) ).

tff(f23628,plain,
    spl250_1139,
    inference(avatar_split_clause,[],[f5216,f23626]) ).

tff(f23626,plain,
    ( spl250_1139
  <=> ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(X0,X1))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK108(X0)),sK109(X0)))
        | ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1139])]) ).

tff(f5216,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,X1))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK108(X0)),sK109(X0)))
      | ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f3961]) ).

tff(f23624,plain,
    spl250_1138,
    inference(avatar_split_clause,[],[f5189,f23622]) ).

tff(f23622,plain,
    ( spl250_1138
  <=> ! [X0: fun_a_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_fun_a_bool_nat(finite_card_a,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1138])]) ).

tff(f5189,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_fun_a_bool_nat(finite_card_a,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(cnf_transformation,[],[f2813]) ).

tff(f2813,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_fun_a_bool_nat(finite_card_a,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(flattening,[],[f2812]) ).

tff(f2812,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_fun_a_bool_nat(finite_card_a,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(ennf_transformation,[],[f1775]) ).

tff(f1775,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X0)),hAPP_fun_a_bool_nat(finite_card_a,X1))) ) ),
    inference(rectify,[],[f77]) ).

tff(f77,axiom,
    ! [X2: fun_a_bool,X7: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X2)),hAPP_fun_a_bool_nat(finite_card_a,X7))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_card__mono) ).

tff(f23620,plain,
    spl250_1137,
    inference(avatar_split_clause,[],[f5181,f23618]) ).

tff(f23618,plain,
    ( spl250_1137
  <=> ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK103(X0)),sK104(X0)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(X0,X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1137])]) ).

tff(f5181,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK103(X0)),sK104(X0)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(X0,X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(cnf_transformation,[],[f3953]) ).

tff(f3953,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,sK104(X0)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK103(X0)),bot_bot_fun_a_bool))))
        & hBOOL(hAPP_fun_a_bool_bool(X0,sK104(X0)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK103(X0)),sK104(X0)))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK104(X0))) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(X0,X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK103,sK104])],[f2801,f3952]) ).

tff(f3952,plain,
    ! [X0: fun_fun_a_bool_bool] :
      ( ? [X2: x_a,X3: fun_a_bool] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X3),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))))
          & hBOOL(hAPP_fun_a_bool_bool(X0,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3)) )
     => ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,sK104(X0)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK103(X0)),bot_bot_fun_a_bool))))
        & hBOOL(hAPP_fun_a_bool_bool(X0,sK104(X0)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK103(X0)),sK104(X0)))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK104(X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f2801,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
      | ? [X2: x_a,X3: fun_a_bool] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X3),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))))
          & hBOOL(hAPP_fun_a_bool_bool(X0,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(X0,X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(flattening,[],[f2800]) ).

tff(f2800,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
      | ? [X2: x_a,X3: fun_a_bool] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X3),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))))
          & hBOOL(hAPP_fun_a_bool_bool(X0,X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(X0,X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(ennf_transformation,[],[f1769]) ).

tff(f1769,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
     => ( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
       => ( ! [X2: x_a,X3: fun_a_bool] :
              ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
             => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
               => ( hBOOL(hAPP_fun_a_bool_bool(X0,X3))
                 => hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X3),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)))) ) ) )
         => hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool)) ) ) ),
    inference(rectify,[],[f684]) ).

tff(f684,axiom,
    ! [X10: fun_fun_a_bool_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(X10,X2))
       => ( ! [X75: x_a,X78: fun_a_bool] :
              ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X78))
             => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X75),X78))
               => ( hBOOL(hAPP_fun_a_bool_bool(X10,X78))
                 => hBOOL(hAPP_fun_a_bool_bool(X10,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X78),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X75),bot_bot_fun_a_bool)))) ) ) )
         => hBOOL(hAPP_fun_a_bool_bool(X10,bot_bot_fun_a_bool)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_683_finite__empty__induct) ).

tff(f23616,plain,
    spl250_1136,
    inference(avatar_split_clause,[],[f5177,f23614]) ).

tff(f23614,plain,
    ( spl250_1136
  <=> ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK101(X0)),sK102(X0)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1136])]) ).

tff(f5177,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK101(X0)),sK102(X0)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(cnf_transformation,[],[f3951]) ).

tff(f23612,plain,
    ( spl250_1135
    | ~ spl250_529
    | ~ spl250_543 ),
    inference(avatar_split_clause,[],[f12338,f10887,f10828,f23609]) ).

tff(f10828,plain,
    ( spl250_529
  <=> ! [X0: nat,X1: nat] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
        | ( hAPP_nat_nat(suc,sK125(X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_529])]) ).

tff(f10887,plain,
    ( spl250_543
  <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_543])]) ).

tff(f12338,plain,
    ( ( one_one_nat = hAPP_nat_nat(suc,sK125(one_one_nat)) )
    | ~ spl250_529
    | ~ spl250_543 ),
    inference(resolution,[],[f10889,f10829]) ).

tff(f10829,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
        | ( hAPP_nat_nat(suc,sK125(X1)) = X1 ) )
    | ~ spl250_529 ),
    inference(avatar_component_clause,[],[f10828]) ).

tff(f10889,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat))
    | ~ spl250_543 ),
    inference(avatar_component_clause,[],[f10887]) ).

tff(f23607,plain,
    spl250_1134,
    inference(avatar_split_clause,[],[f5145,f23605]) ).

tff(f23605,plain,
    ( spl250_1134
  <=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f921600141ol_nat(finite_card_pname,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1134])]) ).

tff(f5145,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f921600141ol_nat(finite_card_pname,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f2769]) ).

tff(f2769,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f921600141ol_nat(finite_card_pname,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(flattening,[],[f2768]) ).

tff(f2768,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f921600141ol_nat(finite_card_pname,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(ennf_transformation,[],[f1745]) ).

tff(f1745,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X0)),hAPP_f921600141ol_nat(finite_card_pname,X1))) ) ),
    inference(rectify,[],[f76]) ).

tff(f76,axiom,
    ! [X2: fun_pname_bool,X7: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X7))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X2)),hAPP_f921600141ol_nat(finite_card_pname,X7))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_card__mono) ).

tff(f23603,plain,
    spl250_1133,
    inference(avatar_split_clause,[],[f5140,f23601]) ).

tff(f23601,plain,
    ( spl250_1133
  <=> ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK96(X0)),sK97(X0)))
        | ~ hBOOL(hAPP_f1664156314l_bool(X0,X1))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1133])]) ).

tff(f5140,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK96(X0)),sK97(X0)))
      | ~ hBOOL(hAPP_f1664156314l_bool(X0,X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f3942]) ).

tff(f3942,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,sK97(X0)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK96(X0)),bot_bo844097828e_bool))))
        & hBOOL(hAPP_f1664156314l_bool(X0,sK97(X0)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK96(X0)),sK97(X0)))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK97(X0))) )
      | ~ hBOOL(hAPP_f1664156314l_bool(X0,X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK96,sK97])],[f2763,f3941]) ).

tff(f3941,plain,
    ! [X0: fun_fu1430349052l_bool] :
      ( ? [X2: pname,X3: fun_pname_bool] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X3),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool))))
          & hBOOL(hAPP_f1664156314l_bool(X0,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3)) )
     => ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,sK97(X0)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK96(X0)),bot_bo844097828e_bool))))
        & hBOOL(hAPP_f1664156314l_bool(X0,sK97(X0)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK96(X0)),sK97(X0)))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK97(X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f2763,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
      | ? [X2: pname,X3: fun_pname_bool] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X3),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool))))
          & hBOOL(hAPP_f1664156314l_bool(X0,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(X0,X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(flattening,[],[f2762]) ).

tff(f2762,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
      | ? [X2: pname,X3: fun_pname_bool] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X3),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool))))
          & hBOOL(hAPP_f1664156314l_bool(X0,X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(X0,X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(ennf_transformation,[],[f1742]) ).

tff(f1742,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
     => ( hBOOL(hAPP_f1664156314l_bool(X0,X1))
       => ( ! [X2: pname,X3: fun_pname_bool] :
              ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
             => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
               => ( hBOOL(hAPP_f1664156314l_bool(X0,X3))
                 => hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X3),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool)))) ) ) )
         => hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool)) ) ) ),
    inference(rectify,[],[f687]) ).

tff(f687,axiom,
    ! [X10: fun_fu1430349052l_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(X10,X2))
       => ( ! [X75: pname,X78: fun_pname_bool] :
              ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X78))
             => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X75),X78))
               => ( hBOOL(hAPP_f1664156314l_bool(X10,X78))
                 => hBOOL(hAPP_f1664156314l_bool(X10,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X78),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X75),bot_bo844097828e_bool)))) ) ) )
         => hBOOL(hAPP_f1664156314l_bool(X10,bot_bo844097828e_bool)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_686_finite__empty__induct) ).

tff(f23599,plain,
    spl250_1132,
    inference(avatar_split_clause,[],[f5136,f23597]) ).

tff(f23597,plain,
    ( spl250_1132
  <=> ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(X0,X1))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK94(X0)),sK95(X0)))
        | ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1132])]) ).

tff(f5136,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK94(X0)),sK95(X0)))
      | ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f3940]) ).

tff(f23595,plain,
    spl250_1131,
    inference(avatar_split_clause,[],[f5104,f23593]) ).

tff(f23593,plain,
    ( spl250_1131
  <=> ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1131])]) ).

tff(f5104,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(cnf_transformation,[],[f2731]) ).

tff(f2731,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(flattening,[],[f2730]) ).

tff(f2730,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(ennf_transformation,[],[f1717]) ).

tff(f1717,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X0)),hAPP_f696928925ol_nat(finite346522414t_bool,X1))) ) ),
    inference(rectify,[],[f73]) ).

tff(f73,axiom,
    ! [X2: fun_fu425979586l_bool,X7: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),X7))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X2)),hAPP_f696928925ol_nat(finite346522414t_bool,X7))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_card__mono) ).

tff(f23591,plain,
    spl250_1130,
    inference(avatar_split_clause,[],[f5103,f23589]) ).

tff(f23589,plain,
    ( spl250_1130
  <=> ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X0)),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1130])]) ).

tff(f5103,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X0)),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(cnf_transformation,[],[f2729]) ).

tff(f2729,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X0)),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(flattening,[],[f2728]) ).

tff(f2728,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X0)),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(ennf_transformation,[],[f1716]) ).

tff(f1716,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X0)),hAPP_f521865025ol_nat(finite1876863882t_bool,X1))) ) ),
    inference(rectify,[],[f72]) ).

tff(f72,axiom,
    ! [X2: fun_fu819804446l_bool,X7: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X7))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),X7))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X2)),hAPP_f521865025ol_nat(finite1876863882t_bool,X7))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_card__mono) ).

tff(f23587,plain,
    spl250_1129,
    inference(avatar_split_clause,[],[f5102,f23585]) ).

tff(f23585,plain,
    ( spl250_1129
  <=> ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1129])]) ).

tff(f5102,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(cnf_transformation,[],[f2727]) ).

tff(f2727,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(flattening,[],[f2726]) ).

tff(f2726,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(ennf_transformation,[],[f1715]) ).

tff(f1715,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X0)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1))) ) ),
    inference(rectify,[],[f74]) ).

tff(f74,axiom,
    ! [X2: fun_fu1430349052l_bool,X7: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),X7))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X2)),hAPP_f55526627ol_nat(finite1340463720e_bool,X7))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_card__mono) ).

tff(f23583,plain,
    spl250_1128,
    inference(avatar_split_clause,[],[f5101,f23581]) ).

tff(f23581,plain,
    ( spl250_1128
  <=> ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1128])]) ).

tff(f5101,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(cnf_transformation,[],[f2725]) ).

tff(f2725,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(flattening,[],[f2724]) ).

tff(f2724,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(ennf_transformation,[],[f1714]) ).

tff(f1714,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X0)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1))) ) ),
    inference(rectify,[],[f75]) ).

tff(f75,axiom,
    ! [X2: fun_fun_a_bool_bool,X7: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),X7))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X7))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_card__mono) ).

tff(f23579,plain,
    spl250_1127,
    inference(avatar_split_clause,[],[f5051,f23577]) ).

tff(f23577,plain,
    ( spl250_1127
  <=> ! [X0: nat,X1: fun_nat_bool,X3: nat] :
        ( ~ hBOOL(hAPP_nat_bool(X1,X3))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),sK90(X0,X1)))
        | ~ hBOOL(hAPP_nat_bool(X1,X0))
        | hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1127])]) ).

tff(f5051,plain,
    ! [X3: nat,X0: nat,X1: fun_nat_bool] :
      ( ~ hBOOL(hAPP_nat_bool(X1,X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),sK90(X0,X1)))
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
    inference(cnf_transformation,[],[f3932]) ).

tff(f3932,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( ( hBOOL(hAPP_nat_bool(X1,sK90(X0,X1)))
        & ! [X3: nat] :
            ( ~ hBOOL(hAPP_nat_bool(X1,X3))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),sK90(X0,X1))) )
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK90(X0,X1)),X0)) )
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK90])],[f2671,f3931]) ).

tff(f3931,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( hBOOL(hAPP_nat_bool(X1,X2))
          & ! [X3: nat] :
              ( ~ hBOOL(hAPP_nat_bool(X1,X3))
              | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) )
     => ( hBOOL(hAPP_nat_bool(X1,sK90(X0,X1)))
        & ! [X3: nat] :
            ( ~ hBOOL(hAPP_nat_bool(X1,X3))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),sK90(X0,X1))) )
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK90(X0,X1)),X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f2671,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( hBOOL(hAPP_nat_bool(X1,X2))
          & ! [X3: nat] :
              ( ~ hBOOL(hAPP_nat_bool(X1,X3))
              | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) )
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
    inference(flattening,[],[f2670]) ).

tff(f2670,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( hBOOL(hAPP_nat_bool(X1,X2))
          & ! [X3: nat] :
              ( ~ hBOOL(hAPP_nat_bool(X1,X3))
              | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) )
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
    inference(ennf_transformation,[],[f1669]) ).

tff(f1669,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
     => ( hBOOL(hAPP_nat_bool(X1,X0))
       => ? [X2: nat] :
            ( hBOOL(hAPP_nat_bool(X1,X2))
            & ! [X3: nat] :
                ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2))
               => ~ hBOOL(hAPP_nat_bool(X1,X3)) )
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0)) ) ) ),
    inference(rectify,[],[f971]) ).

tff(f971,axiom,
    ! [X14: nat,X10: fun_nat_bool] :
      ( ~ hBOOL(hAPP_nat_bool(X10,zero_zero_nat))
     => ( hBOOL(hAPP_nat_bool(X10,X14))
       => ? [X116: nat] :
            ( hBOOL(hAPP_nat_bool(X10,X116))
            & ! [X123: nat] :
                ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X123),X116))
               => ~ hBOOL(hAPP_nat_bool(X10,X123)) )
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X116),X14)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_970_ex__least__nat__le) ).

tff(f23575,plain,
    spl250_1126,
    inference(avatar_split_clause,[],[f5048,f23573]) ).

tff(f23573,plain,
    ( spl250_1126
  <=> ! [X0: nat,X1: fun_nat_bool,X3: nat] :
        ( ~ hBOOL(hAPP_nat_bool(X1,X3))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),sK89(X0,X1)))
        | ~ hBOOL(hAPP_nat_bool(X1,X0))
        | hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1126])]) ).

tff(f5048,plain,
    ! [X3: nat,X0: nat,X1: fun_nat_bool] :
      ( ~ hBOOL(hAPP_nat_bool(X1,X3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),sK89(X0,X1)))
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
    inference(cnf_transformation,[],[f3930]) ).

tff(f3930,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK89(X0,X1)),one_one_nat)))
        & ! [X3: nat] :
            ( ~ hBOOL(hAPP_nat_bool(X1,X3))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),sK89(X0,X1))) )
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK89(X0,X1)),X0)) )
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK89])],[f2669,f3929]) ).

tff(f3929,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),one_one_nat)))
          & ! [X3: nat] :
              ( ~ hBOOL(hAPP_nat_bool(X1,X3))
              | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0)) )
     => ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK89(X0,X1)),one_one_nat)))
        & ! [X3: nat] :
            ( ~ hBOOL(hAPP_nat_bool(X1,X3))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),sK89(X0,X1))) )
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK89(X0,X1)),X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f2669,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),one_one_nat)))
          & ! [X3: nat] :
              ( ~ hBOOL(hAPP_nat_bool(X1,X3))
              | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0)) )
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
    inference(flattening,[],[f2668]) ).

tff(f2668,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),one_one_nat)))
          & ! [X3: nat] :
              ( ~ hBOOL(hAPP_nat_bool(X1,X3))
              | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0)) )
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
    inference(ennf_transformation,[],[f1668]) ).

tff(f1668,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
     => ( hBOOL(hAPP_nat_bool(X1,X0))
       => ? [X2: nat] :
            ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),one_one_nat)))
            & ! [X3: nat] :
                ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
               => ~ hBOOL(hAPP_nat_bool(X1,X3)) )
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0)) ) ) ),
    inference(rectify,[],[f970]) ).

tff(f970,axiom,
    ! [X14: nat,X10: fun_nat_bool] :
      ( ~ hBOOL(hAPP_nat_bool(X10,zero_zero_nat))
     => ( hBOOL(hAPP_nat_bool(X10,X14))
       => ? [X116: nat] :
            ( hBOOL(hAPP_nat_bool(X10,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X116),one_one_nat)))
            & ! [X123: nat] :
                ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X123),X116))
               => ~ hBOOL(hAPP_nat_bool(X10,X123)) )
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X116),X14)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_969_ex__least__nat__less) ).

tff(f23570,plain,
    spl250_1125,
    inference(avatar_split_clause,[],[f4953,f23568]) ).

tff(f4953,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)),X0)) )
      | ( zero_zero_nat = X1 ) ),
    inference(cnf_transformation,[],[f2614]) ).

tff(f2614,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)),X0)) )
        | ( zero_zero_nat = X1 ) )
      & ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0) = X0 )
        | ( zero_zero_nat != X1 ) ) ),
    inference(ennf_transformation,[],[f1597]) ).

tff(f1597,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( zero_zero_nat != X1 )
       => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)),X0)) ) )
      & ( ( zero_zero_nat = X1 )
       => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0) = X0 ) ) ),
    inference(rectify,[],[f969]) ).

tff(f969,axiom,
    ! [X11: nat,X12: nat] :
      ( ( ( zero_zero_nat != X12 )
       => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X12),X11) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X12),one_one_nat)),X11)) ) )
      & ( ( zero_zero_nat = X12 )
       => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X12),X11) = X11 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_968_add__eq__if) ).

tff(f23566,plain,
    ( spl250_1124
    | ~ spl250_428
    | ~ spl250_543 ),
    inference(avatar_split_clause,[],[f12336,f10887,f10403,f23563]) ).

tff(f10403,plain,
    ( spl250_428
  <=> ! [X0: nat] :
        ( ( hAPP_nat_nat(suc,sK35(X0)) = X0 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_428])]) ).

tff(f12336,plain,
    ( ( one_one_nat = hAPP_nat_nat(suc,sK35(one_one_nat)) )
    | ~ spl250_428
    | ~ spl250_543 ),
    inference(resolution,[],[f10889,f10404]) ).

tff(f10404,plain,
    ( ! [X0: nat] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | ( hAPP_nat_nat(suc,sK35(X0)) = X0 ) )
    | ~ spl250_428 ),
    inference(avatar_component_clause,[],[f10403]) ).

tff(f23561,plain,
    spl250_1123,
    inference(avatar_split_clause,[],[f4945,f23559]) ).

tff(f23559,plain,
    ( spl250_1123
  <=> ! [X0: fun_a_bool,X1: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X1) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)),cOMBB_bool_bool_a(fNot,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1123])]) ).

tff(f4945,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X1) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)),cOMBB_bool_bool_a(fNot,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)))) ),
    inference(cnf_transformation,[],[f1593]) ).

tff(f1593,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X1) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X0)),cOMBB_bool_bool_a(fNot,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)))) ),
    inference(rectify,[],[f727]) ).

tff(f727,axiom,
    ! [X2: fun_a_bool,X7: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X7) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)),cOMBB_bool_bool_a(fNot,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X7)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_726_set__diff__eq) ).

tff(f23557,plain,
    spl250_1122,
    inference(avatar_split_clause,[],[f4944,f23555]) ).

tff(f23555,plain,
    ( spl250_1122
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0)),cOMBB_bool_bool_nat(fNot,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1122])]) ).

tff(f4944,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0)),cOMBB_bool_bool_nat(fNot,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)))) ),
    inference(cnf_transformation,[],[f1592]) ).

tff(f1592,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X0)),cOMBB_bool_bool_nat(fNot,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)))) ),
    inference(rectify,[],[f726]) ).

tff(f726,axiom,
    ! [X2: fun_nat_bool,X7: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X7) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2)),cOMBB_bool_bool_nat(fNot,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X7)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_725_set__diff__eq) ).

tff(f23553,plain,
    spl250_1121,
    inference(avatar_split_clause,[],[f4943,f23551]) ).

tff(f23551,plain,
    ( spl250_1121
  <=> ! [X0: fun_int_bool,X1: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X0)),cOMBB_bool_bool_int(fNot,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1121])]) ).

tff(f4943,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X0)),cOMBB_bool_bool_int(fNot,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)))) ),
    inference(cnf_transformation,[],[f1591]) ).

tff(f1591,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X0)),cOMBB_bool_bool_int(fNot,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)))) ),
    inference(rectify,[],[f725]) ).

tff(f725,axiom,
    ! [X2: fun_int_bool,X7: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X7) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X2)),cOMBB_bool_bool_int(fNot,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X7)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_724_set__diff__eq) ).

tff(f23549,plain,
    spl250_1120,
    inference(avatar_split_clause,[],[f4942,f23547]) ).

tff(f23547,plain,
    ( spl250_1120
  <=> ! [X0: fun_pname_bool,X1: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X1) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)),cOMBB_647938656_pname(fNot,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1120])]) ).

tff(f4942,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X1) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)),cOMBB_647938656_pname(fNot,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)))) ),
    inference(cnf_transformation,[],[f1590]) ).

tff(f1590,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X1) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X0)),cOMBB_647938656_pname(fNot,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)))) ),
    inference(rectify,[],[f728]) ).

tff(f728,axiom,
    ! [X2: fun_pname_bool,X7: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X7) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)),cOMBB_647938656_pname(fNot,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X7)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_727_set__diff__eq) ).

tff(f23387,plain,
    ( spl250_1119
    | ~ spl250_442
    | ~ spl250_543 ),
    inference(avatar_split_clause,[],[f12335,f10887,f10459,f23384]) ).

tff(f10459,plain,
    ( spl250_442
  <=> ! [X0: nat] :
        ( ( hAPP_nat_nat(suc,sK62(X0)) = X0 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_442])]) ).

tff(f12335,plain,
    ( ( one_one_nat = hAPP_nat_nat(suc,sK62(one_one_nat)) )
    | ~ spl250_442
    | ~ spl250_543 ),
    inference(resolution,[],[f10889,f10460]) ).

tff(f10460,plain,
    ( ! [X0: nat] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | ( hAPP_nat_nat(suc,sK62(X0)) = X0 ) )
    | ~ spl250_442 ),
    inference(avatar_component_clause,[],[f10459]) ).

tff(f22900,plain,
    ( spl250_1118
    | ~ spl250_85
    | ~ spl250_413 ),
    inference(avatar_split_clause,[],[f10624,f10214,f7733,f22898]) ).

tff(f22898,plain,
    ( spl250_1118
  <=> ! [X0: fun_a_bool] : ( fTrue = hAPP_fun_a_bool_bool(p(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1118])]) ).

tff(f10214,plain,
    ( spl250_413
  <=> ! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(p(X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_413])]) ).

tff(f10624,plain,
    ( ! [X0: fun_a_bool] : ( fTrue = hAPP_fun_a_bool_bool(p(X0),X0) )
    | ~ spl250_85
    | ~ spl250_413 ),
    inference(resolution,[],[f10215,f7734]) ).

tff(f10215,plain,
    ( ! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(p(X0),X0))
    | ~ spl250_413 ),
    inference(avatar_component_clause,[],[f10214]) ).

tff(f22789,plain,
    ( spl250_1117
    | ~ spl250_85
    | ~ spl250_412 ),
    inference(avatar_split_clause,[],[f10582,f10102,f7733,f22787]) ).

tff(f22787,plain,
    ( spl250_1117
  <=> ! [X0: fun_a_bool] : ( fTrue = hAPP_fun_a_bool_bool(p(X0),bot_bot_fun_a_bool) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1117])]) ).

tff(f10102,plain,
    ( spl250_412
  <=> ! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(p(X0),bot_bot_fun_a_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_412])]) ).

tff(f10582,plain,
    ( ! [X0: fun_a_bool] : ( fTrue = hAPP_fun_a_bool_bool(p(X0),bot_bot_fun_a_bool) )
    | ~ spl250_85
    | ~ spl250_412 ),
    inference(resolution,[],[f10103,f7734]) ).

tff(f10103,plain,
    ( ! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(p(X0),bot_bot_fun_a_bool))
    | ~ spl250_412 ),
    inference(avatar_component_clause,[],[f10102]) ).

tff(f22595,plain,
    ( spl250_1116
    | ~ spl250_85
    | ~ spl250_411 ),
    inference(avatar_split_clause,[],[f10028,f9900,f7733,f22592]) ).

tff(f22592,plain,
    ( spl250_1116
  <=> ( fTrue = wt(the_com(body(pn))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1116])]) ).

tff(f9900,plain,
    ( spl250_411
  <=> hBOOL(wt(the_com(body(pn)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_411])]) ).

tff(f10028,plain,
    ( ( fTrue = wt(the_com(body(pn))) )
    | ~ spl250_85
    | ~ spl250_411 ),
    inference(resolution,[],[f9902,f7734]) ).

tff(f9902,plain,
    ( hBOOL(wt(the_com(body(pn))))
    | ~ spl250_411 ),
    inference(avatar_component_clause,[],[f9900]) ).

tff(f21667,plain,
    spl250_1115,
    inference(avatar_split_clause,[],[f7203,f21665]) ).

tff(f21665,plain,
    ( spl250_1115
  <=> ! [X2: nat,X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1115])]) ).

tff(f7203,plain,
    ! [X2: nat,X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)) ),
    inference(forward_demodulation,[],[f5756,f5755]) ).

tff(f5755,plain,
    ! [X2: nat,X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f2131]) ).

tff(f2131,plain,
    ! [X0: nat,X1: nat,X2: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)) ),
    inference(rectify,[],[f836]) ).

tff(f836,axiom,
    ! [X20: nat,X21: nat,X19: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X20),X21)),X19) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X20),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X21),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_835_diff__diff__left) ).

tff(f5756,plain,
    ! [X2: nat,X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X2)),X1) ),
    inference(cnf_transformation,[],[f2132]) ).

tff(f2132,plain,
    ! [X0: nat,X1: nat,X2: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X2)),X1) ),
    inference(rectify,[],[f132]) ).

tff(f132,axiom,
    ! [X20: nat,X21: nat,X19: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X20),X21)),X19) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X20),X19)),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_diff__commute) ).

tff(f21663,plain,
    spl250_1114,
    inference(avatar_split_clause,[],[f7103,f21661]) ).

tff(f21661,plain,
    ( spl250_1114
  <=> ! [X0: nat,X1: fun_nat_nat] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,X1)),X0)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK126(X1)),hAPP_nat_nat(X1,sK126(X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1114])]) ).

tff(f7103,plain,
    ! [X0: nat,X1: fun_nat_nat] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,X1)),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK126(X1)),hAPP_nat_nat(X1,sK126(X1)))) ),
    inference(forward_demodulation,[],[f5416,f4588]) ).

tff(f5416,plain,
    ! [X0: nat,X1: fun_nat_nat] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,X1)),X0))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK126(X1)),hAPP_nat_nat(X1,sK126(X1)))) ),
    inference(cnf_transformation,[],[f4000]) ).

tff(f4000,plain,
    ! [X0: nat,X1: fun_nat_nat] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,X1)),X0))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK126(X1)),hAPP_nat_nat(X1,sK126(X1)))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK126])],[f3056,f3999]) ).

tff(f3999,plain,
    ! [X1: fun_nat_nat] :
      ( ? [X2: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_nat_nat(X1,X2)))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK126(X1)),hAPP_nat_nat(X1,sK126(X1)))) ),
    introduced(choice_axiom,[]) ).

tff(f3056,plain,
    ! [X0: nat,X1: fun_nat_nat] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,X1)),X0))))
      | ? [X2: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_nat_nat(X1,X2))) ),
    inference(ennf_transformation,[],[f1950]) ).

tff(f1950,plain,
    ! [X0: nat,X1: fun_nat_nat] :
      ( ! [X2: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_nat_nat(X1,X2)))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,X1)),X0)))) ),
    inference(rectify,[],[f696]) ).

tff(f696,axiom,
    ! [X79: nat,X6: fun_nat_nat] :
      ( ! [X26: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X26),hAPP_nat_nat(X6,X26)))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,X6)),X79)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_695_finite__less__ub) ).

tff(f21659,plain,
    spl250_1113,
    inference(avatar_split_clause,[],[f7062,f21657]) ).

tff(f21657,plain,
    ( spl250_1113
  <=> ! [X0: nat,X1: fun_nat_bool] :
        ( ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),hAPP_n1699378549t_bool(fequal_nat,X0)) = X1 )
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1113])]) ).

tff(f7062,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),hAPP_n1699378549t_bool(fequal_nat,X0)) = X1 )
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ),
    inference(forward_demodulation,[],[f5284,f6931]) ).

tff(f5284,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)) = X1 )
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2904]) ).

tff(f2904,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)) = X1 )
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1840]) ).

tff(f1840,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
     => ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)) = X1 ) ),
    inference(rectify,[],[f551]) ).

tff(f551,axiom,
    ! [X8: nat,X2: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X2))
     => ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X2)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),bot_bot_fun_nat_bool)) = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_550_Diff__insert__absorb) ).

tff(f21655,plain,
    spl250_1112,
    inference(avatar_split_clause,[],[f7061,f21653]) ).

tff(f21653,plain,
    ( spl250_1112
  <=> ! [X0: int,X1: fun_int_bool] :
        ( ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),hAPP_i1948725293t_bool(fequal_int,X0)) = X1 )
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1112])]) ).

tff(f7061,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),hAPP_i1948725293t_bool(fequal_int,X0)) = X1 )
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ),
    inference(forward_demodulation,[],[f5283,f6930]) ).

tff(f5283,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)) = X1 )
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2903]) ).

tff(f2903,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)) = X1 )
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ),
    inference(ennf_transformation,[],[f1839]) ).

tff(f1839,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
     => ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)) = X1 ) ),
    inference(rectify,[],[f550]) ).

tff(f550,axiom,
    ! [X8: int,X2: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X2))
     => ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X2)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),bot_bot_fun_int_bool)) = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_549_Diff__insert__absorb) ).

tff(f21651,plain,
    spl250_1111,
    inference(avatar_split_clause,[],[f7008,f21649]) ).

tff(f21649,plain,
    ( spl250_1111
  <=> ! [X0: fun_a_bool,X1: com] :
        ( hBOOL(hAPP_fun_a_bool_bool(p(X0),collect_a(hAPP_a_fun_a_bool(fequal_a,mgt(X1)))))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK77(X0)),u))
        | ~ hBOOL(wt(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1111])]) ).

tff(f7008,plain,
    ! [X0: fun_a_bool,X1: com] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(X0),collect_a(hAPP_a_fun_a_bool(fequal_a,mgt(X1)))))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK77(X0)),u))
      | ~ hBOOL(wt(X1)) ),
    inference(forward_demodulation,[],[f5023,f4680]) ).

tff(f5023,plain,
    ! [X0: fun_a_bool,X1: com] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(X1)),bot_bot_fun_a_bool)))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK77(X0)),u))
      | ~ hBOOL(wt(X1)) ),
    inference(cnf_transformation,[],[f3906]) ).

tff(f3906,plain,
    ! [X0: fun_a_bool,X1: com] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(X1)),bot_bot_fun_a_bool)))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(p(X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,sK77(X0))),bot_bot_fun_a_bool)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK77(X0)),u)) )
      | ~ hBOOL(wt(X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK77])],[f2645,f3905]) ).

tff(f3905,plain,
    ! [X0: fun_a_bool] :
      ( ? [X2: pname] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(p(X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,X2)),bot_bot_fun_a_bool)))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),u)) )
     => ( ~ hBOOL(hAPP_fun_a_bool_bool(p(X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,sK77(X0))),bot_bot_fun_a_bool)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK77(X0)),u)) ) ),
    introduced(choice_axiom,[]) ).

tff(f2645,plain,
    ! [X0: fun_a_bool,X1: com] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(X1)),bot_bot_fun_a_bool)))
      | ? [X2: pname] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(p(X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,X2)),bot_bot_fun_a_bool)))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),u)) )
      | ~ hBOOL(wt(X1)) ),
    inference(flattening,[],[f2644]) ).

tff(f2644,plain,
    ! [X0: fun_a_bool,X1: com] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(X1)),bot_bot_fun_a_bool)))
      | ? [X2: pname] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(p(X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,X2)),bot_bot_fun_a_bool)))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),u)) )
      | ~ hBOOL(wt(X1)) ),
    inference(ennf_transformation,[],[f1656]) ).

tff(f1656,plain,
    ! [X0: fun_a_bool,X1: com] :
      ( hBOOL(wt(X1))
     => ( ! [X2: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),u))
           => hBOOL(hAPP_fun_a_bool_bool(p(X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,X2)),bot_bot_fun_a_bool))) )
       => hBOOL(hAPP_fun_a_bool_bool(p(X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(X1)),bot_bot_fun_a_bool))) ) ),
    inference(rectify,[],[f488]) ).

tff(f488,axiom,
    ! [X1: fun_a_bool,X29: com] :
      ( hBOOL(wt(X29))
     => ( ! [X27: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X27),u))
           => hBOOL(hAPP_fun_a_bool_bool(p(X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,X27)),bot_bot_fun_a_bool))) )
       => hBOOL(hAPP_fun_a_bool_bool(p(X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(X29)),bot_bot_fun_a_bool))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_487_assms_I3_J) ).

tff(f21647,plain,
    ( spl250_1110
    | ~ spl250_718
    | ~ spl250_958 ),
    inference(avatar_split_clause,[],[f21430,f18152,f14219,f21645]) ).

tff(f21645,plain,
    ( spl250_1110
  <=> ! [X0: fun_pname_bool] : ~ sP8(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1110])]) ).

tff(f14219,plain,
    ( spl250_718
  <=> ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK160(X0,X1)),sK161(X0,X1))))
        | ~ sP8(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_718])]) ).

tff(f18152,plain,
    ( spl250_958
  <=> ! [X0: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_958])]) ).

tff(f21430,plain,
    ( ! [X0: fun_pname_bool] : ~ sP8(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),X0)
    | ~ spl250_718
    | ~ spl250_958 ),
    inference(resolution,[],[f18153,f14220]) ).

tff(f14220,plain,
    ( ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK160(X0,X1)),sK161(X0,X1))))
        | ~ sP8(X0,X1) )
    | ~ spl250_718 ),
    inference(avatar_component_clause,[],[f14219]) ).

tff(f18153,plain,
    ( ! [X0: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),X0))
    | ~ spl250_958 ),
    inference(avatar_component_clause,[],[f18152]) ).

tff(f21643,plain,
    spl250_1109,
    inference(avatar_split_clause,[],[f6278,f21641]) ).

tff(f21641,plain,
    ( spl250_1109
  <=> ! [X2: fun_nat_bool,X0: fun_nat_int,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X0,X2)),X1))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X0,sK233(X0,X1,X2))),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1109])]) ).

tff(f6278,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_int,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X0,X2)),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X0,sK233(X0,X1,X2))),X1)) ),
    inference(cnf_transformation,[],[f4390]) ).

tff(f4390,plain,
    ! [X0: fun_nat_int,X1: fun_int_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X0,X2)),X1))
      | ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X0,sK233(X0,X1,X2))),X1))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK233(X0,X1,X2)),X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK233])],[f3579,f4389]) ).

tff(f4389,plain,
    ! [X0: fun_nat_int,X1: fun_int_bool,X2: fun_nat_bool] :
      ( ? [X3: nat] :
          ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X0,X3)),X1))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2)) )
     => ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X0,sK233(X0,X1,X2))),X1))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK233(X0,X1,X2)),X2)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3579,plain,
    ! [X0: fun_nat_int,X1: fun_int_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X0,X2)),X1))
      | ? [X3: nat] :
          ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X0,X3)),X1))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2)) ) ),
    inference(ennf_transformation,[],[f2465]) ).

tff(f2465,plain,
    ! [X0: fun_nat_int,X1: fun_int_bool,X2: fun_nat_bool] :
      ( ! [X3: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2))
         => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X0,X3)),X1)) )
     => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X0,X2)),X1)) ),
    inference(rectify,[],[f482]) ).

tff(f482,axiom,
    ! [X6: fun_nat_int,X7: fun_int_bool,X2: fun_nat_bool] :
      ( ! [X27: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X27),X2))
         => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X6,X27)),X7)) )
     => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X6,X2)),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_481_image__subsetI) ).

tff(f21639,plain,
    spl250_1108,
    inference(avatar_split_clause,[],[f6276,f21637]) ).

tff(f21637,plain,
    ( spl250_1108
  <=> ! [X2: fun_pname_bool,X0: fun_pname_a,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,sK232(X0,X1,X2))),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1108])]) ).

tff(f6276,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,sK232(X0,X1,X2))),X1)) ),
    inference(cnf_transformation,[],[f4388]) ).

tff(f4388,plain,
    ! [X0: fun_pname_a,X1: fun_a_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,sK232(X0,X1,X2))),X1))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK232(X0,X1,X2)),X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK232])],[f3578,f4387]) ).

tff(f4387,plain,
    ! [X0: fun_pname_a,X1: fun_a_bool,X2: fun_pname_bool] :
      ( ? [X3: pname] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X3)),X1))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2)) )
     => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,sK232(X0,X1,X2))),X1))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK232(X0,X1,X2)),X2)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3578,plain,
    ! [X0: fun_pname_a,X1: fun_a_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
      | ? [X3: pname] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X3)),X1))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2)) ) ),
    inference(ennf_transformation,[],[f2464]) ).

tff(f2464,plain,
    ! [X0: fun_pname_a,X1: fun_a_bool,X2: fun_pname_bool] :
      ( ! [X3: pname] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
         => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X3)),X1)) )
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1)) ),
    inference(rectify,[],[f483]) ).

tff(f483,axiom,
    ! [X6: fun_pname_a,X7: fun_a_bool,X2: fun_pname_bool] :
      ( ! [X27: pname] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X27),X2))
         => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X6,X27)),X7)) )
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X6,X2)),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_482_image__subsetI) ).

tff(f21635,plain,
    spl250_1107,
    inference(avatar_split_clause,[],[f6264,f21633]) ).

tff(f21633,plain,
    ( spl250_1107
  <=> ! [X2: nat,X0: fun_nat_fun_nat_bool,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
        | ( X1 = X2 )
        | sP17(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1107])]) ).

tff(f6264,plain,
    ! [X2: nat,X0: fun_nat_fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
      | ( X1 = X2 )
      | sP17(X1,X2,X0) ),
    inference(cnf_transformation,[],[f3718]) ).

tff(f3718,plain,
    ! [X0: fun_nat_fun_nat_bool,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) )
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
        & ( X1 = X2 ) )
      | sP17(X1,X2,X0) ),
    inference(definition_folding,[],[f3563,f3717]) ).

tff(f3717,plain,
    ! [X1: nat,X2: nat,X0: fun_nat_fun_nat_bool] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
      | ~ sP17(X1,X2,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).

tff(f3563,plain,
    ! [X0: fun_nat_fun_nat_bool,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) )
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
        & ( X1 = X2 ) )
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
    inference(flattening,[],[f3562]) ).

tff(f3562,plain,
    ! [X0: fun_nat_fun_nat_bool,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) )
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
        & ( X1 = X2 ) )
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
    inference(ennf_transformation,[],[f2456]) ).

tff(f2456,plain,
    ! [X0: fun_nat_fun_nat_bool,X1: nat,X2: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1)) )
     => ( ( ( X1 = X2 )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1)) )
       => ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
           => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1)) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1)) ) ) ),
    inference(rectify,[],[f865]) ).

tff(f865,axiom,
    ! [X10: fun_nat_fun_nat_bool,X22: nat,X14: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X14))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X10,X14),X22)) )
     => ( ( ( X14 = X22 )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X10,X14),X22)) )
       => ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),X22))
           => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X10,X14),X22)) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X10,X14),X22)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_864_nat__less__cases) ).

tff(f21631,plain,
    spl250_1106,
    inference(avatar_split_clause,[],[f6218,f21629]) ).

tff(f21629,plain,
    ( spl250_1106
  <=> ! [X2: fun_nat_bool,X0: nat,X1: nat] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
        | ( X0 = X1 )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1106])]) ).

tff(f6218,plain,
    ! [X2: fun_nat_bool,X0: nat,X1: nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))) ),
    inference(cnf_transformation,[],[f3529]) ).

tff(f3529,plain,
    ! [X0: nat,X1: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))) ),
    inference(flattening,[],[f3528]) ).

tff(f3528,plain,
    ! [X0: nat,X1: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))) ),
    inference(ennf_transformation,[],[f2429]) ).

tff(f2429,plain,
    ! [X0: nat,X1: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))
     => ( ( X0 != X1 )
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) ) ),
    inference(rectify,[],[f298]) ).

tff(f298,axiom,
    ! [X5: nat,X28: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X28),X2)))
     => ( ( X5 != X28 )
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_insertE) ).

tff(f21627,plain,
    spl250_1105,
    inference(avatar_split_clause,[],[f6213,f21625]) ).

tff(f21625,plain,
    ( spl250_1105
  <=> ! [X2: fun_int_bool,X0: int,X1: int] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2))
        | ( X0 = X1 )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1105])]) ).

tff(f6213,plain,
    ! [X2: fun_int_bool,X0: int,X1: int] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))) ),
    inference(cnf_transformation,[],[f3524]) ).

tff(f3524,plain,
    ! [X0: int,X1: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))) ),
    inference(flattening,[],[f3523]) ).

tff(f3523,plain,
    ! [X0: int,X1: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))) ),
    inference(ennf_transformation,[],[f2425]) ).

tff(f2425,plain,
    ! [X0: int,X1: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))
     => ( ( X0 != X1 )
       => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2)) ) ),
    inference(rectify,[],[f297]) ).

tff(f297,axiom,
    ! [X5: int,X28: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X28),X2)))
     => ( ( X5 != X28 )
       => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_insertE) ).

tff(f21623,plain,
    spl250_1104,
    inference(avatar_split_clause,[],[f6208,f21621]) ).

tff(f21621,plain,
    ( spl250_1104
  <=> ! [X2: fun_a_bool,X0: x_a,X1: x_a] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
        | ( X0 = X1 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1104])]) ).

tff(f6208,plain,
    ! [X2: fun_a_bool,X0: x_a,X1: x_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))) ),
    inference(cnf_transformation,[],[f3519]) ).

tff(f3519,plain,
    ! [X0: x_a,X1: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))) ),
    inference(flattening,[],[f3518]) ).

tff(f3518,plain,
    ! [X0: x_a,X1: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))) ),
    inference(ennf_transformation,[],[f2421]) ).

tff(f2421,plain,
    ! [X0: x_a,X1: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))
     => ( ( X0 != X1 )
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ) ),
    inference(rectify,[],[f296]) ).

tff(f296,axiom,
    ! [X5: x_a,X28: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X28),X2)))
     => ( ( X5 != X28 )
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_insertE) ).

tff(f21619,plain,
    spl250_1103,
    inference(avatar_split_clause,[],[f6203,f21617]) ).

tff(f21617,plain,
    ( spl250_1103
  <=> ! [X2: fun_pname_bool,X0: pname,X1: pname] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
        | ( X0 = X1 )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1103])]) ).

tff(f6203,plain,
    ! [X2: fun_pname_bool,X0: pname,X1: pname] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))) ),
    inference(cnf_transformation,[],[f3514]) ).

tff(f3514,plain,
    ! [X0: pname,X1: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))) ),
    inference(flattening,[],[f3513]) ).

tff(f3513,plain,
    ! [X0: pname,X1: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))) ),
    inference(ennf_transformation,[],[f2417]) ).

tff(f2417,plain,
    ! [X0: pname,X1: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))
     => ( ( X0 != X1 )
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) ) ),
    inference(rectify,[],[f299]) ).

tff(f299,axiom,
    ! [X5: pname,X28: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X28),X2)))
     => ( ( X5 != X28 )
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_insertE) ).

tff(f21615,plain,
    spl250_1102,
    inference(avatar_split_clause,[],[f6015,f21613]) ).

tff(f21613,plain,
    ( spl250_1102
  <=> ! [X2: nat,X0: nat,X1: fun_nat_bool] :
        ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0)))
        | hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK207(X1))))
        | ~ hBOOL(hAPP_nat_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1102])]) ).

tff(f6015,plain,
    ! [X2: nat,X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0)))
      | hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK207(X1))))
      | ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f4304]) ).

tff(f4304,plain,
    ! [X0: nat,X1: fun_nat_bool,X2: nat] :
      ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0)))
      | ( ~ hBOOL(hAPP_nat_bool(X1,sK207(X1)))
        & hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK207(X1)))) )
      | ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK207])],[f3291,f4303]) ).

tff(f4303,plain,
    ! [X1: fun_nat_bool] :
      ( ? [X3: nat] :
          ( ~ hBOOL(hAPP_nat_bool(X1,X3))
          & hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,X3))) )
     => ( ~ hBOOL(hAPP_nat_bool(X1,sK207(X1)))
        & hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK207(X1)))) ) ),
    introduced(choice_axiom,[]) ).

tff(f3291,plain,
    ! [X0: nat,X1: fun_nat_bool,X2: nat] :
      ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0)))
      | ? [X3: nat] :
          ( ~ hBOOL(hAPP_nat_bool(X1,X3))
          & hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,X3))) )
      | ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
    inference(flattening,[],[f3290]) ).

tff(f3290,plain,
    ! [X0: nat,X1: fun_nat_bool,X2: nat] :
      ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0)))
      | ? [X3: nat] :
          ( ~ hBOOL(hAPP_nat_bool(X1,X3))
          & hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,X3))) )
      | ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
    inference(ennf_transformation,[],[f2269]) ).

tff(f2269,plain,
    ! [X0: nat,X1: fun_nat_bool,X2: nat] :
      ( hBOOL(hAPP_nat_bool(X1,X2))
     => ( ! [X3: nat] :
            ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,X3)))
           => hBOOL(hAPP_nat_bool(X1,X3)) )
       => hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0))) ) ),
    inference(rectify,[],[f300]) ).

tff(f300,axiom,
    ! [X30: nat,X10: fun_nat_bool,X13: nat] :
      ( hBOOL(hAPP_nat_bool(X10,X13))
     => ( ! [X26: nat] :
            ( hBOOL(hAPP_nat_bool(X10,hAPP_nat_nat(suc,X26)))
           => hBOOL(hAPP_nat_bool(X10,X26)) )
       => hBOOL(hAPP_nat_bool(X10,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X13),X30))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_zero__induct__lemma) ).

tff(f21611,plain,
    spl250_1101,
    inference(avatar_split_clause,[],[f6012,f21609]) ).

tff(f21609,plain,
    ( spl250_1101
  <=> ! [X2: int,X0: int,X1: fun_int_bool] :
        ( hBOOL(hAPP_int_bool(X1,X0))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK206(X1,X2)),X2))
        | sP12(X1,X2)
        | ~ hBOOL(hAPP_int_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1101])]) ).

tff(f6012,plain,
    ! [X2: int,X0: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_int_bool(X1,X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK206(X1,X2)),X2))
      | sP12(X1,X2)
      | ~ hBOOL(hAPP_int_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f4302]) ).

tff(f21607,plain,
    spl250_1100,
    inference(avatar_split_clause,[],[f6000,f21605]) ).

tff(f21605,plain,
    ( spl250_1100
  <=> ! [X2: fun_nat_bool,X0: fun_a_nat,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK196(X0,X1,X2)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_a_nat(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1100])]) ).

tff(f6000,plain,
    ! [X2: fun_nat_bool,X0: fun_a_nat,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK196(X0,X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_a_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f4287]) ).

tff(f21603,plain,
    spl250_1099,
    inference(avatar_split_clause,[],[f5997,f21601]) ).

tff(f21601,plain,
    ( spl250_1099
  <=> ! [X2: fun_nat_bool,X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK195(X0,X1,X2)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1551609309ol_nat(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1099])]) ).

tff(f5997,plain,
    ! [X2: fun_nat_bool,X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK195(X0,X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1551609309ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f4285]) ).

tff(f21599,plain,
    spl250_1098,
    inference(avatar_split_clause,[],[f5994,f21597]) ).

tff(f21597,plain,
    ( spl250_1098
  <=> ! [X2: fun_nat_bool,X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK194(X0,X1,X2)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_496248727ol_nat(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1098])]) ).

tff(f5994,plain,
    ! [X2: fun_nat_bool,X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK194(X0,X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_496248727ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f4283]) ).

tff(f21595,plain,
    spl250_1097,
    inference(avatar_split_clause,[],[f5991,f21593]) ).

tff(f21593,plain,
    ( spl250_1097
  <=> ! [X2: fun_nat_bool,X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK193(X0,X1,X2)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_fun_a_bool_nat(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1097])]) ).

tff(f5991,plain,
    ! [X2: fun_nat_bool,X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK193(X0,X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_fun_a_bool_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f4281]) ).

tff(f21591,plain,
    spl250_1096,
    inference(avatar_split_clause,[],[f5988,f21589]) ).

tff(f21589,plain,
    ( spl250_1096
  <=> ! [X2: fun_nat_bool,X0: fun_fun_int_bool_nat,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK192(X0,X1,X2)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1431733819ol_nat(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1096])]) ).

tff(f5988,plain,
    ! [X2: fun_nat_bool,X0: fun_fun_int_bool_nat,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK192(X0,X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1431733819ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f4279]) ).

tff(f21587,plain,
    spl250_1095,
    inference(avatar_split_clause,[],[f5985,f21585]) ).

tff(f21585,plain,
    ( spl250_1095
  <=> ! [X2: fun_nat_bool,X0: fun_pname_nat,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK191(X0,X1,X2)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_pname_nat(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1095])]) ).

tff(f5985,plain,
    ! [X2: fun_nat_bool,X0: fun_pname_nat,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK191(X0,X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_pname_nat(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f4277]) ).

tff(f21583,plain,
    spl250_1094,
    inference(avatar_split_clause,[],[f5968,f21581]) ).

tff(f21581,plain,
    ( spl250_1094
  <=> ! [X2: fun_int_bool,X0: fun_nat_int,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK188(X0,X1,X2)))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_nat_int(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1094])]) ).

tff(f5968,plain,
    ! [X2: fun_int_bool,X0: fun_nat_int,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK188(X0,X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_nat_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f4271]) ).

tff(f21579,plain,
    spl250_1093,
    inference(avatar_split_clause,[],[f5965,f21577]) ).

tff(f21577,plain,
    ( spl250_1093
  <=> ! [X2: fun_int_bool,X0: fun_a_int,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK187(X0,X1,X2)))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_a_int(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1093])]) ).

tff(f5965,plain,
    ! [X2: fun_int_bool,X0: fun_a_int,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK187(X0,X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_a_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f4269]) ).

tff(f21575,plain,
    spl250_1092,
    inference(avatar_split_clause,[],[f5962,f21573]) ).

tff(f21573,plain,
    ( spl250_1092
  <=> ! [X2: fun_int_bool,X0: fun_fun_a_bool_int,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK186(X0,X1,X2)))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_fun_a_bool_int(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1092])]) ).

tff(f5962,plain,
    ! [X2: fun_int_bool,X0: fun_fun_a_bool_int,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK186(X0,X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_fun_a_bool_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f4267]) ).

tff(f21571,plain,
    spl250_1091,
    inference(avatar_split_clause,[],[f5959,f21569]) ).

tff(f21569,plain,
    ( spl250_1091
  <=> ! [X2: fun_int_bool,X0: fun_fu1830380701ol_int,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK185(X0,X1,X2)))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_41399353ol_int(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1091])]) ).

tff(f5959,plain,
    ! [X2: fun_int_bool,X0: fun_fu1830380701ol_int,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK185(X0,X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_41399353ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f4265]) ).

tff(f21567,plain,
    spl250_1090,
    inference(avatar_split_clause,[],[f5956,f21565]) ).

tff(f21565,plain,
    ( spl250_1090
  <=> ! [X2: fun_int_bool,X0: fun_fun_nat_bool_int,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK184(X0,X1,X2)))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_1133522419ol_int(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1090])]) ).

tff(f5956,plain,
    ! [X2: fun_int_bool,X0: fun_fun_nat_bool_int,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK184(X0,X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_1133522419ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f4263]) ).

tff(f21562,plain,
    spl250_1089,
    inference(avatar_split_clause,[],[f5953,f21560]) ).

tff(f21560,plain,
    ( spl250_1089
  <=> ! [X2: fun_int_bool,X0: fun_fun_int_bool_int,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK183(X0,X1,X2)))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_2069007511ol_int(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1089])]) ).

tff(f5953,plain,
    ! [X2: fun_int_bool,X0: fun_fun_int_bool_int,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK183(X0,X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_2069007511ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f4261]) ).

tff(f21558,plain,
    spl250_1088,
    inference(avatar_split_clause,[],[f5950,f21556]) ).

tff(f21556,plain,
    ( spl250_1088
  <=> ! [X2: fun_int_bool,X0: fun_pname_int,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK182(X0,X1,X2)))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_pname_int(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1088])]) ).

tff(f5950,plain,
    ! [X2: fun_int_bool,X0: fun_pname_int,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK182(X0,X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_pname_int(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f4259]) ).

tff(f21554,plain,
    spl250_1087,
    inference(avatar_split_clause,[],[f5932,f21552]) ).

tff(f21552,plain,
    ( spl250_1087
  <=> ! [X2: fun_a_bool,X0: fun_pname_a,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK179(X0,X1,X2)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1087])]) ).

tff(f5932,plain,
    ! [X2: fun_a_bool,X0: fun_pname_a,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK179(X0,X1,X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4253]) ).

tff(f21550,plain,
    spl250_1086,
    inference(avatar_split_clause,[],[f5929,f21548]) ).

tff(f21548,plain,
    ( spl250_1086
  <=> ! [X2: fun_a_bool,X0: fun_int_a,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK178(X0,X1,X2)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_int_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1086])]) ).

tff(f5929,plain,
    ! [X2: fun_a_bool,X0: fun_int_a,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK178(X0,X1,X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_int_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4251]) ).

tff(f21546,plain,
    spl250_1085,
    inference(avatar_split_clause,[],[f5926,f21544]) ).

tff(f21544,plain,
    ( spl250_1085
  <=> ! [X2: fun_a_bool,X0: fun_nat_a,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK177(X0,X1,X2)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_nat_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1085])]) ).

tff(f5926,plain,
    ! [X2: fun_a_bool,X0: fun_nat_a,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK177(X0,X1,X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_nat_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4249]) ).

tff(f21542,plain,
    spl250_1084,
    inference(avatar_split_clause,[],[f5923,f21540]) ).

tff(f21540,plain,
    ( spl250_1084
  <=> ! [X2: fun_a_bool,X0: fun_a_a,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK176(X0,X1,X2)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_a_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1084])]) ).

tff(f5923,plain,
    ! [X2: fun_a_bool,X0: fun_a_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK176(X0,X1,X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_a_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4247]) ).

tff(f21538,plain,
    spl250_1083,
    inference(avatar_split_clause,[],[f5920,f21536]) ).

tff(f21536,plain,
    ( spl250_1083
  <=> ! [X2: fun_a_bool,X0: fun_fun_nat_bool_a,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK175(X0,X1,X2)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_nat_bool_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1083])]) ).

tff(f5920,plain,
    ! [X2: fun_a_bool,X0: fun_fun_nat_bool_a,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK175(X0,X1,X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_nat_bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4245]) ).

tff(f21534,plain,
    spl250_1082,
    inference(avatar_split_clause,[],[f5917,f21532]) ).

tff(f21532,plain,
    ( spl250_1082
  <=> ! [X2: fun_a_bool,X0: fun_fun_int_bool_a,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK174(X0,X1,X2)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_int_bool_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1082])]) ).

tff(f5917,plain,
    ! [X2: fun_a_bool,X0: fun_fun_int_bool_a,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK174(X0,X1,X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_int_bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4243]) ).

tff(f21530,plain,
    spl250_1081,
    inference(avatar_split_clause,[],[f5914,f21528]) ).

tff(f21528,plain,
    ( spl250_1081
  <=> ! [X2: fun_a_bool,X0: fun_fun_pname_bool_a,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK173(X0,X1,X2)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_876012084bool_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1081])]) ).

tff(f5914,plain,
    ! [X2: fun_a_bool,X0: fun_fun_pname_bool_a,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK173(X0,X1,X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_876012084bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4241]) ).

tff(f21526,plain,
    spl250_1080,
    inference(avatar_split_clause,[],[f5911,f21524]) ).

tff(f21524,plain,
    ( spl250_1080
  <=> ! [X2: fun_a_bool,X0: fun_fun_a_bool_a,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK172(X0,X1,X2)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_a_bool_a(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1080])]) ).

tff(f5911,plain,
    ! [X2: fun_a_bool,X0: fun_fun_a_bool_a,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK172(X0,X1,X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_a_bool_a(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f4239]) ).

tff(f21522,plain,
    ( ~ spl250_1079
    | ~ spl250_453
    | ~ spl250_958 ),
    inference(avatar_split_clause,[],[f21429,f18152,f10503,f21519]) ).

tff(f21519,plain,
    ( spl250_1079
  <=> sP0(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1079])]) ).

tff(f10503,plain,
    ( spl250_453
  <=> ! [X0: fun_fu1430349052l_bool] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK91(X0)),sK92(X0))))
        | ~ sP0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_453])]) ).

tff(f21429,plain,
    ( ~ sP0(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool))
    | ~ spl250_453
    | ~ spl250_958 ),
    inference(resolution,[],[f18153,f10504]) ).

tff(f10504,plain,
    ( ! [X0: fun_fu1430349052l_bool] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK91(X0)),sK92(X0))))
        | ~ sP0(X0) )
    | ~ spl250_453 ),
    inference(avatar_component_clause,[],[f10503]) ).

tff(f21517,plain,
    spl250_1078,
    inference(avatar_split_clause,[],[f5898,f21515]) ).

tff(f21515,plain,
    ( spl250_1078
  <=> ! [X2: fun_pname_bool,X0: fun_a_pname,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK169(X0,X1,X2)))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_a_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1078])]) ).

tff(f5898,plain,
    ! [X2: fun_pname_bool,X0: fun_a_pname,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK169(X0,X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_a_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4233]) ).

tff(f21513,plain,
    spl250_1077,
    inference(avatar_split_clause,[],[f5895,f21511]) ).

tff(f21511,plain,
    ( spl250_1077
  <=> ! [X2: fun_pname_bool,X0: fun_nat_pname,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK168(X0,X1,X2)))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_nat_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1077])]) ).

tff(f5895,plain,
    ! [X2: fun_pname_bool,X0: fun_nat_pname,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK168(X0,X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_nat_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4231]) ).

tff(f21509,plain,
    spl250_1076,
    inference(avatar_split_clause,[],[f5892,f21507]) ).

tff(f21507,plain,
    ( spl250_1076
  <=> ! [X2: fun_pname_bool,X0: fun_int_pname,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK167(X0,X1,X2)))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_int_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1076])]) ).

tff(f5892,plain,
    ! [X2: fun_pname_bool,X0: fun_int_pname,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK167(X0,X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_int_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4229]) ).

tff(f21505,plain,
    spl250_1075,
    inference(avatar_split_clause,[],[f5889,f21503]) ).

tff(f21503,plain,
    ( spl250_1075
  <=> ! [X2: fun_pname_bool,X0: fun_pname_pname,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK166(X0,X1,X2)))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_pname_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1075])]) ).

tff(f5889,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK166(X0,X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_pname_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4227]) ).

tff(f21501,plain,
    spl250_1074,
    inference(avatar_split_clause,[],[f5886,f21499]) ).

tff(f21499,plain,
    ( spl250_1074
  <=> ! [X2: fun_pname_bool,X0: fun_fu1499449723_pname,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK165(X0,X1,X2)))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1283814551_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1074])]) ).

tff(f5886,plain,
    ! [X2: fun_pname_bool,X0: fun_fu1499449723_pname,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK165(X0,X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1283814551_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4225]) ).

tff(f21497,plain,
    spl250_1073,
    inference(avatar_split_clause,[],[f5883,f21495]) ).

tff(f21495,plain,
    ( spl250_1073
  <=> ! [X2: fun_pname_bool,X0: fun_fu953875929_pname,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK164(X0,X1,X2)))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_62782965_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1073])]) ).

tff(f5883,plain,
    ! [X2: fun_pname_bool,X0: fun_fu953875929_pname,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK164(X0,X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_62782965_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4223]) ).

tff(f21493,plain,
    spl250_1072,
    inference(avatar_split_clause,[],[f5880,f21491]) ).

tff(f21491,plain,
    ( spl250_1072
  <=> ! [X2: fun_pname_bool,X0: fun_fu665170229_pname,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK163(X0,X1,X2)))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1921560913_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1072])]) ).

tff(f5880,plain,
    ! [X2: fun_pname_bool,X0: fun_fu665170229_pname,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK163(X0,X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1921560913_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4221]) ).

tff(f21489,plain,
    spl250_1071,
    inference(avatar_split_clause,[],[f5877,f21487]) ).

tff(f21487,plain,
    ( spl250_1071
  <=> ! [X2: fun_pname_bool,X0: fun_fun_a_bool_pname,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK162(X0,X1,X2)))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1854862208_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1071])]) ).

tff(f5877,plain,
    ! [X2: fun_pname_bool,X0: fun_fun_a_bool_pname,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK162(X0,X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1854862208_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f4219]) ).

tff(f21485,plain,
    spl250_1070,
    inference(avatar_split_clause,[],[f5846,f21483]) ).

tff(f21483,plain,
    ( spl250_1070
  <=> ! [X2: fun_fu425979586l_bool,X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK159(X0,X1,X2)))
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_26036933t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1070])]) ).

tff(f5846,plain,
    ! [X2: fun_fu425979586l_bool,X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK159(X0,X1,X2)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_26036933t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(cnf_transformation,[],[f4213]) ).

tff(f21481,plain,
    spl250_1069,
    inference(avatar_split_clause,[],[f5843,f21479]) ).

tff(f21479,plain,
    ( spl250_1069
  <=> ! [X2: fun_fu1430349052l_bool,X0: fun_na936072029e_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK158(X0,X1,X2)))
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_1655916159e_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1069])]) ).

tff(f5843,plain,
    ! [X2: fun_fu1430349052l_bool,X0: fun_na936072029e_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK158(X0,X1,X2)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_1655916159e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(cnf_transformation,[],[f4211]) ).

tff(f21477,plain,
    ( spl250_1068
    | ~ spl250_663
    | ~ spl250_958 ),
    inference(avatar_split_clause,[],[f21428,f18152,f12700,f21475]) ).

tff(f21475,plain,
    ( spl250_1068
  <=> ! [X0: fun_pname_bool,X1: pname] : sP20(X0,bot_bo844097828e_bool,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1068])]) ).

tff(f12700,plain,
    ( spl250_663
  <=> ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
        ( sP20(X2,X0,X1)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_663])]) ).

tff(f21428,plain,
    ( ! [X0: fun_pname_bool,X1: pname] : sP20(X0,bot_bo844097828e_bool,X1)
    | ~ spl250_663
    | ~ spl250_958 ),
    inference(resolution,[],[f18153,f12701]) ).

tff(f12701,plain,
    ( ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))
        | sP20(X2,X0,X1) )
    | ~ spl250_663 ),
    inference(avatar_component_clause,[],[f12700]) ).

tff(f21473,plain,
    spl250_1067,
    inference(avatar_split_clause,[],[f5840,f21471]) ).

tff(f21471,plain,
    ( spl250_1067
  <=> ! [X2: fun_fu819804446l_bool,X0: fun_nat_fun_int_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK157(X0,X1,X2)))
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1556378401t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1067])]) ).

tff(f5840,plain,
    ! [X2: fun_fu819804446l_bool,X0: fun_nat_fun_int_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK157(X0,X1,X2)))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1556378401t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(cnf_transformation,[],[f4209]) ).

tff(f21469,plain,
    spl250_1066,
    inference(avatar_split_clause,[],[f5837,f21467]) ).

tff(f21467,plain,
    ( spl250_1066
  <=> ! [X2: fun_fun_a_bool_bool,X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK156(X0,X1,X2)))
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_nat_fun_a_bool(X0,X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1066])]) ).

tff(f5837,plain,
    ! [X2: fun_fun_a_bool_bool,X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK156(X0,X1,X2)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_nat_fun_a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(cnf_transformation,[],[f4207]) ).

tff(f21465,plain,
    spl250_1065,
    inference(avatar_split_clause,[],[f5834,f21463]) ).

tff(f21463,plain,
    ( spl250_1065
  <=> ! [X2: fun_fu1430349052l_bool,X0: fun_in2065004473e_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK155(X0,X1,X2)))
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_637364955e_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1065])]) ).

tff(f5834,plain,
    ! [X2: fun_fu1430349052l_bool,X0: fun_in2065004473e_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK155(X0,X1,X2)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_637364955e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(cnf_transformation,[],[f4205]) ).

tff(f21461,plain,
    spl250_1064,
    inference(avatar_split_clause,[],[f5831,f21459]) ).

tff(f21459,plain,
    ( spl250_1064
  <=> ! [X2: fun_fun_a_bool_bool,X0: fun_int_fun_a_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK154(X0,X1,X2)))
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_int_fun_a_bool(X0,X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1064])]) ).

tff(f5831,plain,
    ! [X2: fun_fun_a_bool_bool,X0: fun_int_fun_a_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK154(X0,X1,X2)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_int_fun_a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(cnf_transformation,[],[f4203]) ).

tff(f21457,plain,
    spl250_1063,
    inference(avatar_split_clause,[],[f5828,f21455]) ).

tff(f21455,plain,
    ( spl250_1063
  <=> ! [X2: fun_fu819804446l_bool,X0: fun_int_fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK153(X0,X1,X2)))
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_275383677t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1063])]) ).

tff(f5828,plain,
    ! [X2: fun_fu819804446l_bool,X0: fun_int_fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK153(X0,X1,X2)))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_275383677t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(cnf_transformation,[],[f4201]) ).

tff(f21453,plain,
    spl250_1062,
    inference(avatar_split_clause,[],[f5825,f21451]) ).

tff(f21451,plain,
    ( spl250_1062
  <=> ! [X2: fun_fu425979586l_bool,X0: fun_int_fun_nat_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK152(X0,X1,X2)))
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_892525857t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1062])]) ).

tff(f5825,plain,
    ! [X2: fun_fu425979586l_bool,X0: fun_int_fun_nat_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK152(X0,X1,X2)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_892525857t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(cnf_transformation,[],[f4199]) ).

tff(f21449,plain,
    spl250_1061,
    inference(avatar_split_clause,[],[f5822,f21447]) ).

tff(f21447,plain,
    ( spl250_1061
  <=> ! [X2: fun_fu1430349052l_bool,X0: fun_pn800050071e_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK151(X0,X1,X2)))
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_47868345e_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1061])]) ).

tff(f5822,plain,
    ! [X2: fun_fu1430349052l_bool,X0: fun_pn800050071e_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK151(X0,X1,X2)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_47868345e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(cnf_transformation,[],[f4197]) ).

tff(f21445,plain,
    spl250_1060,
    inference(avatar_split_clause,[],[f5819,f21443]) ).

tff(f21443,plain,
    ( spl250_1060
  <=> ! [X2: fun_fu819804446l_bool,X0: fun_pn665169337t_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK150(X0,X1,X2)))
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1512837979t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1060])]) ).

tff(f5819,plain,
    ! [X2: fun_fu819804446l_bool,X0: fun_pn665169337t_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK150(X0,X1,X2)))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1512837979t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(cnf_transformation,[],[f4195]) ).

tff(f21441,plain,
    spl250_1059,
    inference(avatar_split_clause,[],[f5816,f21439]) ).

tff(f21439,plain,
    ( spl250_1059
  <=> ! [X2: fun_fu425979586l_bool,X0: fun_pn406123357t_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK149(X0,X1,X2)))
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_2129980159t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1059])]) ).

tff(f5816,plain,
    ! [X2: fun_fu425979586l_bool,X0: fun_pn406123357t_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK149(X0,X1,X2)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_2129980159t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(cnf_transformation,[],[f4193]) ).

tff(f21437,plain,
    spl250_1058,
    inference(avatar_split_clause,[],[f5813,f21435]) ).

tff(f21435,plain,
    ( spl250_1058
  <=> ! [X2: fun_fun_a_bool_bool,X0: fun_pname_fun_a_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK148(X0,X1,X2)))
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_112932426a_bool(X0,X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1058])]) ).

tff(f5813,plain,
    ! [X2: fun_fun_a_bool_bool,X0: fun_pname_fun_a_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK148(X0,X1,X2)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_112932426a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(cnf_transformation,[],[f4191]) ).

tff(f21416,plain,
    spl250_1057,
    inference(avatar_split_clause,[],[f5810,f21414]) ).

tff(f21414,plain,
    ( spl250_1057
  <=> ! [X2: fun_fu819804446l_bool,X0: fun_a_fun_int_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK147(X0,X1,X2)))
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_a_fun_int_bool(X0,X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1057])]) ).

tff(f5810,plain,
    ! [X2: fun_fu819804446l_bool,X0: fun_a_fun_int_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK147(X0,X1,X2)))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_a_fun_int_bool(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(cnf_transformation,[],[f4189]) ).

tff(f21412,plain,
    spl250_1056,
    inference(avatar_split_clause,[],[f5807,f21410]) ).

tff(f21410,plain,
    ( spl250_1056
  <=> ! [X2: fun_fu425979586l_bool,X0: fun_a_fun_nat_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK146(X0,X1,X2)))
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_a_fun_nat_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1056])]) ).

tff(f5807,plain,
    ! [X2: fun_fu425979586l_bool,X0: fun_a_fun_nat_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK146(X0,X1,X2)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_a_fun_nat_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(cnf_transformation,[],[f4187]) ).

tff(f21408,plain,
    spl250_1055,
    inference(avatar_split_clause,[],[f5804,f21406]) ).

tff(f21406,plain,
    ( spl250_1055
  <=> ! [X2: fun_fu1430349052l_bool,X0: fun_a_fun_pname_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK145(X0,X1,X2)))
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_819518260e_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1055])]) ).

tff(f5804,plain,
    ! [X2: fun_fu1430349052l_bool,X0: fun_a_fun_pname_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK145(X0,X1,X2)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_819518260e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(cnf_transformation,[],[f4185]) ).

tff(f21404,plain,
    spl250_1054,
    inference(avatar_split_clause,[],[f5801,f21402]) ).

tff(f21402,plain,
    ( spl250_1054
  <=> ! [X2: fun_fun_a_bool_bool,X0: fun_a_fun_a_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK144(X0,X1,X2)))
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_a_fun_a_bool(X0,X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1054])]) ).

tff(f5801,plain,
    ! [X2: fun_fun_a_bool_bool,X0: fun_a_fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK144(X0,X1,X2)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_a_fun_a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(cnf_transformation,[],[f4183]) ).

tff(f21400,plain,
    spl250_1053,
    inference(avatar_split_clause,[],[f5757,f21398]) ).

tff(f21398,plain,
    ( spl250_1053
  <=> ! [X2: nat,X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1053])]) ).

tff(f5757,plain,
    ! [X2: nat,X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2) ),
    inference(cnf_transformation,[],[f2133]) ).

tff(f2133,plain,
    ! [X0: nat,X1: nat,X2: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2) ),
    inference(rectify,[],[f788]) ).

tff(f788,axiom,
    ! [X83: nat,X84: nat,X85: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X83),X84)),X85) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X83),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X84),X85)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_787_ab__semigroup__add__class_Oadd__ac_I1_J) ).

tff(f21396,plain,
    spl250_1052,
    inference(avatar_split_clause,[],[f5755,f21394]) ).

tff(f21394,plain,
    ( spl250_1052
  <=> ! [X2: nat,X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1052])]) ).

tff(f21392,plain,
    spl250_1051,
    inference(avatar_split_clause,[],[f5754,f21390]) ).

tff(f21390,plain,
    ( spl250_1051
  <=> ! [X2: nat,X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1051])]) ).

tff(f5754,plain,
    ! [X2: nat,X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f2130]) ).

tff(f2130,plain,
    ! [X0: nat,X1: nat,X2: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)) ),
    inference(rectify,[],[f1018]) ).

tff(f1018,axiom,
    ! [X12: nat,X11: nat,X19: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X12),X11)),X19) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X12),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X11),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1017_nat__mult__assoc) ).

tff(f21388,plain,
    spl250_1050,
    inference(avatar_split_clause,[],[f5753,f21386]) ).

tff(f21386,plain,
    ( spl250_1050
  <=> ! [X2: nat,X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1050])]) ).

tff(f5753,plain,
    ! [X2: nat,X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) ),
    inference(cnf_transformation,[],[f2129]) ).

tff(f2129,plain,
    ! [X0: nat,X1: nat,X2: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) ),
    inference(rectify,[],[f800]) ).

tff(f800,axiom,
    ! [X15: nat,X16: nat,X95: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X16),X95)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X16),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X95)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_799_nat__add__left__commute) ).

tff(f21384,plain,
    spl250_1049,
    inference(avatar_split_clause,[],[f5751,f21382]) ).

tff(f5751,plain,
    ! [X2: int,X0: int,X1: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),X2) ),
    inference(cnf_transformation,[],[f2127]) ).

tff(f2127,plain,
    ! [X0: int,X1: int,X2: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),X2) ),
    inference(rectify,[],[f787]) ).

tff(f787,axiom,
    ! [X83: int,X84: int,X85: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X83),X84)),X85) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X83),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X84),X85)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_786_ab__semigroup__add__class_Oadd__ac_I1_J) ).

tff(f21380,plain,
    spl250_1048,
    inference(avatar_split_clause,[],[f5750,f21378]) ).

tff(f21378,plain,
    ( spl250_1048
  <=> ! [X2: int,X0: int,X1: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X1)),X2) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1048])]) ).

tff(f5750,plain,
    ! [X2: int,X0: int,X1: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X1)),X2) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X2)) ),
    inference(cnf_transformation,[],[f2126]) ).

tff(f2126,plain,
    ! [X0: int,X1: int,X2: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X1)),X2) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X2)) ),
    inference(rectify,[],[f1024]) ).

tff(f1024,axiom,
    ! [X133: int,X134: int,X135: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X133),X134)),X135) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X133),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X134),X135)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1023_zmult__assoc) ).

tff(f21373,plain,
    spl250_1047,
    inference(avatar_split_clause,[],[f5749,f21371]) ).

tff(f21371,plain,
    ( spl250_1047
  <=> ! [X2: int,X0: int,X1: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1047])]) ).

tff(f5749,plain,
    ! [X2: int,X0: int,X1: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2)) ),
    inference(cnf_transformation,[],[f2125]) ).

tff(f2125,plain,
    ! [X0: int,X1: int,X2: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2)) ),
    inference(rectify,[],[f1043]) ).

tff(f1043,axiom,
    ! [X15: int,X16: int,X95: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X15),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X16),X95)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X16),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X15),X95)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1042_zadd__left__commute) ).

tff(f21369,plain,
    spl250_1046,
    inference(avatar_split_clause,[],[f5748,f21367]) ).

tff(f21367,plain,
    ( spl250_1046
  <=> ! [X2: fun_a_bool,X0: x_a,X1: x_a] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1046])]) ).

tff(f5748,plain,
    ! [X2: fun_a_bool,X0: x_a,X1: x_a] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)) ),
    inference(cnf_transformation,[],[f2124]) ).

tff(f2124,plain,
    ! [X0: x_a,X1: x_a,X2: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)) ),
    inference(rectify,[],[f384]) ).

tff(f384,axiom,
    ! [X8: x_a,X36: x_a,X2: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X36),X2)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X36),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_insert__commute) ).

tff(f21365,plain,
    spl250_1045,
    inference(avatar_split_clause,[],[f5747,f21363]) ).

tff(f21363,plain,
    ( spl250_1045
  <=> ! [X2: nat,X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1045])]) ).

tff(f5747,plain,
    ! [X2: nat,X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)) ),
    inference(cnf_transformation,[],[f2123]) ).

tff(f2123,plain,
    ! [X0: nat,X1: nat,X2: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)) ),
    inference(rectify,[],[f838]) ).

tff(f838,axiom,
    ! [X12: nat,X19: nat,X11: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X12),X11) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X12),X19)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X11),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_837_diff__cancel2) ).

tff(f21361,plain,
    spl250_1044,
    inference(avatar_split_clause,[],[f5746,f21359]) ).

tff(f21359,plain,
    ( spl250_1044
  <=> ! [X2: nat,X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1044])]) ).

tff(f5746,plain,
    ! [X2: nat,X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) ),
    inference(cnf_transformation,[],[f2122]) ).

tff(f2122,plain,
    ! [X0: nat,X1: nat,X2: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) ),
    inference(rectify,[],[f837]) ).

tff(f837,axiom,
    ! [X19: nat,X12: nat,X11: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X12),X11) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X19),X12)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X19),X11)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_836_diff__cancel) ).

tff(f21357,plain,
    spl250_1043,
    inference(avatar_split_clause,[],[f5648,f21355]) ).

tff(f21355,plain,
    ( spl250_1043
  <=> ! [X0: int,X1: int] :
        ( ( X0 = X1 )
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1043])]) ).

tff(f5648,plain,
    ! [X0: int,X1: int] :
      ( ( X0 = X1 )
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int))) ),
    inference(cnf_transformation,[],[f4166]) ).

tff(f4166,plain,
    ! [X0: int,X1: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)))
        | ( ( X0 != X1 )
          & ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) )
      & ( ( X0 = X1 )
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int))) ) ),
    inference(flattening,[],[f4165]) ).

tff(f4165,plain,
    ! [X0: int,X1: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)))
        | ( ( X0 != X1 )
          & ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) )
      & ( ( X0 = X1 )
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int))) ) ),
    inference(nnf_transformation,[],[f2041]) ).

tff(f2041,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)))
    <=> ( ( X0 = X1 )
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
    inference(rectify,[],[f1057]) ).

tff(f1057,axiom,
    ! [X136: int,X53: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X136),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X53),one_one_int)))
    <=> ( ( X53 = X136 )
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X136),X53)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1056_zless__add1__eq) ).

tff(f21353,plain,
    spl250_1042,
    inference(avatar_split_clause,[],[f5631,f21351]) ).

tff(f21351,plain,
    ( spl250_1042
  <=> ! [X0: fun_a_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1042])]) ).

tff(f5631,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) ),
    inference(cnf_transformation,[],[f4155]) ).

tff(f4155,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) )
      & ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1)))) ) ),
    inference(flattening,[],[f4154]) ).

tff(f4154,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) )
      & ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1)))) ) ),
    inference(nnf_transformation,[],[f2033]) ).

tff(f2033,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1))))
    <=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) ) ),
    inference(rectify,[],[f133]) ).

tff(f133,axiom,
    ! [X10: fun_a_bool,X9: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X10),X9))))
    <=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X9)))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X10))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_finite__Collect__disjI) ).

tff(f21349,plain,
    spl250_1041,
    inference(avatar_split_clause,[],[f5628,f21347]) ).

tff(f21347,plain,
    ( spl250_1041
  <=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1041])]) ).

tff(f5628,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) ),
    inference(cnf_transformation,[],[f4153]) ).

tff(f4153,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) )
      & ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) )
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))) ) ),
    inference(flattening,[],[f4152]) ).

tff(f4152,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) )
      & ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) )
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))) ) ),
    inference(nnf_transformation,[],[f2032]) ).

tff(f2032,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1))))
    <=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) ) ),
    inference(rectify,[],[f138]) ).

tff(f138,axiom,
    ! [X10: fun_pname_bool,X9: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X10),X9))))
    <=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X9)))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X10))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_finite__Collect__disjI) ).

tff(f21345,plain,
    spl250_1040,
    inference(avatar_split_clause,[],[f5625,f21343]) ).

tff(f21343,plain,
    ( spl250_1040
  <=> ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1))))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1040])]) ).

tff(f5625,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1))))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) ),
    inference(cnf_transformation,[],[f4151]) ).

tff(f4151,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
      ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1))))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) )
      & ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) )
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))) ) ),
    inference(flattening,[],[f4150]) ).

tff(f4150,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
      ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1))))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) )
      & ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) )
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))) ) ),
    inference(nnf_transformation,[],[f2031]) ).

tff(f2031,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1))))
    <=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
        & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) ) ),
    inference(rectify,[],[f135]) ).

tff(f135,axiom,
    ! [X10: fun_fu425979586l_bool,X9: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X10),X9))))
    <=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X9)))
        & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X10))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_finite__Collect__disjI) ).

tff(f21341,plain,
    spl250_1039,
    inference(avatar_split_clause,[],[f5622,f21339]) ).

tff(f21339,plain,
    ( spl250_1039
  <=> ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1))))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1039])]) ).

tff(f5622,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1))))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) ),
    inference(cnf_transformation,[],[f4149]) ).

tff(f4149,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
      ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1))))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) )
      & ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) )
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))) ) ),
    inference(flattening,[],[f4148]) ).

tff(f4148,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
      ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1))))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) )
      & ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) )
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))) ) ),
    inference(nnf_transformation,[],[f2030]) ).

tff(f2030,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1))))
    <=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
        & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) ) ),
    inference(rectify,[],[f137]) ).

tff(f137,axiom,
    ! [X10: fun_fun_a_bool_bool,X9: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X10),X9))))
    <=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X9)))
        & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X10))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_finite__Collect__disjI) ).

tff(f21337,plain,
    spl250_1038,
    inference(avatar_split_clause,[],[f5619,f21335]) ).

tff(f21335,plain,
    ( spl250_1038
  <=> ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1))))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1038])]) ).

tff(f5619,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) ),
    inference(cnf_transformation,[],[f4147]) ).

tff(f4147,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1))))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) )
      & ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) )
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))) ) ),
    inference(flattening,[],[f4146]) ).

tff(f4146,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1))))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) )
      & ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) )
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))) ) ),
    inference(nnf_transformation,[],[f2029]) ).

tff(f2029,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1))))
    <=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) ) ),
    inference(rectify,[],[f136]) ).

tff(f136,axiom,
    ! [X10: fun_fu1430349052l_bool,X9: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X10),X9))))
    <=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X9)))
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X10))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_finite__Collect__disjI) ).

tff(f21331,plain,
    spl250_1037,
    inference(avatar_split_clause,[],[f5616,f21329]) ).

tff(f21329,plain,
    ( spl250_1037
  <=> ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X0),X1))))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1037])]) ).

tff(f5616,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X0),X1))))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0))) ),
    inference(cnf_transformation,[],[f4145]) ).

tff(f4145,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
      ( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X0),X1))))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0))) )
      & ( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1)))
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0))) )
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X0),X1)))) ) ),
    inference(flattening,[],[f4144]) ).

tff(f4144,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
      ( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X0),X1))))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0))) )
      & ( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1)))
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0))) )
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X0),X1)))) ) ),
    inference(nnf_transformation,[],[f2028]) ).

tff(f2028,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X0),X1))))
    <=> ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1)))
        & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0))) ) ),
    inference(rectify,[],[f134]) ).

tff(f134,axiom,
    ! [X10: fun_fu819804446l_bool,X9: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X10),X9))))
    <=> ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X9)))
        & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X10))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_finite__Collect__disjI) ).

tff(f21327,plain,
    spl250_1036,
    inference(avatar_split_clause,[],[f5582,f21325]) ).

tff(f21325,plain,
    ( spl250_1036
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK143(X0,X1)),X1))
        | ( zero_zero_nat = X0 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1036])]) ).

tff(f5582,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK143(X0,X1)),X1))
      | ( zero_zero_nat = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ),
    inference(cnf_transformation,[],[f4127]) ).

tff(f4127,plain,
    ! [X0: nat,X1: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
        | ( ! [X2: nat] :
              ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
              | ( hAPP_nat_nat(suc,X2) != X0 ) )
          & ( zero_zero_nat != X0 ) ) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK143(X0,X1)),X1))
          & ( hAPP_nat_nat(suc,sK143(X0,X1)) = X0 ) )
        | ( zero_zero_nat = X0 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK143])],[f4125,f4126]) ).

tff(f4126,plain,
    ! [X0: nat,X1: nat] :
      ( ? [X3: nat] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X1))
          & ( hAPP_nat_nat(suc,X3) = X0 ) )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK143(X0,X1)),X1))
        & ( hAPP_nat_nat(suc,sK143(X0,X1)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f4125,plain,
    ! [X0: nat,X1: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
        | ( ! [X2: nat] :
              ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
              | ( hAPP_nat_nat(suc,X2) != X0 ) )
          & ( zero_zero_nat != X0 ) ) )
      & ( ? [X3: nat] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X1))
            & ( hAPP_nat_nat(suc,X3) = X0 ) )
        | ( zero_zero_nat = X0 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ) ),
    inference(rectify,[],[f4124]) ).

tff(f4124,plain,
    ! [X0: nat,X1: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
        | ( ! [X2: nat] :
              ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
              | ( hAPP_nat_nat(suc,X2) != X0 ) )
          & ( zero_zero_nat != X0 ) ) )
      & ( ? [X2: nat] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
            & ( hAPP_nat_nat(suc,X2) = X0 ) )
        | ( zero_zero_nat = X0 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ) ),
    inference(flattening,[],[f4123]) ).

tff(f4123,plain,
    ! [X0: nat,X1: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
        | ( ! [X2: nat] :
              ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
              | ( hAPP_nat_nat(suc,X2) != X0 ) )
          & ( zero_zero_nat != X0 ) ) )
      & ( ? [X2: nat] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
            & ( hAPP_nat_nat(suc,X2) = X0 ) )
        | ( zero_zero_nat = X0 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ) ),
    inference(nnf_transformation,[],[f2020]) ).

tff(f2020,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
    <=> ( ? [X2: nat] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
            & ( hAPP_nat_nat(suc,X2) = X0 ) )
        | ( zero_zero_nat = X0 ) ) ),
    inference(rectify,[],[f949]) ).

tff(f949,axiom,
    ! [X22: nat,X14: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),hAPP_nat_nat(suc,X14)))
    <=> ( ? [X124: nat] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X124),X14))
            & ( hAPP_nat_nat(suc,X124) = X22 ) )
        | ( zero_zero_nat = X22 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_948_less__Suc__eq__0__disj) ).

tff(f21323,plain,
    spl250_1035,
    inference(avatar_split_clause,[],[f5515,f21321]) ).

tff(f21321,plain,
    ( spl250_1035
  <=> ! [X0: int,X1: int] :
        ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,sK139(X0,X1)))) = X1 )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1035])]) ).

tff(f5515,plain,
    ! [X0: int,X1: int] :
      ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,sK139(X0,X1)))) = X1 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4078]) ).

tff(f4078,plain,
    ! [X0: int,X1: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | ! [X2: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X2))) != X1 ) )
      & ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,sK139(X0,X1)))) = X1 )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK139])],[f4076,f4077]) ).

tff(f4077,plain,
    ! [X0: int,X1: int] :
      ( ? [X3: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X3))) = X1 )
     => ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,sK139(X0,X1)))) = X1 ) ),
    introduced(choice_axiom,[]) ).

tff(f4076,plain,
    ! [X0: int,X1: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | ! [X2: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X2))) != X1 ) )
      & ( ? [X3: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X3))) = X1 )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
    inference(rectify,[],[f4075]) ).

tff(f4075,plain,
    ! [X0: int,X1: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | ! [X2: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X2))) != X1 ) )
      & ( ? [X2: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X2))) = X1 )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
    inference(nnf_transformation,[],[f1990]) ).

tff(f1990,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
    <=> ? [X2: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X2))) = X1 ) ),
    inference(rectify,[],[f1124]) ).

tff(f1124,axiom,
    ! [X136: int,X53: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X136),X53))
    <=> ? [X26: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X136),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X26))) = X53 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1123_zless__iff__Suc__zadd) ).

tff(f21319,plain,
    spl250_1034,
    inference(avatar_split_clause,[],[f5379,f21317]) ).

tff(f21317,plain,
    ( spl250_1034
  <=> ! [X0: nat,X1: nat] :
        ( ( hAPP_nat_nat(suc,X1) = X0 )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1034])]) ).

tff(f5379,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(suc,X1) = X0 )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1))) ),
    inference(cnf_transformation,[],[f3026]) ).

tff(f3026,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(suc,X1) = X0 )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1))) ),
    inference(flattening,[],[f3025]) ).

tff(f3025,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(suc,X1) = X0 )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1))) ),
    inference(ennf_transformation,[],[f1923]) ).

tff(f1923,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1)))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
       => ( hAPP_nat_nat(suc,X1) = X0 ) ) ),
    inference(rectify,[],[f166]) ).

tff(f166,axiom,
    ! [X12: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),hAPP_nat_nat(suc,X11)))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X11))
       => ( hAPP_nat_nat(suc,X11) = X12 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_le__SucE) ).

tff(f21315,plain,
    spl250_1033,
    inference(avatar_split_clause,[],[f5349,f21313]) ).

tff(f21313,plain,
    ( spl250_1033
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),sK121(X0,X1)))
        | ( hAPP_nat_nat(suc,X0) = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1033])]) ).

tff(f5349,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),sK121(X0,X1)))
      | ( hAPP_nat_nat(suc,X0) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3988]) ).

tff(f3988,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( hAPP_nat_nat(suc,sK121(X0,X1)) = X1 )
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),sK121(X0,X1))) )
      | ( hAPP_nat_nat(suc,X0) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK121])],[f2989,f3987]) ).

tff(f3987,plain,
    ! [X0: nat,X1: nat] :
      ( ? [X2: nat] :
          ( ( hAPP_nat_nat(suc,X2) = X1 )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2)) )
     => ( ( hAPP_nat_nat(suc,sK121(X0,X1)) = X1 )
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),sK121(X0,X1))) ) ),
    introduced(choice_axiom,[]) ).

tff(f2989,plain,
    ! [X0: nat,X1: nat] :
      ( ? [X2: nat] :
          ( ( hAPP_nat_nat(suc,X2) = X1 )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2)) )
      | ( hAPP_nat_nat(suc,X0) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(flattening,[],[f2988]) ).

tff(f2988,plain,
    ! [X0: nat,X1: nat] :
      ( ? [X2: nat] :
          ( ( hAPP_nat_nat(suc,X2) = X1 )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2)) )
      | ( hAPP_nat_nat(suc,X0) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1897]) ).

tff(f1897,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
     => ( ( hAPP_nat_nat(suc,X0) != X1 )
       => ~ ! [X2: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
             => ( hAPP_nat_nat(suc,X2) != X1 ) ) ) ),
    inference(rectify,[],[f920]) ).

tff(f920,axiom,
    ! [X20: nat,X19: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X20),X19))
     => ( ( hAPP_nat_nat(suc,X20) != X19 )
       => ~ ! [X124: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X20),X124))
             => ( hAPP_nat_nat(suc,X124) != X19 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_919_lessE) ).

tff(f21311,plain,
    spl250_1032,
    inference(avatar_split_clause,[],[f5348,f21309]) ).

tff(f21309,plain,
    ( spl250_1032
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1))
        | ( hAPP_nat_nat(suc,X0) = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1032])]) ).

tff(f5348,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1))
      | ( hAPP_nat_nat(suc,X0) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2987]) ).

tff(f2987,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1))
      | ( hAPP_nat_nat(suc,X0) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(flattening,[],[f2986]) ).

tff(f2986,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1))
      | ( hAPP_nat_nat(suc,X0) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1896]) ).

tff(f1896,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
     => ( ( hAPP_nat_nat(suc,X0) != X1 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1)) ) ),
    inference(rectify,[],[f872]) ).

tff(f872,axiom,
    ! [X12: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),X11))
     => ( ( hAPP_nat_nat(suc,X12) != X11 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X12)),X11)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_871_Suc__lessI) ).

tff(f20714,plain,
    ( spl250_1031
    | ~ spl250_158
    | ~ spl250_911 ),
    inference(avatar_split_clause,[],[f20565,f16668,f8119,f20711]) ).

tff(f20711,plain,
    ( spl250_1031
  <=> ( zero_zero_nat = sK34(pls) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1031])]) ).

tff(f8119,plain,
    ( spl250_158
  <=> ! [X0: nat] :
        ( ( zero_zero_nat = X0 )
        | ( pls != hAPP_nat_int(semiri1621563631at_int,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_158])]) ).

tff(f16668,plain,
    ( spl250_911
  <=> ( pls = hAPP_nat_int(semiri1621563631at_int,sK34(pls)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_911])]) ).

tff(f20565,plain,
    ( ( zero_zero_nat = sK34(pls) )
    | ~ spl250_158
    | ~ spl250_911 ),
    inference(trivial_inequality_removal,[],[f20541]) ).

tff(f20541,plain,
    ( ( pls != pls )
    | ( zero_zero_nat = sK34(pls) )
    | ~ spl250_158
    | ~ spl250_911 ),
    inference(superposition,[],[f8120,f16670]) ).

tff(f16670,plain,
    ( ( pls = hAPP_nat_int(semiri1621563631at_int,sK34(pls)) )
    | ~ spl250_911 ),
    inference(avatar_component_clause,[],[f16668]) ).

tff(f8120,plain,
    ( ! [X0: nat] :
        ( ( pls != hAPP_nat_int(semiri1621563631at_int,X0) )
        | ( zero_zero_nat = X0 ) )
    | ~ spl250_158 ),
    inference(avatar_component_clause,[],[f8119]) ).

tff(f20491,plain,
    spl250_1030,
    inference(avatar_split_clause,[],[f7086,f20489]) ).

tff(f20489,plain,
    ( spl250_1030
  <=> ! [X0: fun_a_bool,X1: x_a] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),collect_a(hAPP_a_fun_a_bool(fequal_a,X1))))
        | ( collect_a(hAPP_a_fun_a_bool(fequal_a,X1)) = X0 )
        | ( bot_bot_fun_a_bool = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1030])]) ).

tff(f7086,plain,
    ! [X0: fun_a_bool,X1: x_a] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),collect_a(hAPP_a_fun_a_bool(fequal_a,X1))))
      | ( collect_a(hAPP_a_fun_a_bool(fequal_a,X1)) = X0 )
      | ( bot_bot_fun_a_bool = X0 ) ),
    inference(forward_demodulation,[],[f7085,f4680]) ).

tff(f7085,plain,
    ! [X0: fun_a_bool,X1: x_a] :
      ( ( collect_a(hAPP_a_fun_a_bool(fequal_a,X1)) = X0 )
      | ( bot_bot_fun_a_bool = X0 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))) ),
    inference(forward_demodulation,[],[f5388,f4680]) ).

tff(f5388,plain,
    ! [X0: fun_a_bool,X1: x_a] :
      ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool) = X0 )
      | ( bot_bot_fun_a_bool = X0 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))) ),
    inference(cnf_transformation,[],[f3035]) ).

tff(f3035,plain,
    ! [X0: fun_a_bool,X1: x_a] :
      ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool) = X0 )
      | ( bot_bot_fun_a_bool = X0 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))) ),
    inference(flattening,[],[f3034]) ).

tff(f3034,plain,
    ! [X0: fun_a_bool,X1: x_a] :
      ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool) = X0 )
      | ( bot_bot_fun_a_bool = X0 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))) ),
    inference(ennf_transformation,[],[f1931]) ).

tff(f1931,plain,
    ! [X0: fun_a_bool,X1: x_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)))
     => ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool) = X0 )
        | ( bot_bot_fun_a_bool = X0 ) ) ),
    inference(rectify,[],[f661]) ).

tff(f661,axiom,
    ! [X2: fun_a_bool,X8: x_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),bot_bot_fun_a_bool)))
     => ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),bot_bot_fun_a_bool) = X2 )
        | ( bot_bot_fun_a_bool = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_subset__singletonD) ).

tff(f20487,plain,
    spl250_1029,
    inference(avatar_split_clause,[],[f6986,f20485]) ).

tff(f20485,plain,
    ( spl250_1029
  <=> ! [X0: fun_a_bool,X1: x_a] :
        ( ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),X0)) = collect_a(hAPP_a_fun_a_bool(fequal_a,X1)) )
        | ~ hBOOL(hAPP_a_bool(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1029])]) ).

tff(f6986,plain,
    ! [X0: fun_a_bool,X1: x_a] :
      ( ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),X0)) = collect_a(hAPP_a_fun_a_bool(fequal_a,X1)) )
      | ~ hBOOL(hAPP_a_bool(X0,X1)) ),
    inference(forward_demodulation,[],[f4956,f4680]) ).

tff(f4956,plain,
    ! [X0: fun_a_bool,X1: x_a] :
      ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),X0)) )
      | ~ hBOOL(hAPP_a_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f2616]) ).

tff(f2616,plain,
    ! [X0: fun_a_bool,X1: x_a] :
      ( ( ( bot_bot_fun_a_bool = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),X0)) )
        | hBOOL(hAPP_a_bool(X0,X1)) )
      & ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),X0)) )
        | ~ hBOOL(hAPP_a_bool(X0,X1)) ) ),
    inference(ennf_transformation,[],[f1599]) ).

tff(f1599,plain,
    ! [X0: fun_a_bool,X1: x_a] :
      ( ( ~ hBOOL(hAPP_a_bool(X0,X1))
       => ( bot_bot_fun_a_bool = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),X0)) ) )
      & ( hBOOL(hAPP_a_bool(X0,X1))
       => ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),X0)) ) ) ),
    inference(rectify,[],[f631]) ).

tff(f631,axiom,
    ! [X10: fun_a_bool,X5: x_a] :
      ( ( ~ hBOOL(hAPP_a_bool(X10,X5))
       => ( bot_bot_fun_a_bool = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X5)),X10)) ) )
      & ( hBOOL(hAPP_a_bool(X10,X5))
       => ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),bot_bot_fun_a_bool) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X5)),X10)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_630_Collect__conv__if) ).

tff(f20483,plain,
    spl250_1028,
    inference(avatar_split_clause,[],[f6982,f20481]) ).

tff(f20481,plain,
    ( spl250_1028
  <=> ! [X0: x_a,X1: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),collect_a(hAPP_a_fun_a_bool(fequal_a,X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1028])]) ).

tff(f6982,plain,
    ! [X0: x_a,X1: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),collect_a(hAPP_a_fun_a_bool(fequal_a,X0)))) ),
    inference(forward_demodulation,[],[f4941,f4680]) ).

tff(f4941,plain,
    ! [X0: x_a,X1: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool))) ),
    inference(cnf_transformation,[],[f1589]) ).

tff(f1589,plain,
    ! [X0: x_a,X1: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool))) ),
    inference(rectify,[],[f553]) ).

tff(f553,axiom,
    ! [X5: x_a,X2: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),bot_bot_fun_a_bool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_552_insert__Diff__single) ).

tff(f20479,plain,
    spl250_1027,
    inference(avatar_split_clause,[],[f6457,f20477]) ).

tff(f20477,plain,
    ( spl250_1027
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( X1 = X2 )
        | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1027])]) ).

tff(f6457,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( X1 = X2 )
      | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X2) ) ),
    inference(cnf_transformation,[],[f4510]) ).

tff(f4510,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X2) )
        | ( X1 != X2 ) )
      & ( ( X1 = X2 )
        | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X2) ) ) ),
    inference(nnf_transformation,[],[f2520]) ).

tff(f2520,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X2) )
    <=> ( X1 = X2 ) ),
    inference(rectify,[],[f984]) ).

tff(f984,axiom,
    ! [X13: nat,X22: nat,X14: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X13)),X22) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X13)),X14) )
    <=> ( X14 = X22 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_983_Suc__mult__cancel1) ).

tff(f20438,plain,
    spl250_1026,
    inference(avatar_split_clause,[],[f6317,f20436]) ).

tff(f20436,plain,
    ( spl250_1026
  <=> ! [X2: nat,X0: fun_nat_bool,X1: nat] :
        ( sP19(X0,X1,X2)
        | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK247(X0,X1,X2)) = X1 )
        | ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1026])]) ).

tff(f6317,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: nat] :
      ( sP19(X0,X1,X2)
      | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK247(X0,X1,X2)) = X1 )
      | ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ),
    inference(cnf_transformation,[],[f4431]) ).

tff(f20434,plain,
    spl250_1025,
    inference(avatar_split_clause,[],[f6309,f20432]) ).

tff(f20432,plain,
    ( spl250_1025
  <=> ! [X2: nat,X0: fun_nat_bool,X1: nat] :
        ( sP18(X0,X1,X2)
        | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK246(X0,X1,X2)) = X1 )
        | ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1025])]) ).

tff(f6309,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: nat] :
      ( sP18(X0,X1,X2)
      | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),sK246(X0,X1,X2)) = X1 )
      | ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ),
    inference(cnf_transformation,[],[f4425]) ).

tff(f20430,plain,
    spl250_1024,
    inference(avatar_split_clause,[],[f6181,f20428]) ).

tff(f20428,plain,
    ( spl250_1024
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1024])]) ).

tff(f6181,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f3493]) ).

tff(f3493,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(flattening,[],[f3492]) ).

tff(f3492,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f2403]) ).

tff(f2403,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X0))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0)) ) ),
    inference(rectify,[],[f352]) ).

tff(f352,axiom,
    ! [X54: nat,X55: nat,X56: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X55),X56))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X56),X54))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X55),X54)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_order__trans) ).

tff(f20426,plain,
    spl250_1023,
    inference(avatar_split_clause,[],[f6143,f20424]) ).

tff(f20424,plain,
    ( spl250_1023
  <=> ! [X2: int,X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X0))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1023])]) ).

tff(f6143,plain,
    ! [X2: int,X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
    inference(cnf_transformation,[],[f3446]) ).

tff(f3446,plain,
    ! [X0: int,X1: int,X2: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
    inference(flattening,[],[f3445]) ).

tff(f3445,plain,
    ! [X0: int,X1: int,X2: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
    inference(ennf_transformation,[],[f2367]) ).

tff(f2367,plain,
    ! [X0: int,X1: int,X2: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X0))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0)) ) ),
    inference(rectify,[],[f351]) ).

tff(f351,axiom,
    ! [X54: int,X55: int,X56: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X55),X56))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X56),X54))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X55),X54)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_order__trans) ).

tff(f20422,plain,
    spl250_1022,
    inference(avatar_split_clause,[],[f6119,f20420]) ).

tff(f20420,plain,
    ( spl250_1022
  <=> ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1022])]) ).

tff(f6119,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
    inference(cnf_transformation,[],[f3418]) ).

tff(f3418,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
    inference(flattening,[],[f3417]) ).

tff(f3417,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
    inference(ennf_transformation,[],[f2351]) ).

tff(f2351,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0)) ) ),
    inference(rectify,[],[f427]) ).

tff(f427,axiom,
    ! [X64: fun_nat_bool,X2: fun_nat_bool,X7: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X7))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7),X64))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X64)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_426_subset__trans) ).

tff(f20418,plain,
    spl250_1021,
    inference(avatar_split_clause,[],[f6108,f20416]) ).

tff(f20416,plain,
    ( spl250_1021
  <=> ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1021])]) ).

tff(f6108,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f3401]) ).

tff(f3401,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
    inference(flattening,[],[f3400]) ).

tff(f3400,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f2340]) ).

tff(f2340,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X0))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) ) ),
    inference(rectify,[],[f419]) ).

tff(f419,axiom,
    ! [X7: fun_nat_bool,X8: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X7))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_418_set__rev__mp) ).

tff(f20414,plain,
    spl250_1020,
    inference(avatar_split_clause,[],[f6098,f20412]) ).

tff(f20412,plain,
    ( spl250_1020
  <=> ! [X2: fun_int_bool,X0: fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1020])]) ).

tff(f6098,plain,
    ! [X2: fun_int_bool,X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ),
    inference(cnf_transformation,[],[f3386]) ).

tff(f3386,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ),
    inference(flattening,[],[f3385]) ).

tff(f3385,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ),
    inference(ennf_transformation,[],[f2330]) ).

tff(f2330,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
       => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0)) ) ),
    inference(rectify,[],[f426]) ).

tff(f426,axiom,
    ! [X64: fun_int_bool,X2: fun_int_bool,X7: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X7))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X7),X64))
       => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X64)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_425_subset__trans) ).

tff(f20410,plain,
    spl250_1019,
    inference(avatar_split_clause,[],[f6088,f20408]) ).

tff(f20408,plain,
    ( spl250_1019
  <=> ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1019])]) ).

tff(f6088,plain,
    ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
    inference(cnf_transformation,[],[f3370]) ).

tff(f3370,plain,
    ! [X0: fun_int_bool,X1: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
    inference(flattening,[],[f3369]) ).

tff(f3369,plain,
    ! [X0: fun_int_bool,X1: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
    inference(ennf_transformation,[],[f2320]) ).

tff(f2320,plain,
    ! [X0: fun_int_bool,X1: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X0))
       => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) ) ),
    inference(rectify,[],[f418]) ).

tff(f418,axiom,
    ! [X7: fun_int_bool,X8: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X7))
       => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_417_set__rev__mp) ).

tff(f20406,plain,
    spl250_1018,
    inference(avatar_split_clause,[],[f6081,f20404]) ).

tff(f20404,plain,
    ( spl250_1018
  <=> ! [X2: fun_a_bool,X0: fun_a_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X2))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1018])]) ).

tff(f6081,plain,
    ! [X2: fun_a_bool,X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
    inference(cnf_transformation,[],[f3358]) ).

tff(f3358,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
    inference(flattening,[],[f3357]) ).

tff(f3357,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
    inference(ennf_transformation,[],[f2313]) ).

tff(f2313,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X2)) ) ),
    inference(rectify,[],[f363]) ).

tff(f363,axiom,
    ! [X53: fun_a_bool,X36: fun_a_bool,X8: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X36),X8))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X53),X36))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X53),X8)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_xt1_I6_J) ).

tff(f20402,plain,
    spl250_1017,
    inference(avatar_split_clause,[],[f6071,f20400]) ).

tff(f20400,plain,
    ( spl250_1017
  <=> ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1017])]) ).

tff(f6071,plain,
    ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
    inference(cnf_transformation,[],[f3342]) ).

tff(f3342,plain,
    ! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
    inference(flattening,[],[f3341]) ).

tff(f3341,plain,
    ! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
    inference(ennf_transformation,[],[f2303]) ).

tff(f2303,plain,
    ! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X0))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) ) ),
    inference(rectify,[],[f420]) ).

tff(f420,axiom,
    ! [X7: fun_a_bool,X8: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_419_set__rev__mp) ).

tff(f20397,plain,
    spl250_1016,
    inference(avatar_split_clause,[],[f6058,f20395]) ).

tff(f20395,plain,
    ( spl250_1016
  <=> ! [X2: fun_pname_bool,X0: pname,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1016])]) ).

tff(f6058,plain,
    ! [X2: fun_pname_bool,X0: pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
    inference(cnf_transformation,[],[f3323]) ).

tff(f3323,plain,
    ! [X0: pname,X1: fun_pname_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
    inference(flattening,[],[f3322]) ).

tff(f3322,plain,
    ! [X0: pname,X1: fun_pname_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
    inference(ennf_transformation,[],[f2290]) ).

tff(f2290,plain,
    ! [X0: pname,X1: fun_pname_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) ) ),
    inference(rectify,[],[f425]) ).

tff(f425,axiom,
    ! [X8: pname,X2: fun_pname_bool,X7: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X7))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X2))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_424_set__mp) ).

tff(f20393,plain,
    spl250_1015,
    inference(avatar_split_clause,[],[f5581,f20391]) ).

tff(f20391,plain,
    ( spl250_1015
  <=> ! [X0: nat,X1: nat] :
        ( ( hAPP_nat_nat(suc,sK143(X0,X1)) = X0 )
        | ( zero_zero_nat = X0 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1015])]) ).

tff(f5581,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(suc,sK143(X0,X1)) = X0 )
      | ( zero_zero_nat = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ),
    inference(cnf_transformation,[],[f4127]) ).

tff(f20389,plain,
    spl250_1014,
    inference(avatar_split_clause,[],[f5350,f20387]) ).

tff(f20387,plain,
    ( spl250_1014
  <=> ! [X0: nat,X1: nat] :
        ( ( hAPP_nat_nat(suc,sK121(X0,X1)) = X1 )
        | ( hAPP_nat_nat(suc,X0) = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1014])]) ).

tff(f5350,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(suc,sK121(X0,X1)) = X1 )
      | ( hAPP_nat_nat(suc,X0) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3988]) ).

tff(f20385,plain,
    spl250_1013,
    inference(avatar_split_clause,[],[f5299,f20383]) ).

tff(f20383,plain,
    ( spl250_1013
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(suc,X0))),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1013])]) ).

tff(f5299,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(suc,X0))),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
    inference(cnf_transformation,[],[f2920]) ).

tff(f2920,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(suc,X0))),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
    inference(ennf_transformation,[],[f1852]) ).

tff(f1852,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(suc,X0))),X1)) ),
    inference(rectify,[],[f961]) ).

tff(f961,axiom,
    ! [X20: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X11))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X11),hAPP_nat_nat(suc,X20))),X11)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_960_diff__Suc__less) ).

tff(f20381,plain,
    spl250_1012,
    inference(avatar_split_clause,[],[f5243,f20379]) ).

tff(f20379,plain,
    ( spl250_1012
  <=> ! [X0: nat,X1: fun_nat_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1))))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1012])]) ).

tff(f5243,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f2866]) ).

tff(f2866,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(ennf_transformation,[],[f1815]) ).

tff(f1815,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)))) ),
    inference(rectify,[],[f93]) ).

tff(f93,axiom,
    ! [X8: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X2)),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_card__insert__le) ).

tff(f20377,plain,
    spl250_1011,
    inference(avatar_split_clause,[],[f5200,f20375]) ).

tff(f20375,plain,
    ( spl250_1011
  <=> ! [X0: int,X1: fun_int_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X1)),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1))))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1011])]) ).

tff(f5200,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X1)),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1))))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f2826]) ).

tff(f2826,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X1)),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1))))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(ennf_transformation,[],[f1786]) ).

tff(f1786,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X1)),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)))) ),
    inference(rectify,[],[f94]) ).

tff(f94,axiom,
    ! [X8: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X2)),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_card__insert__le) ).

tff(f20373,plain,
    spl250_1010,
    inference(avatar_split_clause,[],[f5161,f20371]) ).

tff(f20371,plain,
    ( spl250_1010
  <=> ! [X0: x_a,X1: fun_a_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1010])]) ).

tff(f5161,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(cnf_transformation,[],[f2789]) ).

tff(f2789,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(ennf_transformation,[],[f1760]) ).

tff(f1760,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)))) ),
    inference(rectify,[],[f95]) ).

tff(f95,axiom,
    ! [X8: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X2)),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_card__insert__le) ).

tff(f20369,plain,
    spl250_1009,
    inference(avatar_split_clause,[],[f5120,f20367]) ).

tff(f20367,plain,
    ( spl250_1009
  <=> ! [X0: pname,X1: fun_pname_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1009])]) ).

tff(f5120,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f2751]) ).

tff(f2751,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(ennf_transformation,[],[f1733]) ).

tff(f1733,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)))) ),
    inference(rectify,[],[f92]) ).

tff(f92,axiom,
    ! [X8: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X2)),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_card__insert__le) ).

tff(f20365,plain,
    spl250_1008,
    inference(avatar_split_clause,[],[f5084,f20363]) ).

tff(f20363,plain,
    ( spl250_1008
  <=> ! [X0: fun_int_bool,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X1)),hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1))))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1008])]) ).

tff(f5084,plain,
    ! [X0: fun_int_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X1)),hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1))))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(cnf_transformation,[],[f2703]) ).

tff(f2703,plain,
    ! [X0: fun_int_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X1)),hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1))))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(ennf_transformation,[],[f1701]) ).

tff(f1701,plain,
    ! [X0: fun_int_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X1)),hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1)))) ),
    inference(rectify,[],[f88]) ).

tff(f88,axiom,
    ! [X8: fun_int_bool,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X2)),hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X8),X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_card__insert__le) ).

tff(f20361,plain,
    spl250_1007,
    inference(avatar_split_clause,[],[f5083,f20359]) ).

tff(f20359,plain,
    ( spl250_1007
  <=> ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1))))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1007])]) ).

tff(f5083,plain,
    ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1))))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(cnf_transformation,[],[f2702]) ).

tff(f2702,plain,
    ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1))))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(ennf_transformation,[],[f1700]) ).

tff(f1700,plain,
    ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1)))) ),
    inference(rectify,[],[f89]) ).

tff(f89,axiom,
    ! [X8: fun_nat_bool,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X2)),hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X8),X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_card__insert__le) ).

tff(f20357,plain,
    ( spl250_1006
    | ~ spl250_158
    | ~ spl250_905 ),
    inference(avatar_split_clause,[],[f20283,f16398,f8119,f20354]) ).

tff(f20354,plain,
    ( spl250_1006
  <=> ( zero_zero_nat = sK33(pls) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1006])]) ).

tff(f16398,plain,
    ( spl250_905
  <=> ( pls = hAPP_nat_int(semiri1621563631at_int,sK33(pls)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_905])]) ).

tff(f20283,plain,
    ( ( zero_zero_nat = sK33(pls) )
    | ~ spl250_158
    | ~ spl250_905 ),
    inference(trivial_inequality_removal,[],[f20259]) ).

tff(f20259,plain,
    ( ( pls != pls )
    | ( zero_zero_nat = sK33(pls) )
    | ~ spl250_158
    | ~ spl250_905 ),
    inference(superposition,[],[f8120,f16400]) ).

tff(f16400,plain,
    ( ( pls = hAPP_nat_int(semiri1621563631at_int,sK33(pls)) )
    | ~ spl250_905 ),
    inference(avatar_component_clause,[],[f16398]) ).

tff(f20352,plain,
    spl250_1005,
    inference(avatar_split_clause,[],[f5082,f20350]) ).

tff(f20350,plain,
    ( spl250_1005
  <=> ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1))))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1005])]) ).

tff(f5082,plain,
    ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(cnf_transformation,[],[f2701]) ).

tff(f2701,plain,
    ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(ennf_transformation,[],[f1699]) ).

tff(f1699,plain,
    ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1)))) ),
    inference(rectify,[],[f90]) ).

tff(f90,axiom,
    ! [X8: fun_pname_bool,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X2)),hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X8),X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_card__insert__le) ).

tff(f20348,plain,
    spl250_1004,
    inference(avatar_split_clause,[],[f5081,f20346]) ).

tff(f20346,plain,
    ( spl250_1004
  <=> ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1))))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1004])]) ).

tff(f5081,plain,
    ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1))))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(cnf_transformation,[],[f2700]) ).

tff(f2700,plain,
    ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1))))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(ennf_transformation,[],[f1698]) ).

tff(f1698,plain,
    ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1)))) ),
    inference(rectify,[],[f91]) ).

tff(f91,axiom,
    ! [X8: fun_a_bool,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)),hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X8),X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_card__insert__le) ).

tff(f20344,plain,
    spl250_1003,
    inference(avatar_split_clause,[],[f5045,f20342]) ).

tff(f20342,plain,
    ( spl250_1003
  <=> ! [X0: fun_nat_int,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK88(X0,X1)),X1))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X0,X1)))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1003])]) ).

tff(f5045,plain,
    ! [X0: fun_nat_int,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK88(X0,X1)),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X0,X1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f3928]) ).

tff(f3928,plain,
    ! [X0: fun_nat_int,X1: fun_nat_bool] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,X0)),hAPP_nat_int(X0,sK88(X0,X1)))))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK88(X0,X1)),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X0,X1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK88])],[f2667,f3927]) ).

tff(f3927,plain,
    ! [X0: fun_nat_int,X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,X0)),hAPP_nat_int(X0,X2))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
     => ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,X0)),hAPP_nat_int(X0,sK88(X0,X1)))))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK88(X0,X1)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f2667,plain,
    ! [X0: fun_nat_int,X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,X0)),hAPP_nat_int(X0,X2))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X0,X1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(flattening,[],[f2666]) ).

tff(f2666,plain,
    ! [X0: fun_nat_int,X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,X0)),hAPP_nat_int(X0,X2))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X0,X1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(ennf_transformation,[],[f1667]) ).

tff(f1667,plain,
    ! [X0: fun_nat_int,X1: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
     => ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X0,X1)))
       => ? [X2: nat] :
            ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,X0)),hAPP_nat_int(X0,X2))))))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ) ) ),
    inference(rectify,[],[f282]) ).

tff(f282,axiom,
    ! [X6: fun_nat_int,X2: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X6,X2)))
       => ? [X27: nat] :
            ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,X6)),hAPP_nat_int(X6,X27))))))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X27),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_pigeonhole__infinite) ).

tff(f20340,plain,
    spl250_1002,
    inference(avatar_split_clause,[],[f5043,f20338]) ).

tff(f20338,plain,
    ( spl250_1002
  <=> ! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK87(X0,X1)),X1))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1)))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1002])]) ).

tff(f5043,plain,
    ! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK87(X0,X1)),X1))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f3926]) ).

tff(f3926,plain,
    ! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,X0)),hAPP_n1699378549t_bool(X0,sK87(X0,X1)))))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK87(X0,X1)),X1)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK87])],[f2665,f3925]) ).

tff(f3925,plain,
    ! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,X0)),hAPP_n1699378549t_bool(X0,X2))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
     => ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,X0)),hAPP_n1699378549t_bool(X0,sK87(X0,X1)))))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK87(X0,X1)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f2665,plain,
    ! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,X0)),hAPP_n1699378549t_bool(X0,X2))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(flattening,[],[f2664]) ).

tff(f2664,plain,
    ! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,X0)),hAPP_n1699378549t_bool(X0,X2))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(ennf_transformation,[],[f1666]) ).

tff(f1666,plain,
    ! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
     => ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1)))
       => ? [X2: nat] :
            ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,X0)),hAPP_n1699378549t_bool(X0,X2))))))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ) ) ),
    inference(rectify,[],[f273]) ).

tff(f273,axiom,
    ! [X6: fun_nat_fun_nat_bool,X2: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X6,X2)))
       => ? [X27: nat] :
            ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,X6)),hAPP_n1699378549t_bool(X6,X27))))))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X27),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_pigeonhole__infinite) ).

tff(f20336,plain,
    spl250_1001,
    inference(avatar_split_clause,[],[f5041,f20334]) ).

tff(f20334,plain,
    ( spl250_1001
  <=> ! [X0: fun_nat_fun_int_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK86(X0,X1)),X1))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X0,X1)))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1001])]) ).

tff(f5041,plain,
    ! [X0: fun_nat_fun_int_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK86(X0,X1)),X1))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X0,X1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f3924]) ).

tff(f3924,plain,
    ! [X0: fun_nat_fun_int_bool,X1: fun_nat_bool] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,X0)),hAPP_n1082236369t_bool(X0,sK86(X0,X1)))))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK86(X0,X1)),X1)) )
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X0,X1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK86])],[f2663,f3923]) ).

tff(f3923,plain,
    ! [X0: fun_nat_fun_int_bool,X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,X0)),hAPP_n1082236369t_bool(X0,X2))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
     => ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,X0)),hAPP_n1082236369t_bool(X0,sK86(X0,X1)))))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK86(X0,X1)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f2663,plain,
    ! [X0: fun_nat_fun_int_bool,X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,X0)),hAPP_n1082236369t_bool(X0,X2))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X0,X1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(flattening,[],[f2662]) ).

tff(f2662,plain,
    ! [X0: fun_nat_fun_int_bool,X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,X0)),hAPP_n1082236369t_bool(X0,X2))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X0,X1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(ennf_transformation,[],[f1665]) ).

tff(f1665,plain,
    ! [X0: fun_nat_fun_int_bool,X1: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
     => ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X0,X1)))
       => ? [X2: nat] :
            ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,X0)),hAPP_n1082236369t_bool(X0,X2))))))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ) ) ),
    inference(rectify,[],[f272]) ).

tff(f272,axiom,
    ! [X6: fun_nat_fun_int_bool,X2: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X6,X2)))
       => ? [X27: nat] :
            ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,X6)),hAPP_n1082236369t_bool(X6,X27))))))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X27),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_pigeonhole__infinite) ).

tff(f20332,plain,
    spl250_1000,
    inference(avatar_split_clause,[],[f5039,f20330]) ).

tff(f20330,plain,
    ( spl250_1000
  <=> ! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK85(X0,X1)),X1))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1)))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_1000])]) ).

tff(f5039,plain,
    ! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK85(X0,X1)),X1))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f3922]) ).

tff(f3922,plain,
    ! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,X0)),hAPP_nat_fun_a_bool(X0,sK85(X0,X1)))))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK85(X0,X1)),X1)) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK85])],[f2661,f3921]) ).

tff(f3921,plain,
    ! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,X0)),hAPP_nat_fun_a_bool(X0,X2))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
     => ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,X0)),hAPP_nat_fun_a_bool(X0,sK85(X0,X1)))))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK85(X0,X1)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f2661,plain,
    ! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,X0)),hAPP_nat_fun_a_bool(X0,X2))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(flattening,[],[f2660]) ).

tff(f2660,plain,
    ! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,X0)),hAPP_nat_fun_a_bool(X0,X2))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(ennf_transformation,[],[f1664]) ).

tff(f1664,plain,
    ! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
     => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1)))
       => ? [X2: nat] :
            ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,X0)),hAPP_nat_fun_a_bool(X0,X2))))))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ) ) ),
    inference(rectify,[],[f275]) ).

tff(f275,axiom,
    ! [X6: fun_nat_fun_a_bool,X2: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X6,X2)))
       => ? [X27: nat] :
            ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,X6)),hAPP_nat_fun_a_bool(X6,X27))))))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X27),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_pigeonhole__infinite) ).

tff(f20328,plain,
    spl250_999,
    inference(avatar_split_clause,[],[f5037,f20326]) ).

tff(f20326,plain,
    ( spl250_999
  <=> ! [X0: fun_na936072029e_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK84(X0,X1)),X1))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1)))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_999])]) ).

tff(f5037,plain,
    ! [X0: fun_na936072029e_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK84(X0,X1)),X1))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f3920]) ).

tff(f3920,plain,
    ! [X0: fun_na936072029e_bool,X1: fun_nat_bool] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,X0)),hAPP_n1025906991e_bool(X0,sK84(X0,X1)))))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK84(X0,X1)),X1)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK84])],[f2659,f3919]) ).

tff(f3919,plain,
    ! [X0: fun_na936072029e_bool,X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,X0)),hAPP_n1025906991e_bool(X0,X2))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
     => ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,X0)),hAPP_n1025906991e_bool(X0,sK84(X0,X1)))))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK84(X0,X1)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f2659,plain,
    ! [X0: fun_na936072029e_bool,X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,X0)),hAPP_n1025906991e_bool(X0,X2))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(flattening,[],[f2658]) ).

tff(f2658,plain,
    ! [X0: fun_na936072029e_bool,X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,X0)),hAPP_n1025906991e_bool(X0,X2))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(ennf_transformation,[],[f1663]) ).

tff(f1663,plain,
    ! [X0: fun_na936072029e_bool,X1: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1)))
       => ? [X2: nat] :
            ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,X0)),hAPP_n1025906991e_bool(X0,X2))))))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ) ) ),
    inference(rectify,[],[f274]) ).

tff(f274,axiom,
    ! [X6: fun_na936072029e_bool,X2: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X6,X2)))
       => ? [X27: nat] :
            ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,X6)),hAPP_n1025906991e_bool(X6,X27))))))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X27),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_pigeonhole__infinite) ).

tff(f20324,plain,
    spl250_998,
    inference(avatar_split_clause,[],[f5035,f20322]) ).

tff(f20322,plain,
    ( spl250_998
  <=> ! [X0: fun_int_a,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK83(X0,X1)),X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X0,X1)))
        | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_998])]) ).

tff(f5035,plain,
    ! [X0: fun_int_a,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK83(X0,X1)),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X0,X1)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f3918]) ).

tff(f3918,plain,
    ! [X0: fun_int_a,X1: fun_int_bool] :
      ( ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,X0)),hAPP_int_a(X0,sK83(X0,X1)))))))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK83(X0,X1)),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X0,X1)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK83])],[f2657,f3917]) ).

tff(f3917,plain,
    ! [X0: fun_int_a,X1: fun_int_bool] :
      ( ? [X2: int] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,X0)),hAPP_int_a(X0,X2))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
     => ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,X0)),hAPP_int_a(X0,sK83(X0,X1)))))))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK83(X0,X1)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f2657,plain,
    ! [X0: fun_int_a,X1: fun_int_bool] :
      ( ? [X2: int] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,X0)),hAPP_int_a(X0,X2))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X0,X1)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(flattening,[],[f2656]) ).

tff(f2656,plain,
    ! [X0: fun_int_a,X1: fun_int_bool] :
      ( ? [X2: int] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,X0)),hAPP_int_a(X0,X2))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X0,X1)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(ennf_transformation,[],[f1662]) ).

tff(f1662,plain,
    ! [X0: fun_int_a,X1: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
     => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X0,X1)))
       => ? [X2: int] :
            ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,X0)),hAPP_int_a(X0,X2))))))
            & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ) ) ),
    inference(rectify,[],[f276]) ).

tff(f276,axiom,
    ! [X6: fun_int_a,X2: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X6,X2)))
       => ? [X27: int] :
            ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X2)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,X6)),hAPP_int_a(X6,X27))))))
            & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X27),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_pigeonhole__infinite) ).

tff(f20320,plain,
    spl250_997,
    inference(avatar_split_clause,[],[f5033,f20318]) ).

tff(f20318,plain,
    ( spl250_997
  <=> ! [X0: fun_int_fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK82(X0,X1)),X1))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X0,X1)))
        | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_997])]) ).

tff(f5033,plain,
    ! [X0: fun_int_fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK82(X0,X1)),X1))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X0,X1)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f3916]) ).

tff(f3916,plain,
    ! [X0: fun_int_fun_int_bool,X1: fun_int_bool] :
      ( ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,X0)),hAPP_i1948725293t_bool(X0,sK82(X0,X1)))))))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK82(X0,X1)),X1)) )
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X0,X1)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK82])],[f2655,f3915]) ).

tff(f3915,plain,
    ! [X0: fun_int_fun_int_bool,X1: fun_int_bool] :
      ( ? [X2: int] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,X0)),hAPP_i1948725293t_bool(X0,X2))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
     => ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,X0)),hAPP_i1948725293t_bool(X0,sK82(X0,X1)))))))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK82(X0,X1)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f2655,plain,
    ! [X0: fun_int_fun_int_bool,X1: fun_int_bool] :
      ( ? [X2: int] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,X0)),hAPP_i1948725293t_bool(X0,X2))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X0,X1)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(flattening,[],[f2654]) ).

tff(f2654,plain,
    ! [X0: fun_int_fun_int_bool,X1: fun_int_bool] :
      ( ? [X2: int] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,X0)),hAPP_i1948725293t_bool(X0,X2))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X0,X1)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(ennf_transformation,[],[f1661]) ).

tff(f1661,plain,
    ! [X0: fun_int_fun_int_bool,X1: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
     => ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X0,X1)))
       => ? [X2: int] :
            ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,X0)),hAPP_i1948725293t_bool(X0,X2))))))
            & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ) ) ),
    inference(rectify,[],[f277]) ).

tff(f277,axiom,
    ! [X6: fun_int_fun_int_bool,X2: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X6,X2)))
       => ? [X27: int] :
            ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X2)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,X6)),hAPP_i1948725293t_bool(X6,X27))))))
            & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X27),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_pigeonhole__infinite) ).

tff(f20316,plain,
    spl250_996,
    inference(avatar_split_clause,[],[f5031,f20314]) ).

tff(f20314,plain,
    ( spl250_996
  <=> ! [X0: fun_int_fun_nat_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK81(X0,X1)),X1))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X0,X1)))
        | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_996])]) ).

tff(f5031,plain,
    ! [X0: fun_int_fun_nat_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK81(X0,X1)),X1))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X0,X1)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f3914]) ).

tff(f3914,plain,
    ! [X0: fun_int_fun_nat_bool,X1: fun_int_bool] :
      ( ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,X0)),hAPP_i418383825t_bool(X0,sK81(X0,X1)))))))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK81(X0,X1)),X1)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X0,X1)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK81])],[f2653,f3913]) ).

tff(f3913,plain,
    ! [X0: fun_int_fun_nat_bool,X1: fun_int_bool] :
      ( ? [X2: int] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,X0)),hAPP_i418383825t_bool(X0,X2))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
     => ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,X0)),hAPP_i418383825t_bool(X0,sK81(X0,X1)))))))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK81(X0,X1)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f2653,plain,
    ! [X0: fun_int_fun_nat_bool,X1: fun_int_bool] :
      ( ? [X2: int] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,X0)),hAPP_i418383825t_bool(X0,X2))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X0,X1)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(flattening,[],[f2652]) ).

tff(f2652,plain,
    ! [X0: fun_int_fun_nat_bool,X1: fun_int_bool] :
      ( ? [X2: int] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,X0)),hAPP_i418383825t_bool(X0,X2))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X0,X1)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(ennf_transformation,[],[f1660]) ).

tff(f1660,plain,
    ! [X0: fun_int_fun_nat_bool,X1: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
     => ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X0,X1)))
       => ? [X2: int] :
            ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,X0)),hAPP_i418383825t_bool(X0,X2))))))
            & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ) ) ),
    inference(rectify,[],[f278]) ).

tff(f278,axiom,
    ! [X6: fun_int_fun_nat_bool,X2: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X6,X2)))
       => ? [X27: int] :
            ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X2)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,X6)),hAPP_i418383825t_bool(X6,X27))))))
            & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X27),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_pigeonhole__infinite) ).

tff(f20255,plain,
    spl250_995,
    inference(avatar_split_clause,[],[f5029,f20253]) ).

tff(f20253,plain,
    ( spl250_995
  <=> ! [X0: fun_int_fun_a_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK80(X0,X1)),X1))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X0,X1)))
        | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_995])]) ).

tff(f5029,plain,
    ! [X0: fun_int_fun_a_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK80(X0,X1)),X1))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X0,X1)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f3912]) ).

tff(f3912,plain,
    ! [X0: fun_int_fun_a_bool,X1: fun_int_bool] :
      ( ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,X0)),hAPP_int_fun_a_bool(X0,sK80(X0,X1)))))))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK80(X0,X1)),X1)) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X0,X1)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK80])],[f2651,f3911]) ).

tff(f3911,plain,
    ! [X0: fun_int_fun_a_bool,X1: fun_int_bool] :
      ( ? [X2: int] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,X0)),hAPP_int_fun_a_bool(X0,X2))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
     => ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,X0)),hAPP_int_fun_a_bool(X0,sK80(X0,X1)))))))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK80(X0,X1)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f2651,plain,
    ! [X0: fun_int_fun_a_bool,X1: fun_int_bool] :
      ( ? [X2: int] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,X0)),hAPP_int_fun_a_bool(X0,X2))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X0,X1)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(flattening,[],[f2650]) ).

tff(f2650,plain,
    ! [X0: fun_int_fun_a_bool,X1: fun_int_bool] :
      ( ? [X2: int] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,X0)),hAPP_int_fun_a_bool(X0,X2))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X0,X1)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(ennf_transformation,[],[f1659]) ).

tff(f1659,plain,
    ! [X0: fun_int_fun_a_bool,X1: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
     => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X0,X1)))
       => ? [X2: int] :
            ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,X0)),hAPP_int_fun_a_bool(X0,X2))))))
            & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ) ) ),
    inference(rectify,[],[f280]) ).

tff(f280,axiom,
    ! [X6: fun_int_fun_a_bool,X2: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X6,X2)))
       => ? [X27: int] :
            ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X2)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,X6)),hAPP_int_fun_a_bool(X6,X27))))))
            & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X27),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_pigeonhole__infinite) ).

tff(f20251,plain,
    spl250_994,
    inference(avatar_split_clause,[],[f5027,f20249]) ).

tff(f20249,plain,
    ( spl250_994
  <=> ! [X0: fun_in2065004473e_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK79(X0,X1)),X1))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X0,X1)))
        | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_994])]) ).

tff(f5027,plain,
    ! [X0: fun_in2065004473e_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK79(X0,X1)),X1))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X0,X1)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f3910]) ).

tff(f3910,plain,
    ! [X0: fun_in2065004473e_bool,X1: fun_int_bool] :
      ( ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,X0)),hAPP_i7355787e_bool(X0,sK79(X0,X1)))))))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK79(X0,X1)),X1)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X0,X1)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK79])],[f2649,f3909]) ).

tff(f3909,plain,
    ! [X0: fun_in2065004473e_bool,X1: fun_int_bool] :
      ( ? [X2: int] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,X0)),hAPP_i7355787e_bool(X0,X2))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
     => ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,X0)),hAPP_i7355787e_bool(X0,sK79(X0,X1)))))))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK79(X0,X1)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f2649,plain,
    ! [X0: fun_in2065004473e_bool,X1: fun_int_bool] :
      ( ? [X2: int] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,X0)),hAPP_i7355787e_bool(X0,X2))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X0,X1)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(flattening,[],[f2648]) ).

tff(f2648,plain,
    ! [X0: fun_in2065004473e_bool,X1: fun_int_bool] :
      ( ? [X2: int] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,X0)),hAPP_i7355787e_bool(X0,X2))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X0,X1)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(ennf_transformation,[],[f1658]) ).

tff(f1658,plain,
    ! [X0: fun_in2065004473e_bool,X1: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X0,X1)))
       => ? [X2: int] :
            ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,X0)),hAPP_i7355787e_bool(X0,X2))))))
            & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ) ) ),
    inference(rectify,[],[f279]) ).

tff(f279,axiom,
    ! [X6: fun_in2065004473e_bool,X2: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X6,X2)))
       => ? [X27: int] :
            ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X2)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,X6)),hAPP_i7355787e_bool(X6,X27))))))
            & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X27),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_pigeonhole__infinite) ).

tff(f20247,plain,
    spl250_993,
    inference(avatar_split_clause,[],[f5025,f20245]) ).

tff(f20245,plain,
    ( spl250_993
  <=> ! [X0: fun_pname_a,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK78(X0,X1)),X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
        | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_993])]) ).

tff(f5025,plain,
    ! [X0: fun_pname_a,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK78(X0,X1)),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f3908]) ).

tff(f3908,plain,
    ! [X0: fun_pname_a,X1: fun_pname_bool] :
      ( ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X0)),hAPP_pname_a(X0,sK78(X0,X1)))))))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK78(X0,X1)),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK78])],[f2647,f3907]) ).

tff(f3907,plain,
    ! [X0: fun_pname_a,X1: fun_pname_bool] :
      ( ? [X2: pname] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X0)),hAPP_pname_a(X0,X2))))))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) )
     => ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X0)),hAPP_pname_a(X0,sK78(X0,X1)))))))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK78(X0,X1)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f2647,plain,
    ! [X0: fun_pname_a,X1: fun_pname_bool] :
      ( ? [X2: pname] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X0)),hAPP_pname_a(X0,X2))))))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(flattening,[],[f2646]) ).

tff(f2646,plain,
    ! [X0: fun_pname_a,X1: fun_pname_bool] :
      ( ? [X2: pname] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X0)),hAPP_pname_a(X0,X2))))))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(ennf_transformation,[],[f1657]) ).

tff(f1657,plain,
    ! [X0: fun_pname_a,X1: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
     => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
       => ? [X2: pname] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X0)),hAPP_pname_a(X0,X2))))))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ) ) ),
    inference(rectify,[],[f281]) ).

tff(f281,axiom,
    ! [X6: fun_pname_a,X2: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X6,X2)))
       => ? [X27: pname] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X6)),hAPP_pname_a(X6,X27))))))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X27),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_pigeonhole__infinite) ).

tff(f20243,plain,
    spl250_992,
    inference(avatar_split_clause,[],[f4938,f20241]) ).

tff(f20241,plain,
    ( spl250_992
  <=> ! [X0: x_a,X1: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),collect_a(X1)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0))),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_992])]) ).

tff(f4938,plain,
    ! [X0: x_a,X1: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),collect_a(X1)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0))),X1)) ),
    inference(cnf_transformation,[],[f1586]) ).

tff(f1586,plain,
    ! [X0: x_a,X1: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),collect_a(X1)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0))),X1)) ),
    inference(rectify,[],[f374]) ).

tff(f374,axiom,
    ! [X5: x_a,X10: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),collect_a(X10)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X5))),X10)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_373_insert__Collect) ).

tff(f20239,plain,
    spl250_991,
    inference(avatar_split_clause,[],[f4934,f20237]) ).

tff(f20237,plain,
    ( spl250_991
  <=> ! [X0: x_a,X1: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_991])]) ).

tff(f4934,plain,
    ! [X0: x_a,X1: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))) ),
    inference(cnf_transformation,[],[f1582]) ).

tff(f1582,plain,
    ! [X0: x_a,X1: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))) ),
    inference(rectify,[],[f370]) ).

tff(f370,axiom,
    ! [X5: x_a,X7: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),X7) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X5)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_369_insert__compr) ).

tff(f20235,plain,
    spl250_990,
    inference(avatar_split_clause,[],[f4928,f20233]) ).

tff(f20233,plain,
    ( spl250_990
  <=> ! [X0: pname,X1: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_990])]) ).

tff(f4928,plain,
    ! [X0: pname,X1: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))) ),
    inference(cnf_transformation,[],[f1576]) ).

tff(f1576,plain,
    ! [X0: pname,X1: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X0)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))) ),
    inference(rectify,[],[f373]) ).

tff(f373,axiom,
    ! [X5: pname,X7: fun_pname_bool] : ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5),X7) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X5)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_372_insert__compr) ).

tff(f19734,plain,
    ( spl250_989
    | ~ spl250_158
    | ~ spl250_903 ),
    inference(avatar_split_clause,[],[f19248,f16173,f8119,f19731]) ).

tff(f19731,plain,
    ( spl250_989
  <=> ( zero_zero_nat = sK32(pls) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_989])]) ).

tff(f16173,plain,
    ( spl250_903
  <=> ( pls = hAPP_nat_int(semiri1621563631at_int,sK32(pls)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_903])]) ).

tff(f19248,plain,
    ( ( zero_zero_nat = sK32(pls) )
    | ~ spl250_158
    | ~ spl250_903 ),
    inference(trivial_inequality_removal,[],[f19225]) ).

tff(f19225,plain,
    ( ( pls != pls )
    | ( zero_zero_nat = sK32(pls) )
    | ~ spl250_158
    | ~ spl250_903 ),
    inference(superposition,[],[f8120,f16175]) ).

tff(f16175,plain,
    ( ( pls = hAPP_nat_int(semiri1621563631at_int,sK32(pls)) )
    | ~ spl250_903 ),
    inference(avatar_component_clause,[],[f16173]) ).

tff(f18274,plain,
    spl250_988,
    inference(avatar_split_clause,[],[f7233,f18272]) ).

tff(f18272,plain,
    ( spl250_988
  <=> ! [X2: fun_nat_bool,X0: fun_nat_int,X1: nat] :
        ( ( image_nat_int(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = image_nat_int(X0,X2) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_988])]) ).

tff(f7233,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_int,X1: nat] :
      ( ( image_nat_int(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = image_nat_int(X0,X2) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
    inference(forward_demodulation,[],[f6105,f5745]) ).

tff(f5745,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_int,X1: nat] : ( image_nat_int(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X0,X1)),image_nat_int(X0,X2)) ),
    inference(cnf_transformation,[],[f2121]) ).

tff(f2121,plain,
    ! [X0: fun_nat_int,X1: nat,X2: fun_nat_bool] : ( image_nat_int(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X0,X1)),image_nat_int(X0,X2)) ),
    inference(rectify,[],[f468]) ).

tff(f468,axiom,
    ! [X6: fun_nat_int,X5: nat,X7: fun_nat_bool] : ( image_nat_int(X6,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5),X7)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X6,X5)),image_nat_int(X6,X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_467_image__insert) ).

tff(f6105,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_int,X1: nat] :
      ( ( image_nat_int(X0,X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X0,X1)),image_nat_int(X0,X2)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f3396]) ).

tff(f3396,plain,
    ! [X0: fun_nat_int,X1: nat,X2: fun_nat_bool] :
      ( ( image_nat_int(X0,X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X0,X1)),image_nat_int(X0,X2)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f2337]) ).

tff(f2337,plain,
    ! [X0: fun_nat_int,X1: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
     => ( image_nat_int(X0,X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X0,X1)),image_nat_int(X0,X2)) ) ),
    inference(rectify,[],[f470]) ).

tff(f470,axiom,
    ! [X6: fun_nat_int,X8: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X2))
     => ( image_nat_int(X6,X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X6,X8)),image_nat_int(X6,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_469_insert__image) ).

tff(f18270,plain,
    spl250_987,
    inference(avatar_split_clause,[],[f7231,f18268]) ).

tff(f18268,plain,
    ( spl250_987
  <=> ! [X2: fun_pname_bool,X0: fun_pname_a,X1: pname] :
        ( ( image_pname_a(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)) = image_pname_a(X0,X2) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_987])]) ).

tff(f7231,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_a,X1: pname] :
      ( ( image_pname_a(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)) = image_pname_a(X0,X2) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
    inference(forward_demodulation,[],[f6064,f5744]) ).

tff(f5744,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_a,X1: pname] : ( image_pname_a(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)) ),
    inference(cnf_transformation,[],[f2120]) ).

tff(f2120,plain,
    ! [X0: fun_pname_a,X1: pname,X2: fun_pname_bool] : ( image_pname_a(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)) ),
    inference(rectify,[],[f469]) ).

tff(f469,axiom,
    ! [X6: fun_pname_a,X5: pname,X7: fun_pname_bool] : ( image_pname_a(X6,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5),X7)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X6,X5)),image_pname_a(X6,X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_468_image__insert) ).

tff(f6064,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_a,X1: pname] :
      ( ( image_pname_a(X0,X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
    inference(cnf_transformation,[],[f3331]) ).

tff(f3331,plain,
    ! [X0: fun_pname_a,X1: pname,X2: fun_pname_bool] :
      ( ( image_pname_a(X0,X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
    inference(ennf_transformation,[],[f2296]) ).

tff(f2296,plain,
    ! [X0: fun_pname_a,X1: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
     => ( image_pname_a(X0,X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)) ) ),
    inference(rectify,[],[f471]) ).

tff(f471,axiom,
    ! [X6: fun_pname_a,X8: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X2))
     => ( image_pname_a(X6,X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X6,X8)),image_pname_a(X6,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_insert__image) ).

tff(f18266,plain,
    spl250_986,
    inference(avatar_split_clause,[],[f6985,f18264]) ).

tff(f18264,plain,
    ( spl250_986
  <=> ! [X0: fun_a_bool,X1: x_a] :
        ( ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X1)),X0)) = collect_a(hAPP_a_fun_a_bool(fequal_a,X1)) )
        | ~ hBOOL(hAPP_a_bool(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_986])]) ).

tff(f6985,plain,
    ! [X0: fun_a_bool,X1: x_a] :
      ( ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X1)),X0)) = collect_a(hAPP_a_fun_a_bool(fequal_a,X1)) )
      | ~ hBOOL(hAPP_a_bool(X0,X1)) ),
    inference(forward_demodulation,[],[f4954,f4680]) ).

tff(f4954,plain,
    ! [X0: fun_a_bool,X1: x_a] :
      ( ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X1)),X0)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool) )
      | ~ hBOOL(hAPP_a_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f2615]) ).

tff(f2615,plain,
    ! [X0: fun_a_bool,X1: x_a] :
      ( ( ( bot_bot_fun_a_bool = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X1)),X0)) )
        | hBOOL(hAPP_a_bool(X0,X1)) )
      & ( ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X1)),X0)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool) )
        | ~ hBOOL(hAPP_a_bool(X0,X1)) ) ),
    inference(ennf_transformation,[],[f1598]) ).

tff(f1598,plain,
    ! [X0: fun_a_bool,X1: x_a] :
      ( ( ~ hBOOL(hAPP_a_bool(X0,X1))
       => ( bot_bot_fun_a_bool = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X1)),X0)) ) )
      & ( hBOOL(hAPP_a_bool(X0,X1))
       => ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X1)),X0)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool) ) ) ),
    inference(rectify,[],[f634]) ).

tff(f634,axiom,
    ! [X10: fun_a_bool,X5: x_a] :
      ( ( ~ hBOOL(hAPP_a_bool(X10,X5))
       => ( bot_bot_fun_a_bool = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X5)),X10)) ) )
      & ( hBOOL(hAPP_a_bool(X10,X5))
       => ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),bot_bot_fun_a_bool) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X5)),X10)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_633_Collect__conv__if2) ).

tff(f18262,plain,
    spl250_985,
    inference(avatar_split_clause,[],[f6981,f18260]) ).

tff(f18260,plain,
    ( spl250_985
  <=> ! [X0: nat,X1: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_n1699378549t_bool(fequal_nat,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_985])]) ).

tff(f6981,plain,
    ! [X0: nat,X1: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_n1699378549t_bool(fequal_nat,X0))) ),
    inference(forward_demodulation,[],[f4940,f6931]) ).

tff(f4940,plain,
    ! [X0: nat,X1: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool))) ),
    inference(cnf_transformation,[],[f1588]) ).

tff(f1588,plain,
    ! [X0: nat,X1: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool))) ),
    inference(rectify,[],[f554]) ).

tff(f554,axiom,
    ! [X5: nat,X2: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5),X2) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5),bot_bot_fun_nat_bool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_553_insert__Diff__single) ).

tff(f18258,plain,
    spl250_984,
    inference(avatar_split_clause,[],[f6980,f18256]) ).

tff(f18256,plain,
    ( spl250_984
  <=> ! [X0: int,X1: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_i1948725293t_bool(fequal_int,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_984])]) ).

tff(f6980,plain,
    ! [X0: int,X1: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_i1948725293t_bool(fequal_int,X0))) ),
    inference(forward_demodulation,[],[f4939,f6930]) ).

tff(f4939,plain,
    ! [X0: int,X1: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool))) ),
    inference(cnf_transformation,[],[f1587]) ).

tff(f1587,plain,
    ! [X0: int,X1: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool))) ),
    inference(rectify,[],[f555]) ).

tff(f555,axiom,
    ! [X5: int,X2: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5),X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5),bot_bot_fun_int_bool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_554_insert__Diff__single) ).

tff(f18254,plain,
    spl250_983,
    inference(avatar_split_clause,[],[f6974,f18252]) ).

tff(f18252,plain,
    ( spl250_983
  <=> ! [X0: nat,X1: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(fequal_nat,X0)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_983])]) ).

tff(f6974,plain,
    ! [X0: nat,X1: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(fequal_nat,X0)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))) ),
    inference(forward_demodulation,[],[f4932,f6935]) ).

tff(f6935,plain,
    ! [X0: nat] : ( hAPP_n1699378549t_bool(fequal_nat,X0) = hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0) ),
    inference(forward_demodulation,[],[f6934,f6931]) ).

tff(f6934,plain,
    ! [X0: nat] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) = hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0) ),
    inference(forward_demodulation,[],[f4684,f4588]) ).

tff(f4684,plain,
    ! [X0: nat] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) = collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0)) ),
    inference(cnf_transformation,[],[f1412]) ).

tff(f1412,plain,
    ! [X0: nat] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) = collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0)) ),
    inference(rectify,[],[f639]) ).

tff(f639,axiom,
    ! [X5: nat] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5),bot_bot_fun_nat_bool) = collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_638_singleton__conv) ).

tff(f4932,plain,
    ! [X0: nat,X1: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))) ),
    inference(cnf_transformation,[],[f1580]) ).

tff(f1580,plain,
    ! [X0: nat,X1: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))) ),
    inference(rectify,[],[f440]) ).

tff(f440,axiom,
    ! [X27: nat,X65: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X27),X65) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X27)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X65))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_439_insert__compr__raw) ).

tff(f18250,plain,
    spl250_982,
    inference(avatar_split_clause,[],[f6972,f18248]) ).

tff(f18248,plain,
    ( spl250_982
  <=> ! [X0: int,X1: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(fequal_int,X0)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_982])]) ).

tff(f6972,plain,
    ! [X0: int,X1: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(fequal_int,X0)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1))) ),
    inference(forward_demodulation,[],[f4930,f6933]) ).

tff(f6933,plain,
    ! [X0: int] : ( hAPP_i1948725293t_bool(fequal_int,X0) = hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X0) ),
    inference(forward_demodulation,[],[f6932,f6930]) ).

tff(f6932,plain,
    ! [X0: int] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X0) ),
    inference(forward_demodulation,[],[f4683,f4586]) ).

tff(f4683,plain,
    ! [X0: int] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = collect_int(hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X0)) ),
    inference(cnf_transformation,[],[f1411]) ).

tff(f1411,plain,
    ! [X0: int] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = collect_int(hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X0)) ),
    inference(rectify,[],[f638]) ).

tff(f638,axiom,
    ! [X5: int] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5),bot_bot_fun_int_bool) = collect_int(hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_637_singleton__conv) ).

tff(f4930,plain,
    ! [X0: int,X1: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X0)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1))) ),
    inference(cnf_transformation,[],[f1578]) ).

tff(f1578,plain,
    ! [X0: int,X1: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X0)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1))) ),
    inference(rectify,[],[f371]) ).

tff(f371,axiom,
    ! [X5: int,X7: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5),X7) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X5)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_370_insert__compr) ).

tff(f18246,plain,
    spl250_981,
    inference(avatar_split_clause,[],[f6948,f18244]) ).

tff(f18244,plain,
    ( spl250_981
  <=> ! [X0: int] :
        ( ( hAPP_nat_nat(suc,number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)) )
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_981])]) ).

tff(f6948,plain,
    ! [X0: int] :
      ( ( hAPP_nat_nat(suc,number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)) )
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(forward_demodulation,[],[f6589,f4671]) ).

tff(f4671,plain,
    ! [X0: nat] : ( hAPP_nat_nat(suc,X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X0) ),
    inference(cnf_transformation,[],[f1399]) ).

tff(f1399,plain,
    ! [X0: nat] : ( hAPP_nat_nat(suc,X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X0) ),
    inference(rectify,[],[f850]) ).

tff(f850,axiom,
    ! [X11: nat] : ( hAPP_nat_nat(suc,X11) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_849_Suc__eq__plus1__left) ).

tff(f6589,plain,
    ! [X0: int] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)) )
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(definition_unfolding,[],[f4702,f4661]) ).

tff(f4661,plain,
    ! [X0: int] : ( succ(X0) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int) ),
    inference(cnf_transformation,[],[f1389]) ).

tff(f1389,plain,
    ! [X0: int] : ( succ(X0) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int) ),
    inference(rectify,[],[f1163]) ).

tff(f1163,axiom,
    ! [X19: int] : ( succ(X19) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X19),one_one_int) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1162_succ__def) ).

tff(f4702,plain,
    ! [X0: int] :
      ( ( number_number_of_nat(succ(X0)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X0)) )
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(cnf_transformation,[],[f2579]) ).

tff(f2579,plain,
    ! [X0: int] :
      ( ( ( number_number_of_nat(succ(X0)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X0)) )
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
      & ( ( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X0)) )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
    inference(ennf_transformation,[],[f1426]) ).

tff(f1426,plain,
    ! [X0: int] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
       => ( number_number_of_nat(succ(X0)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X0)) ) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
       => ( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X0)) ) ) ),
    inference(rectify,[],[f1166]) ).

tff(f1166,axiom,
    ! [X130: int] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X130),pls))
       => ( number_number_of_nat(succ(X130)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X130)) ) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X130),pls))
       => ( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X130)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1165_nat__1__add__number__of) ).

tff(f18242,plain,
    ( spl250_980
    | ~ spl250_157
    | ~ spl250_672 ),
    inference(avatar_split_clause,[],[f13806,f12737,f8115,f18240]) ).

tff(f18240,plain,
    ( spl250_980
  <=> ! [X0: nat,X1: nat] : sP24(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_980])]) ).

tff(f8115,plain,
    ( spl250_157
  <=> ! [X0: nat] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_157])]) ).

tff(f12737,plain,
    ( spl250_672
  <=> ! [X2: nat,X0: fun_int_bool,X1: nat] :
        ( sP24(X0,X2,X1)
        | ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_672])]) ).

tff(f13806,plain,
    ( ! [X0: nat,X1: nat] : sP24(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0,X1)
    | ~ spl250_157
    | ~ spl250_672 ),
    inference(resolution,[],[f12738,f8116]) ).

tff(f8116,plain,
    ( ! [X0: nat] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,X0)))
    | ~ spl250_157 ),
    inference(avatar_component_clause,[],[f8115]) ).

tff(f12738,plain,
    ( ! [X2: nat,X0: fun_int_bool,X1: nat] :
        ( ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))))
        | sP24(X0,X2,X1) )
    | ~ spl250_672 ),
    inference(avatar_component_clause,[],[f12737]) ).

tff(f18238,plain,
    spl250_979,
    inference(avatar_split_clause,[],[f6940,f18236]) ).

tff(f18236,plain,
    ( spl250_979
  <=> ! [X0: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X0))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,hAPP_nat_nat(suc,one_one_nat))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_979])]) ).

tff(f6940,plain,
    ! [X0: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X0))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,hAPP_nat_nat(suc,one_one_nat))),X0) ),
    inference(forward_demodulation,[],[f6939,f6926]) ).

tff(f6926,plain,
    number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),one_one_int))),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),one_one_int))) = hAPP_nat_nat(suc,hAPP_nat_nat(suc,one_one_nat)),
    inference(forward_demodulation,[],[f6925,f4566]) ).

tff(f6925,plain,
    hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))) = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),one_one_int))),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),one_one_int))),
    inference(forward_demodulation,[],[f6573,f6566]) ).

tff(f6566,plain,
    hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),one_one_int),
    inference(definition_unfolding,[],[f4573,f4661,f4687]) ).

tff(f4573,plain,
    succ(pls) = bit1(pls),
    inference(cnf_transformation,[],[f1167]) ).

tff(f1167,axiom,
    succ(pls) = bit1(pls),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1166_succ__Pls) ).

tff(f6573,plain,
    hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))) = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls))),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls))),
    inference(definition_unfolding,[],[f4583,f4687,f4687]) ).

tff(f4583,plain,
    number_number_of_nat(bit1(bit1(pls))) = hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))),
    inference(cnf_transformation,[],[f1172]) ).

tff(f1172,axiom,
    number_number_of_nat(bit1(bit1(pls))) = hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1171_numeral__3__eq__3) ).

tff(f6939,plain,
    ! [X0: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X0))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),one_one_int))),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),one_one_int)))),X0) ),
    inference(forward_demodulation,[],[f6584,f6566]) ).

tff(f6584,plain,
    ! [X0: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X0))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls))),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls)))),X0) ),
    inference(definition_unfolding,[],[f4694,f4687,f4687]) ).

tff(f4694,plain,
    ! [X0: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X0))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(bit1(bit1(pls)))),X0) ),
    inference(cnf_transformation,[],[f1422]) ).

tff(f1422,plain,
    ! [X0: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X0))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(bit1(bit1(pls)))),X0) ),
    inference(rectify,[],[f1173]) ).

tff(f1173,axiom,
    ! [X11: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X11))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(bit1(bit1(pls)))),X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1172_Suc3__eq__add__3) ).

tff(f18234,plain,
    spl250_978,
    inference(avatar_split_clause,[],[f6628,f18232]) ).

tff(f18232,plain,
    ( spl250_978
  <=> ! [X4: int,X0: fun_int_bool] :
        ( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK74(X0))))
        | ~ hBOOL(hAPP_int_bool(X0,X4))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_978])]) ).

tff(f6628,plain,
    ! [X0: fun_int_bool,X4: int] :
      ( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK74(X0))))
      | ~ hBOOL(hAPP_int_bool(X0,X4))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X4)) ),
    inference(definition_unfolding,[],[f4866,f4550]) ).

tff(f4866,plain,
    ! [X0: fun_int_bool,X4: int] :
      ( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK74(X0))))
      | ~ hBOOL(hAPP_int_bool(X0,X4))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4)) ),
    inference(cnf_transformation,[],[f3902]) ).

tff(f3902,plain,
    ! [X0: fun_int_bool] :
      ( ( ( hBOOL(hAPP_int_bool(X0,sK73(X0)))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK73(X0))) )
        | ! [X2: nat] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) )
      & ( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK74(X0))))
        | ! [X4: int] :
            ( ~ hBOOL(hAPP_int_bool(X0,X4))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK73,sK74])],[f3899,f3901,f3900]) ).

tff(f3900,plain,
    ! [X0: fun_int_bool] :
      ( ? [X1: int] :
          ( hBOOL(hAPP_int_bool(X0,X1))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
     => ( hBOOL(hAPP_int_bool(X0,sK73(X0)))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK73(X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f3901,plain,
    ! [X0: fun_int_bool] :
      ( ? [X3: nat] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
     => hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK74(X0)))) ),
    introduced(choice_axiom,[]) ).

tff(f3899,plain,
    ! [X0: fun_int_bool] :
      ( ( ? [X1: int] :
            ( hBOOL(hAPP_int_bool(X0,X1))
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
        | ! [X2: nat] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) )
      & ( ? [X3: nat] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
        | ! [X4: int] :
            ( ~ hBOOL(hAPP_int_bool(X0,X4))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4)) ) ) ),
    inference(rectify,[],[f3898]) ).

tff(f3898,plain,
    ! [X0: fun_int_bool] :
      ( ( ? [X1: int] :
            ( hBOOL(hAPP_int_bool(X0,X1))
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
        | ! [X2: nat] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) )
      & ( ? [X2: nat] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2)))
        | ! [X1: int] :
            ( ~ hBOOL(hAPP_int_bool(X0,X1))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) ) ),
    inference(nnf_transformation,[],[f1516]) ).

tff(f1516,plain,
    ! [X0: fun_int_bool] :
      ( ? [X1: int] :
          ( hBOOL(hAPP_int_bool(X0,X1))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
    <=> ? [X2: nat] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
    inference(rectify,[],[f1120]) ).

tff(f1120,axiom,
    ! [X10: fun_int_bool] :
      ( ? [X27: int] :
          ( hBOOL(hAPP_int_bool(X10,X27))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X27)) )
    <=> ? [X27: nat] : hBOOL(hAPP_int_bool(X10,hAPP_nat_int(semiri1621563631at_int,X27))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1119_transfer__int__nat__quantifiers_I2_J) ).

tff(f18230,plain,
    spl250_977,
    inference(avatar_split_clause,[],[f6625,f18228]) ).

tff(f18228,plain,
    ( spl250_977
  <=> ! [X0: fun_int_bool,X1: int] :
        ( hBOOL(hAPP_int_bool(X0,X1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
        | ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK67(X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_977])]) ).

tff(f6625,plain,
    ! [X0: fun_int_bool,X1: int] :
      ( hBOOL(hAPP_int_bool(X0,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK67(X0)))) ),
    inference(definition_unfolding,[],[f4857,f4550]) ).

tff(f4857,plain,
    ! [X0: fun_int_bool,X1: int] :
      ( hBOOL(hAPP_int_bool(X0,X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK67(X0)))) ),
    inference(cnf_transformation,[],[f3881]) ).

tff(f3881,plain,
    ! [X0: fun_int_bool] :
      ( ( ! [X1: int] :
            ( hBOOL(hAPP_int_bool(X0,X1))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
        | ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK67(X0)))) )
      & ( ! [X3: nat] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
        | ( ~ hBOOL(hAPP_int_bool(X0,sK68(X0)))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK68(X0))) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68])],[f3878,f3880,f3879]) ).

tff(f3879,plain,
    ! [X0: fun_int_bool] :
      ( ? [X2: nat] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2)))
     => ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK67(X0)))) ),
    introduced(choice_axiom,[]) ).

tff(f3880,plain,
    ! [X0: fun_int_bool] :
      ( ? [X4: int] :
          ( ~ hBOOL(hAPP_int_bool(X0,X4))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4)) )
     => ( ~ hBOOL(hAPP_int_bool(X0,sK68(X0)))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK68(X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f3878,plain,
    ! [X0: fun_int_bool] :
      ( ( ! [X1: int] :
            ( hBOOL(hAPP_int_bool(X0,X1))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
        | ? [X2: nat] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) )
      & ( ! [X3: nat] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
        | ? [X4: int] :
            ( ~ hBOOL(hAPP_int_bool(X0,X4))
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4)) ) ) ),
    inference(rectify,[],[f3877]) ).

tff(f3877,plain,
    ! [X0: fun_int_bool] :
      ( ( ! [X1: int] :
            ( hBOOL(hAPP_int_bool(X0,X1))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
        | ? [X2: nat] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) )
      & ( ! [X2: nat] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2)))
        | ? [X1: int] :
            ( ~ hBOOL(hAPP_int_bool(X0,X1))
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) ) ),
    inference(nnf_transformation,[],[f2609]) ).

tff(f2609,plain,
    ! [X0: fun_int_bool] :
      ( ! [X1: int] :
          ( hBOOL(hAPP_int_bool(X0,X1))
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
    <=> ! [X2: nat] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
    inference(ennf_transformation,[],[f1511]) ).

tff(f1511,plain,
    ! [X0: fun_int_bool] :
      ( ! [X1: int] :
          ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
         => hBOOL(hAPP_int_bool(X0,X1)) )
    <=> ! [X2: nat] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
    inference(rectify,[],[f1121]) ).

tff(f1121,axiom,
    ! [X10: fun_int_bool] :
      ( ! [X27: int] :
          ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X27))
         => hBOOL(hAPP_int_bool(X10,X27)) )
    <=> ! [X27: nat] : hBOOL(hAPP_int_bool(X10,hAPP_nat_int(semiri1621563631at_int,X27))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1120_transfer__int__nat__quantifiers_I1_J) ).

tff(f18226,plain,
    spl250_976,
    inference(avatar_split_clause,[],[f6411,f18224]) ).

tff(f18224,plain,
    ( spl250_976
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( zero_zero_nat = X0 )
        | ( X1 = X2 )
        | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_976])]) ).

tff(f6411,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( zero_zero_nat = X0 )
      | ( X1 = X2 )
      | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2) ) ),
    inference(cnf_transformation,[],[f4485]) ).

tff(f4485,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2) )
        | ( ( zero_zero_nat != X0 )
          & ( X1 != X2 ) ) )
      & ( ( zero_zero_nat = X0 )
        | ( X1 = X2 )
        | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2) ) ) ),
    inference(flattening,[],[f4484]) ).

tff(f4484,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2) )
        | ( ( zero_zero_nat != X0 )
          & ( X1 != X2 ) ) )
      & ( ( zero_zero_nat = X0 )
        | ( X1 = X2 )
        | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2) ) ) ),
    inference(nnf_transformation,[],[f2500]) ).

tff(f2500,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X2) )
    <=> ( ( zero_zero_nat = X0 )
        | ( X1 = X2 ) ) ),
    inference(rectify,[],[f982]) ).

tff(f982,axiom,
    ! [X13: nat,X22: nat,X14: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X13),X22) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X13),X14) )
    <=> ( ( zero_zero_nat = X13 )
        | ( X14 = X22 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_981_mult__cancel1) ).

tff(f18222,plain,
    spl250_975,
    inference(avatar_split_clause,[],[f6408,f18220]) ).

tff(f18220,plain,
    ( spl250_975
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( zero_zero_nat = X1 )
        | ( X0 = X2 )
        | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_975])]) ).

tff(f6408,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( zero_zero_nat = X1 )
      | ( X0 = X2 )
      | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1) ) ),
    inference(cnf_transformation,[],[f4483]) ).

tff(f4483,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1) )
        | ( ( zero_zero_nat != X1 )
          & ( X0 != X2 ) ) )
      & ( ( zero_zero_nat = X1 )
        | ( X0 = X2 )
        | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1) ) ) ),
    inference(flattening,[],[f4482]) ).

tff(f4482,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1) )
        | ( ( zero_zero_nat != X1 )
          & ( X0 != X2 ) ) )
      & ( ( zero_zero_nat = X1 )
        | ( X0 = X2 )
        | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1) ) ) ),
    inference(nnf_transformation,[],[f2499]) ).

tff(f2499,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1) )
    <=> ( ( zero_zero_nat = X1 )
        | ( X0 = X2 ) ) ),
    inference(rectify,[],[f983]) ).

tff(f983,axiom,
    ! [X22: nat,X13: nat,X14: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X22),X13) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),X13) )
    <=> ( ( zero_zero_nat = X13 )
        | ( X14 = X22 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_982_mult__cancel2) ).

tff(f18218,plain,
    spl250_974,
    inference(avatar_split_clause,[],[f6318,f18216]) ).

tff(f18216,plain,
    ( spl250_974
  <=> ! [X2: nat,X0: fun_nat_bool,X1: nat] :
        ( sP19(X0,X1,X2)
        | ~ hBOOL(hAPP_nat_bool(X0,sK247(X0,X1,X2)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_974])]) ).

tff(f6318,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: nat] :
      ( sP19(X0,X1,X2)
      | ~ hBOOL(hAPP_nat_bool(X0,sK247(X0,X1,X2)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f4431]) ).

tff(f18214,plain,
    spl250_973,
    inference(avatar_split_clause,[],[f6310,f18212]) ).

tff(f18212,plain,
    ( spl250_973
  <=> ! [X2: nat,X0: fun_nat_bool,X1: nat] :
        ( sP18(X0,X1,X2)
        | ~ hBOOL(hAPP_nat_bool(X0,sK246(X0,X1,X2)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_973])]) ).

tff(f6310,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: nat] :
      ( sP18(X0,X1,X2)
      | ~ hBOOL(hAPP_nat_bool(X0,sK246(X0,X1,X2)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f4425]) ).

tff(f18210,plain,
    spl250_972,
    inference(avatar_split_clause,[],[f6303,f18208]) ).

tff(f18208,plain,
    ( spl250_972
  <=> ! [X2: fun_nat_bool,X0: fun_int_bool,X1: fun_nat_int] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK245(X0,X1,X2)),X2))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_972])]) ).

tff(f6303,plain,
    ! [X2: fun_nat_bool,X0: fun_int_bool,X1: fun_nat_int] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK245(X0,X1,X2)),X2))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2))) ),
    inference(cnf_transformation,[],[f4420]) ).

tff(f4420,plain,
    ! [X0: fun_int_bool,X1: fun_nat_int,X2: fun_nat_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2)))
        | ! [X3: fun_nat_bool] :
            ( ( image_nat_int(X1,X3) != X0 )
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) ) )
      & ( ( ( image_nat_int(X1,sK245(X0,X1,X2)) = X0 )
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK245(X0,X1,X2)),X2)) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK245])],[f4418,f4419]) ).

tff(f4419,plain,
    ! [X0: fun_int_bool,X1: fun_nat_int,X2: fun_nat_bool] :
      ( ? [X4: fun_nat_bool] :
          ( ( image_nat_int(X1,X4) = X0 )
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X2)) )
     => ( ( image_nat_int(X1,sK245(X0,X1,X2)) = X0 )
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK245(X0,X1,X2)),X2)) ) ),
    introduced(choice_axiom,[]) ).

tff(f4418,plain,
    ! [X0: fun_int_bool,X1: fun_nat_int,X2: fun_nat_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2)))
        | ! [X3: fun_nat_bool] :
            ( ( image_nat_int(X1,X3) != X0 )
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) ) )
      & ( ? [X4: fun_nat_bool] :
            ( ( image_nat_int(X1,X4) = X0 )
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X2)) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2))) ) ),
    inference(rectify,[],[f4417]) ).

tff(f4417,plain,
    ! [X0: fun_int_bool,X1: fun_nat_int,X2: fun_nat_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2)))
        | ! [X3: fun_nat_bool] :
            ( ( image_nat_int(X1,X3) != X0 )
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) ) )
      & ( ? [X3: fun_nat_bool] :
            ( ( image_nat_int(X1,X3) = X0 )
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2))) ) ),
    inference(nnf_transformation,[],[f2474]) ).

tff(f2474,plain,
    ! [X0: fun_int_bool,X1: fun_nat_int,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2)))
    <=> ? [X3: fun_nat_bool] :
          ( ( image_nat_int(X1,X3) = X0 )
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) ) ),
    inference(rectify,[],[f472]) ).

tff(f472,axiom,
    ! [X7: fun_int_bool,X6: fun_nat_int,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X7),image_nat_int(X6,X2)))
    <=> ? [X68: fun_nat_bool] :
          ( ( image_nat_int(X6,X68) = X7 )
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X68),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_subset__image__iff) ).

tff(f18206,plain,
    spl250_971,
    inference(avatar_split_clause,[],[f6300,f18204]) ).

tff(f18204,plain,
    ( spl250_971
  <=> ! [X2: fun_nat_bool,X0: int,X1: fun_nat_int] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK244(X0,X1,X2)),X2))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_971])]) ).

tff(f6300,plain,
    ! [X2: fun_nat_bool,X0: int,X1: fun_nat_int] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK244(X0,X1,X2)),X2))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ),
    inference(cnf_transformation,[],[f4416]) ).

tff(f4416,plain,
    ! [X0: int,X1: fun_nat_int,X2: fun_nat_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2)))
        | ! [X3: nat] :
            ( ( hAPP_nat_int(X1,X3) != X0 )
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2)) ) )
      & ( ( ( hAPP_nat_int(X1,sK244(X0,X1,X2)) = X0 )
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK244(X0,X1,X2)),X2)) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK244])],[f4414,f4415]) ).

tff(f4415,plain,
    ! [X0: int,X1: fun_nat_int,X2: fun_nat_bool] :
      ( ? [X4: nat] :
          ( ( hAPP_nat_int(X1,X4) = X0 )
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X2)) )
     => ( ( hAPP_nat_int(X1,sK244(X0,X1,X2)) = X0 )
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK244(X0,X1,X2)),X2)) ) ),
    introduced(choice_axiom,[]) ).

tff(f4414,plain,
    ! [X0: int,X1: fun_nat_int,X2: fun_nat_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2)))
        | ! [X3: nat] :
            ( ( hAPP_nat_int(X1,X3) != X0 )
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2)) ) )
      & ( ? [X4: nat] :
            ( ( hAPP_nat_int(X1,X4) = X0 )
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X2)) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ) ),
    inference(rectify,[],[f4413]) ).

tff(f4413,plain,
    ! [X0: int,X1: fun_nat_int,X2: fun_nat_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2)))
        | ! [X3: nat] :
            ( ( hAPP_nat_int(X1,X3) != X0 )
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2)) ) )
      & ( ? [X3: nat] :
            ( ( hAPP_nat_int(X1,X3) = X0 )
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2)) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ) ),
    inference(nnf_transformation,[],[f2473]) ).

tff(f2473,plain,
    ! [X0: int,X1: fun_nat_int,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2)))
    <=> ? [X3: nat] :
          ( ( hAPP_nat_int(X1,X3) = X0 )
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2)) ) ),
    inference(rectify,[],[f432]) ).

tff(f432,axiom,
    ! [X53: int,X6: fun_nat_int,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X53),image_nat_int(X6,X2)))
    <=> ? [X27: nat] :
          ( ( hAPP_nat_int(X6,X27) = X53 )
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X27),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_431_image__iff) ).

tff(f18202,plain,
    spl250_970,
    inference(avatar_split_clause,[],[f6297,f18200]) ).

tff(f18200,plain,
    ( spl250_970
  <=> ! [X2: fun_pname_bool,X0: fun_a_bool,X1: fun_pname_a] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK243(X0,X1,X2)),X2))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_970])]) ).

tff(f6297,plain,
    ! [X2: fun_pname_bool,X0: fun_a_bool,X1: fun_pname_a] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK243(X0,X1,X2)),X2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2))) ),
    inference(cnf_transformation,[],[f4412]) ).

tff(f4412,plain,
    ! [X0: fun_a_bool,X1: fun_pname_a,X2: fun_pname_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
        | ! [X3: fun_pname_bool] :
            ( ( image_pname_a(X1,X3) != X0 )
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ) )
      & ( ( ( image_pname_a(X1,sK243(X0,X1,X2)) = X0 )
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK243(X0,X1,X2)),X2)) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK243])],[f4410,f4411]) ).

tff(f4411,plain,
    ! [X0: fun_a_bool,X1: fun_pname_a,X2: fun_pname_bool] :
      ( ? [X4: fun_pname_bool] :
          ( ( image_pname_a(X1,X4) = X0 )
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X2)) )
     => ( ( image_pname_a(X1,sK243(X0,X1,X2)) = X0 )
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK243(X0,X1,X2)),X2)) ) ),
    introduced(choice_axiom,[]) ).

tff(f4410,plain,
    ! [X0: fun_a_bool,X1: fun_pname_a,X2: fun_pname_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
        | ! [X3: fun_pname_bool] :
            ( ( image_pname_a(X1,X3) != X0 )
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ) )
      & ( ? [X4: fun_pname_bool] :
            ( ( image_pname_a(X1,X4) = X0 )
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4),X2)) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2))) ) ),
    inference(rectify,[],[f4409]) ).

tff(f4409,plain,
    ! [X0: fun_a_bool,X1: fun_pname_a,X2: fun_pname_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
        | ! [X3: fun_pname_bool] :
            ( ( image_pname_a(X1,X3) != X0 )
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ) )
      & ( ? [X3: fun_pname_bool] :
            ( ( image_pname_a(X1,X3) = X0 )
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2))) ) ),
    inference(nnf_transformation,[],[f2472]) ).

tff(f2472,plain,
    ! [X0: fun_a_bool,X1: fun_pname_a,X2: fun_pname_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
    <=> ? [X3: fun_pname_bool] :
          ( ( image_pname_a(X1,X3) = X0 )
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ) ),
    inference(rectify,[],[f473]) ).

tff(f473,axiom,
    ! [X7: fun_a_bool,X6: fun_pname_a,X2: fun_pname_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),image_pname_a(X6,X2)))
    <=> ? [X68: fun_pname_bool] :
          ( ( image_pname_a(X6,X68) = X7 )
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X68),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_472_subset__image__iff) ).

tff(f18198,plain,
    ( spl250_969
    | ~ spl250_631
    | ~ spl250_632 ),
    inference(avatar_split_clause,[],[f13064,f12449,f12445,f18196]) ).

tff(f18196,plain,
    ( spl250_969
  <=> ! [X0: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_969])]) ).

tff(f12445,plain,
    ( spl250_631
  <=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK131(X0,X1)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_631])]) ).

tff(f12449,plain,
    ( spl250_632
  <=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK131(X0,X1)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_632])]) ).

tff(f13064,plain,
    ( ! [X0: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X0))
    | ~ spl250_631
    | ~ spl250_632 ),
    inference(duplicate_literal_removal,[],[f13060]) ).

tff(f13060,plain,
    ( ! [X0: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X0))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X0)) )
    | ~ spl250_631
    | ~ spl250_632 ),
    inference(resolution,[],[f12450,f12446]) ).

tff(f12446,plain,
    ( ! [X0: fun_pname_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK131(X0,X1)),X1))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0)) )
    | ~ spl250_631 ),
    inference(avatar_component_clause,[],[f12445]) ).

tff(f12450,plain,
    ( ! [X0: fun_pname_bool,X1: fun_pname_bool] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK131(X0,X1)),X0))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0)) )
    | ~ spl250_632 ),
    inference(avatar_component_clause,[],[f12449]) ).

tff(f18194,plain,
    spl250_968,
    inference(avatar_split_clause,[],[f6294,f18192]) ).

tff(f18192,plain,
    ( spl250_968
  <=> ! [X2: fun_pname_bool,X0: x_a,X1: fun_pname_a] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK242(X0,X1,X2)),X2))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_968])]) ).

tff(f6294,plain,
    ! [X2: fun_pname_bool,X0: x_a,X1: fun_pname_a] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK242(X0,X1,X2)),X2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ),
    inference(cnf_transformation,[],[f4408]) ).

tff(f4408,plain,
    ! [X0: x_a,X1: fun_pname_a,X2: fun_pname_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
        | ! [X3: pname] :
            ( ( hAPP_pname_a(X1,X3) != X0 )
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2)) ) )
      & ( ( ( hAPP_pname_a(X1,sK242(X0,X1,X2)) = X0 )
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK242(X0,X1,X2)),X2)) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK242])],[f4406,f4407]) ).

tff(f4407,plain,
    ! [X0: x_a,X1: fun_pname_a,X2: fun_pname_bool] :
      ( ? [X4: pname] :
          ( ( hAPP_pname_a(X1,X4) = X0 )
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X2)) )
     => ( ( hAPP_pname_a(X1,sK242(X0,X1,X2)) = X0 )
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK242(X0,X1,X2)),X2)) ) ),
    introduced(choice_axiom,[]) ).

tff(f4406,plain,
    ! [X0: x_a,X1: fun_pname_a,X2: fun_pname_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
        | ! [X3: pname] :
            ( ( hAPP_pname_a(X1,X3) != X0 )
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2)) ) )
      & ( ? [X4: pname] :
            ( ( hAPP_pname_a(X1,X4) = X0 )
            & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X2)) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ) ),
    inference(rectify,[],[f4405]) ).

tff(f4405,plain,
    ! [X0: x_a,X1: fun_pname_a,X2: fun_pname_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
        | ! [X3: pname] :
            ( ( hAPP_pname_a(X1,X3) != X0 )
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2)) ) )
      & ( ? [X3: pname] :
            ( ( hAPP_pname_a(X1,X3) = X0 )
            & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2)) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ) ),
    inference(nnf_transformation,[],[f2471]) ).

tff(f2471,plain,
    ! [X0: x_a,X1: fun_pname_a,X2: fun_pname_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
    <=> ? [X3: pname] :
          ( ( hAPP_pname_a(X1,X3) = X0 )
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2)) ) ),
    inference(rectify,[],[f433]) ).

tff(f433,axiom,
    ! [X53: x_a,X6: fun_pname_a,X2: fun_pname_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X53),image_pname_a(X6,X2)))
    <=> ? [X27: pname] :
          ( ( hAPP_pname_a(X6,X27) = X53 )
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X27),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_432_image__iff) ).

tff(f18190,plain,
    spl250_967,
    inference(avatar_split_clause,[],[f6277,f18188]) ).

tff(f18188,plain,
    ( spl250_967
  <=> ! [X2: fun_nat_bool,X0: fun_nat_int,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X0,X2)),X1))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK233(X0,X1,X2)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_967])]) ).

tff(f6277,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_int,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X0,X2)),X1))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK233(X0,X1,X2)),X2)) ),
    inference(cnf_transformation,[],[f4390]) ).

tff(f18186,plain,
    spl250_966,
    inference(avatar_split_clause,[],[f6275,f18184]) ).

tff(f18184,plain,
    ( spl250_966
  <=> ! [X2: fun_pname_bool,X0: fun_pname_a,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK232(X0,X1,X2)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_966])]) ).

tff(f6275,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X2)),X1))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK232(X0,X1,X2)),X2)) ),
    inference(cnf_transformation,[],[f4388]) ).

tff(f18182,plain,
    spl250_965,
    inference(avatar_split_clause,[],[f6198,f18180]) ).

tff(f18180,plain,
    ( spl250_965
  <=> ! [X2: fun_nat_bool,X0: int,X1: fun_nat_int] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK224(X0,X1,X2)),X2))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_965])]) ).

tff(f6198,plain,
    ! [X2: fun_nat_bool,X0: int,X1: fun_nat_int] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK224(X0,X1,X2)),X2))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ),
    inference(cnf_transformation,[],[f4360]) ).

tff(f4360,plain,
    ! [X0: int,X1: fun_nat_int,X2: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK224(X0,X1,X2)),X2))
        & ( hAPP_nat_int(X1,sK224(X0,X1,X2)) = X0 ) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK224])],[f3509,f4359]) ).

tff(f4359,plain,
    ! [X0: int,X1: fun_nat_int,X2: fun_nat_bool] :
      ( ? [X3: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2))
          & ( hAPP_nat_int(X1,X3) = X0 ) )
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK224(X0,X1,X2)),X2))
        & ( hAPP_nat_int(X1,sK224(X0,X1,X2)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f3509,plain,
    ! [X0: int,X1: fun_nat_int,X2: fun_nat_bool] :
      ( ? [X3: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2))
          & ( hAPP_nat_int(X1,X3) = X0 ) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ),
    inference(ennf_transformation,[],[f2413]) ).

tff(f2413,plain,
    ! [X0: int,X1: fun_nat_int,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2)))
     => ~ ! [X3: nat] :
            ( ( hAPP_nat_int(X1,X3) = X0 )
           => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2)) ) ),
    inference(rectify,[],[f476]) ).

tff(f476,axiom,
    ! [X28: int,X6: fun_nat_int,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X28),image_nat_int(X6,X2)))
     => ~ ! [X27: nat] :
            ( ( hAPP_nat_int(X6,X27) = X28 )
           => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X27),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_475_imageE) ).

tff(f18178,plain,
    spl250_964,
    inference(avatar_split_clause,[],[f6196,f18176]) ).

tff(f18176,plain,
    ( spl250_964
  <=> ! [X2: fun_pname_bool,X0: x_a,X1: fun_pname_a] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK223(X0,X1,X2)),X2))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_964])]) ).

tff(f6196,plain,
    ! [X2: fun_pname_bool,X0: x_a,X1: fun_pname_a] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK223(X0,X1,X2)),X2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ),
    inference(cnf_transformation,[],[f4358]) ).

tff(f4358,plain,
    ! [X0: x_a,X1: fun_pname_a,X2: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK223(X0,X1,X2)),X2))
        & ( hAPP_pname_a(X1,sK223(X0,X1,X2)) = X0 ) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK223])],[f3508,f4357]) ).

tff(f4357,plain,
    ! [X0: x_a,X1: fun_pname_a,X2: fun_pname_bool] :
      ( ? [X3: pname] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
          & ( hAPP_pname_a(X1,X3) = X0 ) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK223(X0,X1,X2)),X2))
        & ( hAPP_pname_a(X1,sK223(X0,X1,X2)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f3508,plain,
    ! [X0: x_a,X1: fun_pname_a,X2: fun_pname_bool] :
      ( ? [X3: pname] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
          & ( hAPP_pname_a(X1,X3) = X0 ) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ),
    inference(ennf_transformation,[],[f2412]) ).

tff(f2412,plain,
    ! [X0: x_a,X1: fun_pname_a,X2: fun_pname_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2)))
     => ~ ! [X3: pname] :
            ( ( hAPP_pname_a(X1,X3) = X0 )
           => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2)) ) ),
    inference(rectify,[],[f477]) ).

tff(f477,axiom,
    ! [X28: x_a,X6: fun_pname_a,X2: fun_pname_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X28),image_pname_a(X6,X2)))
     => ~ ! [X27: pname] :
            ( ( hAPP_pname_a(X6,X27) = X28 )
           => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X27),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_476_imageE) ).

tff(f18174,plain,
    spl250_963,
    inference(avatar_split_clause,[],[f6048,f18172]) ).

tff(f18172,plain,
    ( spl250_963
  <=> ! [X2: int,X0: fun_int_bool,X1: fun_int_bool] :
        ( ~ hBOOL(hAPP_int_bool(X0,sK214(X0,X1,X2)))
        | ~ hBOOL(hAPP_int_bool(X1,sK214(X0,X1,X2)))
        | ~ sP14(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_963])]) ).

tff(f6048,plain,
    ! [X2: int,X0: fun_int_bool,X1: fun_int_bool] :
      ( ~ hBOOL(hAPP_int_bool(X0,sK214(X0,X1,X2)))
      | ~ hBOOL(hAPP_int_bool(X1,sK214(X0,X1,X2)))
      | ~ sP14(X0,X1) ),
    inference(cnf_transformation,[],[f4333]) ).

tff(f4333,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ! [X2: int] :
          ( ( ~ hBOOL(hAPP_int_bool(X0,sK214(X0,X1,X2)))
            | ~ hBOOL(hAPP_int_bool(X1,sK214(X0,X1,X2))) )
          & ( hBOOL(hAPP_int_bool(X0,sK214(X0,X1,X2)))
            | hBOOL(hAPP_int_bool(X1,sK214(X0,X1,X2))) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),sK214(X0,X1,X2))) )
      | ~ sP14(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK214])],[f4331,f4332]) ).

tff(f4332,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool,X2: int] :
      ( ? [X3: int] :
          ( ( ~ hBOOL(hAPP_int_bool(X0,X3))
            | ~ hBOOL(hAPP_int_bool(X1,X3)) )
          & ( hBOOL(hAPP_int_bool(X0,X3))
            | hBOOL(hAPP_int_bool(X1,X3)) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X3)) )
     => ( ( ~ hBOOL(hAPP_int_bool(X0,sK214(X0,X1,X2)))
          | ~ hBOOL(hAPP_int_bool(X1,sK214(X0,X1,X2))) )
        & ( hBOOL(hAPP_int_bool(X0,sK214(X0,X1,X2)))
          | hBOOL(hAPP_int_bool(X1,sK214(X0,X1,X2))) )
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),sK214(X0,X1,X2))) ) ),
    introduced(choice_axiom,[]) ).

tff(f4331,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ! [X2: int] :
        ? [X3: int] :
          ( ( ~ hBOOL(hAPP_int_bool(X0,X3))
            | ~ hBOOL(hAPP_int_bool(X1,X3)) )
          & ( hBOOL(hAPP_int_bool(X0,X3))
            | hBOOL(hAPP_int_bool(X1,X3)) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X3)) )
      | ~ sP14(X0,X1) ),
    inference(rectify,[],[f4330]) ).

tff(f4330,plain,
    ! [X1: fun_int_bool,X0: fun_int_bool] :
      ( ! [X5: int] :
        ? [X6: int] :
          ( ( ~ hBOOL(hAPP_int_bool(X1,X6))
            | ~ hBOOL(hAPP_int_bool(X0,X6)) )
          & ( hBOOL(hAPP_int_bool(X1,X6))
            | hBOOL(hAPP_int_bool(X0,X6)) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),X6)) )
      | ~ sP14(X1,X0) ),
    inference(flattening,[],[f4329]) ).

tff(f4329,plain,
    ! [X1: fun_int_bool,X0: fun_int_bool] :
      ( ! [X5: int] :
        ? [X6: int] :
          ( ( ~ hBOOL(hAPP_int_bool(X1,X6))
            | ~ hBOOL(hAPP_int_bool(X0,X6)) )
          & ( hBOOL(hAPP_int_bool(X1,X6))
            | hBOOL(hAPP_int_bool(X0,X6)) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),X6)) )
      | ~ sP14(X1,X0) ),
    inference(nnf_transformation,[],[f3711]) ).

tff(f3711,plain,
    ! [X1: fun_int_bool,X0: fun_int_bool] :
      ( ! [X5: int] :
        ? [X6: int] :
          ( ( hBOOL(hAPP_int_bool(X0,X6))
          <~> hBOOL(hAPP_int_bool(X1,X6)) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),X6)) )
      | ~ sP14(X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).

tff(f18170,plain,
    spl250_962,
    inference(avatar_split_clause,[],[f6047,f18168]) ).

tff(f18168,plain,
    ( spl250_962
  <=> ! [X2: int,X0: fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_int_bool(X0,sK214(X0,X1,X2)))
        | hBOOL(hAPP_int_bool(X1,sK214(X0,X1,X2)))
        | ~ sP14(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_962])]) ).

tff(f6047,plain,
    ! [X2: int,X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_int_bool(X0,sK214(X0,X1,X2)))
      | hBOOL(hAPP_int_bool(X1,sK214(X0,X1,X2)))
      | ~ sP14(X0,X1) ),
    inference(cnf_transformation,[],[f4333]) ).

tff(f18166,plain,
    spl250_961,
    inference(avatar_split_clause,[],[f6043,f18164]) ).

tff(f18164,plain,
    ( spl250_961
  <=> ! [X2: int,X0: fun_int_bool,X1: fun_int_bool] :
        ( ~ hBOOL(hAPP_int_bool(X0,sK210(X0,X1,X2)))
        | ~ hBOOL(hAPP_int_bool(X1,sK210(X0,X1,X2)))
        | ~ sP13(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_961])]) ).

tff(f6043,plain,
    ! [X2: int,X0: fun_int_bool,X1: fun_int_bool] :
      ( ~ hBOOL(hAPP_int_bool(X0,sK210(X0,X1,X2)))
      | ~ hBOOL(hAPP_int_bool(X1,sK210(X0,X1,X2)))
      | ~ sP13(X0,X1) ),
    inference(cnf_transformation,[],[f4323]) ).

tff(f4323,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ! [X2: int] :
          ( ( ~ hBOOL(hAPP_int_bool(X0,sK210(X0,X1,X2)))
            | ~ hBOOL(hAPP_int_bool(X1,sK210(X0,X1,X2))) )
          & ( hBOOL(hAPP_int_bool(X0,sK210(X0,X1,X2)))
            | hBOOL(hAPP_int_bool(X1,sK210(X0,X1,X2))) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK210(X0,X1,X2)),X2)) )
      | ~ sP13(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK210])],[f4321,f4322]) ).

tff(f4322,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool,X2: int] :
      ( ? [X3: int] :
          ( ( ~ hBOOL(hAPP_int_bool(X0,X3))
            | ~ hBOOL(hAPP_int_bool(X1,X3)) )
          & ( hBOOL(hAPP_int_bool(X0,X3))
            | hBOOL(hAPP_int_bool(X1,X3)) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X2)) )
     => ( ( ~ hBOOL(hAPP_int_bool(X0,sK210(X0,X1,X2)))
          | ~ hBOOL(hAPP_int_bool(X1,sK210(X0,X1,X2))) )
        & ( hBOOL(hAPP_int_bool(X0,sK210(X0,X1,X2)))
          | hBOOL(hAPP_int_bool(X1,sK210(X0,X1,X2))) )
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK210(X0,X1,X2)),X2)) ) ),
    introduced(choice_axiom,[]) ).

tff(f4321,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ! [X2: int] :
        ? [X3: int] :
          ( ( ~ hBOOL(hAPP_int_bool(X0,X3))
            | ~ hBOOL(hAPP_int_bool(X1,X3)) )
          & ( hBOOL(hAPP_int_bool(X0,X3))
            | hBOOL(hAPP_int_bool(X1,X3)) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X2)) )
      | ~ sP13(X0,X1) ),
    inference(rectify,[],[f4320]) ).

tff(f4320,plain,
    ! [X1: fun_int_bool,X0: fun_int_bool] :
      ( ! [X5: int] :
        ? [X6: int] :
          ( ( ~ hBOOL(hAPP_int_bool(X1,X6))
            | ~ hBOOL(hAPP_int_bool(X0,X6)) )
          & ( hBOOL(hAPP_int_bool(X1,X6))
            | hBOOL(hAPP_int_bool(X0,X6)) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6),X5)) )
      | ~ sP13(X1,X0) ),
    inference(flattening,[],[f4319]) ).

tff(f4319,plain,
    ! [X1: fun_int_bool,X0: fun_int_bool] :
      ( ! [X5: int] :
        ? [X6: int] :
          ( ( ~ hBOOL(hAPP_int_bool(X1,X6))
            | ~ hBOOL(hAPP_int_bool(X0,X6)) )
          & ( hBOOL(hAPP_int_bool(X1,X6))
            | hBOOL(hAPP_int_bool(X0,X6)) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6),X5)) )
      | ~ sP13(X1,X0) ),
    inference(nnf_transformation,[],[f3709]) ).

tff(f3709,plain,
    ! [X1: fun_int_bool,X0: fun_int_bool] :
      ( ! [X5: int] :
        ? [X6: int] :
          ( ( hBOOL(hAPP_int_bool(X0,X6))
          <~> hBOOL(hAPP_int_bool(X1,X6)) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6),X5)) )
      | ~ sP13(X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).

tff(f18162,plain,
    spl250_960,
    inference(avatar_split_clause,[],[f6042,f18160]) ).

tff(f18160,plain,
    ( spl250_960
  <=> ! [X2: int,X0: fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_int_bool(X0,sK210(X0,X1,X2)))
        | hBOOL(hAPP_int_bool(X1,sK210(X0,X1,X2)))
        | ~ sP13(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_960])]) ).

tff(f6042,plain,
    ! [X2: int,X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_int_bool(X0,sK210(X0,X1,X2)))
      | hBOOL(hAPP_int_bool(X1,sK210(X0,X1,X2)))
      | ~ sP13(X0,X1) ),
    inference(cnf_transformation,[],[f4323]) ).

tff(f18158,plain,
    spl250_959,
    inference(avatar_split_clause,[],[f6016,f18156]) ).

tff(f18156,plain,
    ( spl250_959
  <=> ! [X2: nat,X0: nat,X1: fun_nat_bool] :
        ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0)))
        | ~ hBOOL(hAPP_nat_bool(X1,sK207(X1)))
        | ~ hBOOL(hAPP_nat_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_959])]) ).

tff(f6016,plain,
    ! [X2: nat,X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X0)))
      | ~ hBOOL(hAPP_nat_bool(X1,sK207(X1)))
      | ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f4304]) ).

tff(f18154,plain,
    ( spl250_958
    | ~ spl250_39
    | ~ spl250_631 ),
    inference(avatar_split_clause,[],[f13055,f12445,f7496,f18152]) ).

tff(f7496,plain,
    ( spl250_39
  <=> ! [X0: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),bot_bo844097828e_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_39])]) ).

tff(f13055,plain,
    ( ! [X0: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),X0))
    | ~ spl250_39
    | ~ spl250_631 ),
    inference(resolution,[],[f12446,f7497]) ).

tff(f7497,plain,
    ( ! [X0: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),bot_bo844097828e_bool))
    | ~ spl250_39 ),
    inference(avatar_component_clause,[],[f7496]) ).

tff(f18150,plain,
    spl250_957,
    inference(avatar_split_clause,[],[f6013,f18148]) ).

tff(f18148,plain,
    ( spl250_957
  <=> ! [X2: int,X0: int,X1: fun_int_bool] :
        ( hBOOL(hAPP_int_bool(X1,X0))
        | hBOOL(hAPP_int_bool(X1,sK206(X1,X2)))
        | sP12(X1,X2)
        | ~ hBOOL(hAPP_int_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_957])]) ).

tff(f6013,plain,
    ! [X2: int,X0: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_int_bool(X1,X0))
      | hBOOL(hAPP_int_bool(X1,sK206(X1,X2)))
      | sP12(X1,X2)
      | ~ hBOOL(hAPP_int_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f4302]) ).

tff(f18146,plain,
    spl250_956,
    inference(avatar_split_clause,[],[f5745,f18144]) ).

tff(f18144,plain,
    ( spl250_956
  <=> ! [X2: fun_nat_bool,X0: fun_nat_int,X1: nat] : ( image_nat_int(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X0,X1)),image_nat_int(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_956])]) ).

tff(f18142,plain,
    spl250_955,
    inference(avatar_split_clause,[],[f5744,f18140]) ).

tff(f18140,plain,
    ( spl250_955
  <=> ! [X2: fun_pname_bool,X0: fun_pname_a,X1: pname] : ( image_pname_a(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_955])]) ).

tff(f18138,plain,
    spl250_954,
    inference(avatar_split_clause,[],[f5524,f18136]) ).

tff(f18136,plain,
    ( spl250_954
  <=> ! [X0: nat,X1: nat] :
        ( ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK141(X0,X1))) = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_954])]) ).

tff(f5524,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK141(X0,X1))) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4089]) ).

tff(f4089,plain,
    ! [X0: nat,X1: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
        | ! [X2: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) != X1 ) )
      & ( ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK141(X0,X1))) = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK141])],[f4087,f4088]) ).

tff(f4088,plain,
    ! [X0: nat,X1: nat] :
      ( ? [X3: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X3)) = X1 )
     => ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK141(X0,X1))) = X1 ) ),
    introduced(choice_axiom,[]) ).

tff(f4087,plain,
    ! [X0: nat,X1: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
        | ! [X2: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) != X1 ) )
      & ( ? [X3: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X3)) = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    inference(rectify,[],[f4086]) ).

tff(f4086,plain,
    ! [X0: nat,X1: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
        | ! [X2: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) != X1 ) )
      & ( ? [X2: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    inference(nnf_transformation,[],[f1994]) ).

tff(f1994,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
    <=> ? [X2: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) = X1 ) ),
    inference(rectify,[],[f901]) ).

tff(f901,axiom,
    ! [X22: nat,X14: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X14))
    <=> ? [X116: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X22),X116)) = X14 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_900_less__iff__Suc__add) ).

tff(f18134,plain,
    spl250_953,
    inference(avatar_split_clause,[],[f5517,f18132]) ).

tff(f18132,plain,
    ( spl250_953
  <=> ! [X0: int,X1: int] :
        ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,sK140(X0,X1))) = X1 )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_953])]) ).

tff(f5517,plain,
    ! [X0: int,X1: int] :
      ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,sK140(X0,X1))) = X1 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4082]) ).

tff(f4082,plain,
    ! [X0: int,X1: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
        | ! [X2: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,X2)) != X1 ) )
      & ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,sK140(X0,X1))) = X1 )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK140])],[f4080,f4081]) ).

tff(f4081,plain,
    ! [X0: int,X1: int] :
      ( ? [X3: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,X3)) = X1 )
     => ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,sK140(X0,X1))) = X1 ) ),
    introduced(choice_axiom,[]) ).

tff(f4080,plain,
    ! [X0: int,X1: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
        | ! [X2: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,X2)) != X1 ) )
      & ( ? [X3: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,X3)) = X1 )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
    inference(rectify,[],[f4079]) ).

tff(f4079,plain,
    ! [X0: int,X1: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
        | ! [X2: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,X2)) != X1 ) )
      & ( ? [X2: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,X2)) = X1 )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
    inference(nnf_transformation,[],[f1991]) ).

tff(f1991,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
    <=> ? [X2: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,X2)) = X1 ) ),
    inference(rectify,[],[f1106]) ).

tff(f1106,axiom,
    ! [X136: int,X53: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X136),X53))
    <=> ? [X26: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X136),hAPP_nat_int(semiri1621563631at_int,X26)) = X53 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1105_zle__iff__zadd) ).

tff(f18130,plain,
    spl250_952,
    inference(avatar_split_clause,[],[f5372,f18128]) ).

tff(f18128,plain,
    ( spl250_952
  <=> ! [X0: nat,X1: nat] :
        ( ( X0 = X1 )
        | ( zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0) )
        | ( zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_952])]) ).

tff(f5372,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ( zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0) )
      | ( zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) ) ),
    inference(cnf_transformation,[],[f3014]) ).

tff(f3014,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ( zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0) )
      | ( zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) ) ),
    inference(flattening,[],[f3013]) ).

tff(f3013,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ( zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0) )
      | ( zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) ) ),
    inference(ennf_transformation,[],[f1916]) ).

tff(f1916,plain,
    ! [X0: nat,X1: nat] :
      ( ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) )
     => ( ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0) )
       => ( X0 = X1 ) ) ),
    inference(rectify,[],[f927]) ).

tff(f927,axiom,
    ! [X12: nat,X11: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X12),X11) = zero_zero_nat )
     => ( ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X11),X12) )
       => ( X11 = X12 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_926_diffs0__imp__equal) ).

tff(f18126,plain,
    spl250_951,
    inference(avatar_split_clause,[],[f5368,f18124]) ).

tff(f18124,plain,
    ( spl250_951
  <=> ! [X0: nat,X1: nat] :
        ( ( X0 = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_951])]) ).

tff(f5368,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3994]) ).

tff(f3994,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0)))
          | ( X0 != X1 ) )
        & ( ( X0 = X1 )
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(nnf_transformation,[],[f3009]) ).

tff(f3009,plain,
    ! [X0: nat,X1: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0)))
      <=> ( X0 = X1 ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1913]) ).

tff(f1913,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0)))
      <=> ( X0 = X1 ) ) ),
    inference(rectify,[],[f907]) ).

tff(f907,axiom,
    ! [X22: nat,X14: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X14))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),hAPP_nat_nat(suc,X22)))
      <=> ( X14 = X22 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_906_le__less__Suc__eq) ).

tff(f18122,plain,
    spl250_950,
    inference(avatar_split_clause,[],[f5358,f18120]) ).

tff(f18120,plain,
    ( spl250_950
  <=> ! [X0: nat,X1: nat] :
        ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)) = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_950])]) ).

tff(f5358,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2996]) ).

tff(f2996,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1904]) ).

tff(f1904,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
     => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)) = X1 ) ),
    inference(rectify,[],[f842]) ).

tff(f842,axiom,
    ! [X11: nat,X12: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X11),X12))
     => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X11),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X12),X11)) = X12 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_841_le__add__diff__inverse) ).

tff(f18118,plain,
    spl250_949,
    inference(avatar_split_clause,[],[f5357,f18116]) ).

tff(f18116,plain,
    ( spl250_949
  <=> ! [X0: nat,X1: nat] :
        ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)) = X0 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_949])]) ).

tff(f5357,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)) = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2995]) ).

tff(f2995,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)) = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1903]) ).

tff(f1903,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
     => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)) = X0 ) ),
    inference(rectify,[],[f177]) ).

tff(f177,axiom,
    ! [X20: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X20),X11))
     => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X11),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X11),X20)) = X20 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_diff__diff__cancel) ).

tff(f18114,plain,
    spl250_948,
    inference(avatar_split_clause,[],[f5351,f18112]) ).

tff(f18112,plain,
    ( spl250_948
  <=> ! [X0: nat,X1: nat] :
        ( ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK122(X0,X1))) = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_948])]) ).

tff(f5351,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK122(X0,X1))) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3990]) ).

tff(f3990,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK122(X0,X1))) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK122])],[f2990,f3989]) ).

tff(f3989,plain,
    ! [X0: nat,X1: nat] :
      ( ? [X2: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) = X1 )
     => ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK122(X0,X1))) = X1 ) ),
    introduced(choice_axiom,[]) ).

tff(f2990,plain,
    ! [X0: nat,X1: nat] :
      ( ? [X2: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1898]) ).

tff(f1898,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
     => ? [X2: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)) = X1 ) ),
    inference(rectify,[],[f917]) ).

tff(f917,axiom,
    ! [X12: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),X11))
     => ? [X116: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X12),X116)) = X11 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_916_less__imp__Suc__add) ).

tff(f18110,plain,
    ( spl250_947
    | ~ spl250_66
    | ~ spl250_592 ),
    inference(avatar_split_clause,[],[f12286,f11826,f7608,f18108]) ).

tff(f18108,plain,
    ( spl250_947
  <=> ! [X0: bool,X1: int] :
        ( ~ hBOOL(X0)
        | ~ sP12(cOMBK_bool_int(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_947])]) ).

tff(f11826,plain,
    ( spl250_592
  <=> ! [X0: fun_int_bool,X1: int] :
        ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),sK205(X0,X1))))
        | ~ sP12(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_592])]) ).

tff(f12286,plain,
    ( ! [X0: bool,X1: int] :
        ( ~ hBOOL(X0)
        | ~ sP12(cOMBK_bool_int(X0),X1) )
    | ~ spl250_66
    | ~ spl250_592 ),
    inference(superposition,[],[f11827,f7609]) ).

tff(f11827,plain,
    ( ! [X0: fun_int_bool,X1: int] :
        ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),sK205(X0,X1))))
        | ~ sP12(X0,X1) )
    | ~ spl250_592 ),
    inference(avatar_component_clause,[],[f11826]) ).

tff(f18106,plain,
    spl250_946,
    inference(avatar_split_clause,[],[f5287,f18104]) ).

tff(f18104,plain,
    ( spl250_946
  <=> ! [X0: nat,X1: nat] :
        ( ( X0 = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_946])]) ).

tff(f5287,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2908]) ).

tff(f2908,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(flattening,[],[f2907]) ).

tff(f2907,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1843]) ).

tff(f1843,plain,
    ! [X0: nat,X1: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
       => ( X0 = X1 ) ) ),
    inference(rectify,[],[f870]) ).

tff(f870,axiom,
    ! [X11: nat,X12: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X11),X12))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X11),hAPP_nat_nat(suc,X12)))
       => ( X11 = X12 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_869_less__antisym) ).

tff(f18102,plain,
    spl250_945,
    inference(avatar_split_clause,[],[f5286,f18100]) ).

tff(f18100,plain,
    ( spl250_945
  <=> ! [X0: nat,X1: nat] :
        ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)) = X0 )
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_945])]) ).

tff(f5286,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)) = X0 )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2906]) ).

tff(f2906,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)) = X0 )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1842]) ).

tff(f1842,plain,
    ! [X0: nat,X1: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
     => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)) = X0 ) ),
    inference(rectify,[],[f911]) ).

tff(f911,axiom,
    ! [X12: nat,X11: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),X11))
     => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X11),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X12),X11)) = X12 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_910_add__diff__inverse) ).

tff(f18098,plain,
    spl250_944,
    inference(avatar_split_clause,[],[f5264,f18096]) ).

tff(f18096,plain,
    ( spl250_944
  <=> ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
        | hBOOL(hAPP_f54304608l_bool(X0,sK118(X0)))
        | ~ hBOOL(hAPP_f54304608l_bool(X0,X1))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_944])]) ).

tff(f5264,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
      | hBOOL(hAPP_f54304608l_bool(X0,sK118(X0)))
      | ~ hBOOL(hAPP_f54304608l_bool(X0,X1))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f3974]) ).

tff(f18094,plain,
    spl250_943,
    inference(avatar_split_clause,[],[f5262,f18092]) ).

tff(f18092,plain,
    ( spl250_943
  <=> ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK118(X0)))
        | ~ hBOOL(hAPP_f54304608l_bool(X0,X1))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_943])]) ).

tff(f5262,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK118(X0)))
      | ~ hBOOL(hAPP_f54304608l_bool(X0,X1))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f3974]) ).

tff(f18090,plain,
    spl250_942,
    inference(avatar_split_clause,[],[f5260,f18088]) ).

tff(f18088,plain,
    ( spl250_942
  <=> ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(X0,X1))
        | hBOOL(hAPP_f54304608l_bool(X0,sK116(X0)))
        | ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_942])]) ).

tff(f5260,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,X1))
      | hBOOL(hAPP_f54304608l_bool(X0,sK116(X0)))
      | ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f3972]) ).

tff(f18086,plain,
    spl250_941,
    inference(avatar_split_clause,[],[f5258,f18084]) ).

tff(f18084,plain,
    ( spl250_941
  <=> ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(X0,X1))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK116(X0)))
        | ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_941])]) ).

tff(f5258,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,X1))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK116(X0)))
      | ~ hBOOL(hAPP_f54304608l_bool(X0,bot_bot_fun_nat_bool))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f3972]) ).

tff(f18082,plain,
    spl250_940,
    inference(avatar_split_clause,[],[f5221,f18080]) ).

tff(f18080,plain,
    ( spl250_940
  <=> ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
        | hBOOL(hAPP_f448129468l_bool(X0,sK111(X0)))
        | ~ hBOOL(hAPP_f448129468l_bool(X0,X1))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_940])]) ).

tff(f5221,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
      | hBOOL(hAPP_f448129468l_bool(X0,sK111(X0)))
      | ~ hBOOL(hAPP_f448129468l_bool(X0,X1))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f3963]) ).

tff(f18078,plain,
    spl250_939,
    inference(avatar_split_clause,[],[f5219,f18076]) ).

tff(f18076,plain,
    ( spl250_939
  <=> ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
        | hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK111(X0)))
        | ~ hBOOL(hAPP_f448129468l_bool(X0,X1))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_939])]) ).

tff(f5219,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK111(X0)))
      | ~ hBOOL(hAPP_f448129468l_bool(X0,X1))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f3963]) ).

tff(f18074,plain,
    spl250_938,
    inference(avatar_split_clause,[],[f5217,f18072]) ).

tff(f18072,plain,
    ( spl250_938
  <=> ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(X0,X1))
        | hBOOL(hAPP_f448129468l_bool(X0,sK109(X0)))
        | ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_938])]) ).

tff(f5217,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,X1))
      | hBOOL(hAPP_f448129468l_bool(X0,sK109(X0)))
      | ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f3961]) ).

tff(f18070,plain,
    spl250_937,
    inference(avatar_split_clause,[],[f5215,f18068]) ).

tff(f18068,plain,
    ( spl250_937
  <=> ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(X0,X1))
        | hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK109(X0)))
        | ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_937])]) ).

tff(f5215,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,X1))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK109(X0)))
      | ~ hBOOL(hAPP_f448129468l_bool(X0,bot_bot_fun_int_bool))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f3961]) ).

tff(f18065,plain,
    spl250_936,
    inference(avatar_split_clause,[],[f5182,f18063]) ).

tff(f18063,plain,
    ( spl250_936
  <=> ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
        | hBOOL(hAPP_fun_a_bool_bool(X0,sK104(X0)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(X0,X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_936])]) ).

tff(f5182,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
      | hBOOL(hAPP_fun_a_bool_bool(X0,sK104(X0)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(X0,X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(cnf_transformation,[],[f3953]) ).

tff(f18061,plain,
    spl250_935,
    inference(avatar_split_clause,[],[f5180,f18059]) ).

tff(f18059,plain,
    ( spl250_935
  <=> ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
        | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK104(X0)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(X0,X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_935])]) ).

tff(f5180,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
      | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK104(X0)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(X0,X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(cnf_transformation,[],[f3953]) ).

tff(f18057,plain,
    spl250_934,
    inference(avatar_split_clause,[],[f5178,f18055]) ).

tff(f18055,plain,
    ( spl250_934
  <=> ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
        | hBOOL(hAPP_fun_a_bool_bool(X0,sK102(X0)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_934])]) ).

tff(f5178,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
      | hBOOL(hAPP_fun_a_bool_bool(X0,sK102(X0)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(cnf_transformation,[],[f3951]) ).

tff(f18053,plain,
    spl250_933,
    inference(avatar_split_clause,[],[f5176,f18051]) ).

tff(f18051,plain,
    ( spl250_933
  <=> ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
        | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK102(X0)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_933])]) ).

tff(f5176,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,X1))
      | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK102(X0)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(X0,bot_bot_fun_a_bool))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(cnf_transformation,[],[f3951]) ).

tff(f18049,plain,
    spl250_932,
    inference(avatar_split_clause,[],[f5141,f18047]) ).

tff(f18047,plain,
    ( spl250_932
  <=> ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
        | hBOOL(hAPP_f1664156314l_bool(X0,sK97(X0)))
        | ~ hBOOL(hAPP_f1664156314l_bool(X0,X1))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_932])]) ).

tff(f5141,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
      | hBOOL(hAPP_f1664156314l_bool(X0,sK97(X0)))
      | ~ hBOOL(hAPP_f1664156314l_bool(X0,X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f3942]) ).

tff(f18045,plain,
    spl250_931,
    inference(avatar_split_clause,[],[f5139,f18043]) ).

tff(f18043,plain,
    ( spl250_931
  <=> ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
        | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK97(X0)))
        | ~ hBOOL(hAPP_f1664156314l_bool(X0,X1))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_931])]) ).

tff(f5139,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK97(X0)))
      | ~ hBOOL(hAPP_f1664156314l_bool(X0,X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f3942]) ).

tff(f18041,plain,
    spl250_930,
    inference(avatar_split_clause,[],[f5137,f18039]) ).

tff(f18039,plain,
    ( spl250_930
  <=> ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(X0,X1))
        | hBOOL(hAPP_f1664156314l_bool(X0,sK95(X0)))
        | ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_930])]) ).

tff(f5137,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,X1))
      | hBOOL(hAPP_f1664156314l_bool(X0,sK95(X0)))
      | ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f3940]) ).

tff(f18037,plain,
    spl250_929,
    inference(avatar_split_clause,[],[f5135,f18035]) ).

tff(f18035,plain,
    ( spl250_929
  <=> ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(X0,X1))
        | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK95(X0)))
        | ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_929])]) ).

tff(f5135,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,X1))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK95(X0)))
      | ~ hBOOL(hAPP_f1664156314l_bool(X0,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f3940]) ).

tff(f18033,plain,
    spl250_928,
    inference(avatar_split_clause,[],[f4968,f18031]) ).

tff(f18031,plain,
    ( spl250_928
  <=> ! [X0: int,X1: int] :
        ( ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),X0) )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_928])]) ).

tff(f4968,plain,
    ! [X0: int,X1: int] :
      ( ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),X0) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2622]) ).

tff(f2622,plain,
    ! [X0: int,X1: int] :
      ( ( ( zero_zero_int = hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0) )
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
      & ( ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),X0) )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
    inference(ennf_transformation,[],[f1605]) ).

tff(f1605,plain,
    ! [X0: int,X1: int] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
       => ( zero_zero_int = hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0) ) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
       => ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),X0) ) ) ),
    inference(rectify,[],[f1096]) ).

tff(f1096,axiom,
    ! [X16: int,X15: int] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X16),X15))
       => ( zero_zero_int = hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X15),X16) ) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X16),X15))
       => ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X15),X16) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X15),X16) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1095_tsub__def) ).

tff(f18029,plain,
    spl250_927,
    inference(avatar_split_clause,[],[f4926,f18027]) ).

tff(f18027,plain,
    ( spl250_927
  <=> ! [X0: nat,X1: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_927])]) ).

tff(f4926,plain,
    ! [X0: nat,X1: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f1574]) ).

tff(f1574,plain,
    ! [X0: nat,X1: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)) ),
    inference(rectify,[],[f1113]) ).

tff(f1113,axiom,
    ! [X15: nat,X16: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X15)),hAPP_nat_int(semiri1621563631at_int,X16)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X16)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1112_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).

tff(f18024,plain,
    spl250_926,
    inference(avatar_split_clause,[],[f4923,f18022]) ).

tff(f18022,plain,
    ( spl250_926
  <=> ! [X0: nat,X1: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_926])]) ).

tff(f4923,plain,
    ! [X0: nat,X1: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f1571]) ).

tff(f1571,plain,
    ! [X0: nat,X1: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)) ),
    inference(rectify,[],[f1109]) ).

tff(f1109,axiom,
    ! [X15: nat,X16: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X15)),hAPP_nat_int(semiri1621563631at_int,X16)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X16)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1108_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).

tff(f18020,plain,
    spl250_925,
    inference(avatar_split_clause,[],[f4922,f18018]) ).

tff(f18018,plain,
    ( spl250_925
  <=> ! [X0: nat,X1: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_925])]) ).

tff(f4922,plain,
    ! [X0: nat,X1: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f1570]) ).

tff(f1570,plain,
    ! [X0: nat,X1: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)) ),
    inference(rectify,[],[f1112]) ).

tff(f1112,axiom,
    ! [X15: nat,X16: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,hAPP_nat_int(semiri1621563631at_int,X15)),hAPP_nat_int(semiri1621563631at_int,X16)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),X16)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1111_Nat__Transfer_Otransfer__int__nat__functions_I3_J) ).

tff(f18016,plain,
    spl250_924,
    inference(avatar_split_clause,[],[f4921,f18014]) ).

tff(f18014,plain,
    ( spl250_924
  <=> ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_924])]) ).

tff(f4921,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f1569]) ).

tff(f1569,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X0)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)) ),
    inference(rectify,[],[f1006]) ).

tff(f1006,axiom,
    ! [X12: nat,X11: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X12)),X11) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X11),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X12),X11)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1005_mult__Suc) ).

tff(f18012,plain,
    spl250_923,
    inference(avatar_split_clause,[],[f4920,f18010]) ).

tff(f18010,plain,
    ( spl250_923
  <=> ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),one_one_nat)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_923])]) ).

tff(f4920,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),one_one_nat)),X1) ),
    inference(cnf_transformation,[],[f1568]) ).

tff(f1568,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),one_one_nat)),X1) ),
    inference(rectify,[],[f748]) ).

tff(f748,axiom,
    ! [X12: nat,X11: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X12),hAPP_nat_nat(suc,X11)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X12),one_one_nat)),X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_747_diff__Suc__eq__diff__pred) ).

tff(f18008,plain,
    spl250_922,
    inference(avatar_split_clause,[],[f4919,f18006]) ).

tff(f4919,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f1567]) ).

tff(f1567,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)) ),
    inference(rectify,[],[f959]) ).

tff(f959,axiom,
    ! [X22: nat,X14: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X22),hAPP_nat_nat(suc,X14)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X22),X14)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_958_diff__Suc) ).

tff(f18004,plain,
    spl250_921,
    inference(avatar_split_clause,[],[f4918,f18002]) ).

tff(f18002,plain,
    ( spl250_921
  <=> ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_921])]) ).

tff(f4918,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f1566]) ).

tff(f1566,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1)) ),
    inference(rectify,[],[f1005]) ).

tff(f1005,axiom,
    ! [X12: nat,X11: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X12),hAPP_nat_nat(suc,X11)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X12),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X12),X11)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1004_mult__Suc__right) ).

tff(f18000,plain,
    spl250_920,
    inference(avatar_split_clause,[],[f4792,f17998]) ).

tff(f17998,plain,
    ( spl250_920
  <=> ! [X4: nat,X0: fun_nat_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),sK61(X0)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_920])]) ).

tff(f4792,plain,
    ! [X0: fun_nat_bool,X4: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),sK61(X0)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ),
    inference(cnf_transformation,[],[f3831]) ).

tff(f3831,plain,
    ! [X0: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | ! [X1: nat] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK60(X0,X1)),X1))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK60(X0,X1)),X0)) ) )
      & ( ! [X4: nat] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),sK61(X0)))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK60,sK61])],[f3828,f3830,f3829]) ).

tff(f3829,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( ? [X2: nat] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) )
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK60(X0,X1)),X1))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK60(X0,X1)),X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3830,plain,
    ! [X0: fun_nat_bool] :
      ( ? [X3: nat] :
        ! [X4: nat] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X3))
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0)) )
     => ! [X4: nat] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),sK61(X0)))
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3828,plain,
    ! [X0: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | ! [X1: nat] :
          ? [X2: nat] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) ) )
      & ( ? [X3: nat] :
          ! [X4: nat] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X3))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    inference(rectify,[],[f3827]) ).

tff(f3827,plain,
    ! [X0: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | ! [X1: nat] :
          ? [X2: nat] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) ) )
      & ( ? [X1: nat] :
          ! [X2: nat] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    inference(nnf_transformation,[],[f2608]) ).

tff(f2608,plain,
    ! [X0: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
    <=> ? [X1: nat] :
        ! [X2: nat] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) ) ),
    inference(ennf_transformation,[],[f1480]) ).

tff(f1480,plain,
    ! [X0: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
    <=> ? [X1: nat] :
        ! [X2: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ) ),
    inference(rectify,[],[f487]) ).

tff(f487,axiom,
    ! [X69: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X69))
    <=> ? [X32: nat] :
        ! [X27: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X27),X69))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X27),X32)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_486_finite__nat__set__iff__bounded__le) ).

tff(f17996,plain,
    spl250_919,
    inference(avatar_split_clause,[],[f4789,f17994]) ).

tff(f17994,plain,
    ( spl250_919
  <=> ! [X4: nat,X0: fun_nat_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),sK59(X0)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_919])]) ).

tff(f4789,plain,
    ! [X0: fun_nat_bool,X4: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),sK59(X0)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ),
    inference(cnf_transformation,[],[f3826]) ).

tff(f3826,plain,
    ! [X0: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | ! [X1: nat] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK58(X0,X1)),X1))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK58(X0,X1)),X0)) ) )
      & ( ! [X4: nat] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),sK59(X0)))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK58,sK59])],[f3823,f3825,f3824]) ).

tff(f3824,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( ? [X2: nat] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) )
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK58(X0,X1)),X1))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK58(X0,X1)),X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3825,plain,
    ! [X0: fun_nat_bool] :
      ( ? [X3: nat] :
        ! [X4: nat] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X3))
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0)) )
     => ! [X4: nat] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),sK59(X0)))
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3823,plain,
    ! [X0: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | ! [X1: nat] :
          ? [X2: nat] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) ) )
      & ( ? [X3: nat] :
          ! [X4: nat] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X3))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X0)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    inference(rectify,[],[f3822]) ).

tff(f3822,plain,
    ! [X0: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | ! [X1: nat] :
          ? [X2: nat] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) ) )
      & ( ? [X1: nat] :
          ! [X2: nat] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    inference(nnf_transformation,[],[f2607]) ).

tff(f2607,plain,
    ! [X0: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
    <=> ? [X1: nat] :
        ! [X2: nat] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) ) ),
    inference(ennf_transformation,[],[f1479]) ).

tff(f1479,plain,
    ! [X0: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
    <=> ? [X1: nat] :
        ! [X2: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ) ),
    inference(rectify,[],[f896]) ).

tff(f896,axiom,
    ! [X69: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X69))
    <=> ? [X32: nat] :
        ! [X27: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X27),X69))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X27),X32)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_895_finite__nat__set__iff__bounded) ).

tff(f17791,plain,
    ( spl250_918
    | ~ spl250_893 ),
    inference(avatar_split_clause,[],[f15983,f15980,f17789]) ).

tff(f17789,plain,
    ( spl250_918
  <=> ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
        | hBOOL(hAPP_int_bool(nat_neg,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_918])]) ).

tff(f15980,plain,
    ( spl250_893
  <=> ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))
        | hBOOL(hAPP_int_bool(nat_neg,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_893])]) ).

tff(f15983,plain,
    ( ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
        | hBOOL(hAPP_int_bool(nat_neg,X0)) )
    | ~ spl250_893 ),
    inference(forward_demodulation,[],[f15981,f5751]) ).

tff(f15981,plain,
    ( ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))
        | hBOOL(hAPP_int_bool(nat_neg,X0)) )
    | ~ spl250_893 ),
    inference(avatar_component_clause,[],[f15980]) ).

tff(f17787,plain,
    ( spl250_917
    | ~ spl250_892 ),
    inference(avatar_split_clause,[],[f15978,f15975,f17785]) ).

tff(f17785,plain,
    ( spl250_917
  <=> ! [X0: int] :
        ( hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
        | ~ hBOOL(hAPP_int_bool(nat_neg,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_917])]) ).

tff(f15975,plain,
    ( spl250_892
  <=> ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
        | hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_892])]) ).

tff(f15978,plain,
    ( ! [X0: int] :
        ( hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))))
        | ~ hBOOL(hAPP_int_bool(nat_neg,X0)) )
    | ~ spl250_892 ),
    inference(forward_demodulation,[],[f15976,f5751]) ).

tff(f15976,plain,
    ( ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
        | hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0))) )
    | ~ spl250_892 ),
    inference(avatar_component_clause,[],[f15975]) ).

tff(f17783,plain,
    ( spl250_916
    | ~ spl250_891 ),
    inference(avatar_split_clause,[],[f15973,f15970,f17781]) ).

tff(f17781,plain,
    ( spl250_916
  <=> ! [X0: int] :
        ( ( zero_zero_nat = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))) )
        | ~ hBOOL(hAPP_int_bool(nat_neg,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_916])]) ).

tff(f15970,plain,
    ( spl250_891
  <=> ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
        | ( zero_zero_nat = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_891])]) ).

tff(f15973,plain,
    ( ! [X0: int] :
        ( ( zero_zero_nat = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X0))) )
        | ~ hBOOL(hAPP_int_bool(nat_neg,X0)) )
    | ~ spl250_891 ),
    inference(forward_demodulation,[],[f15971,f5751]) ).

tff(f15971,plain,
    ( ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
        | ( zero_zero_nat = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)) ) )
    | ~ spl250_891 ),
    inference(avatar_component_clause,[],[f15970]) ).

tff(f17469,plain,
    ( spl250_915
    | ~ spl250_52
    | ~ spl250_535 ),
    inference(avatar_split_clause,[],[f11606,f10853,f7548,f17467]) ).

tff(f17467,plain,
    ( spl250_915
  <=> ! [X0: int] :
        ( sP5(X0,pls)
        | ~ sP4(pls,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_915])]) ).

tff(f7548,plain,
    ( spl250_52
  <=> ! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_52])]) ).

tff(f10853,plain,
    ( spl250_535
  <=> ! [X0: int,X1: int] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
        | sP5(X0,X1)
        | ~ sP4(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_535])]) ).

tff(f11606,plain,
    ( ! [X0: int] :
        ( sP5(X0,pls)
        | ~ sP4(pls,X0) )
    | ~ spl250_52
    | ~ spl250_535 ),
    inference(resolution,[],[f10854,f7549]) ).

tff(f7549,plain,
    ( ! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X0))
    | ~ spl250_52 ),
    inference(avatar_component_clause,[],[f7548]) ).

tff(f10854,plain,
    ( ! [X0: int,X1: int] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
        | sP5(X0,X1)
        | ~ sP4(X1,X0) )
    | ~ spl250_535 ),
    inference(avatar_component_clause,[],[f10853]) ).

tff(f17139,plain,
    ( spl250_914
    | ~ spl250_85
    | ~ spl250_913 ),
    inference(avatar_split_clause,[],[f17035,f16977,f7733,f17136]) ).

tff(f17136,plain,
    ( spl250_914
  <=> ( fTrue = hAPP_fun_a_bool_bool(finite_finite_a,g) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_914])]) ).

tff(f16977,plain,
    ( spl250_913
  <=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,g)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_913])]) ).

tff(f17035,plain,
    ( ( fTrue = hAPP_fun_a_bool_bool(finite_finite_a,g) )
    | ~ spl250_85
    | ~ spl250_913 ),
    inference(resolution,[],[f16979,f7734]) ).

tff(f16979,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,g))
    | ~ spl250_913 ),
    inference(avatar_component_clause,[],[f16977]) ).

tff(f16980,plain,
    ( spl250_913
    | ~ spl250_130
    | ~ spl250_129
    | ~ spl250_132
    | ~ spl250_817 ),
    inference(avatar_split_clause,[],[f16950,f15476,f8007,f7958,f7965,f16977]) ).

tff(f7958,plain,
    ( spl250_129
  <=> ( fTrue = hAPP_f1664156314l_bool(finite_finite_pname,u) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_129])]) ).

tff(f15476,plain,
    ( spl250_817
  <=> ! [X2: fun_pname_bool,X0: fun_a_bool,X1: fun_pname_a] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_817])]) ).

tff(f16950,plain,
    ( ~ hBOOL(fTrue)
    | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,g))
    | ~ spl250_129
    | ~ spl250_132
    | ~ spl250_817 ),
    inference(forward_demodulation,[],[f16937,f7960]) ).

tff(f7960,plain,
    ( ( fTrue = hAPP_f1664156314l_bool(finite_finite_pname,u) )
    | ~ spl250_129 ),
    inference(avatar_component_clause,[],[f7958]) ).

tff(f16937,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,g))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u))
    | ~ spl250_132
    | ~ spl250_817 ),
    inference(resolution,[],[f15477,f8009]) ).

tff(f15477,plain,
    ( ! [X2: fun_pname_bool,X0: fun_a_bool,X1: fun_pname_a] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
        | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) )
    | ~ spl250_817 ),
    inference(avatar_component_clause,[],[f15476]) ).

tff(f16813,plain,
    ( spl250_912
    | ~ spl250_73
    | ~ spl250_516 ),
    inference(avatar_split_clause,[],[f11483,f10775,f7638,f16810]) ).

tff(f16810,plain,
    ( spl250_912
  <=> ( one_one_int = hAPP_nat_int(semiri1621563631at_int,sK34(one_one_int)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_912])]) ).

tff(f7638,plain,
    ( spl250_73
  <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),one_one_int)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_73])]) ).

tff(f10775,plain,
    ( spl250_516
  <=> ! [X0: int] :
        ( ( hAPP_nat_int(semiri1621563631at_int,sK34(X0)) = X0 )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_516])]) ).

tff(f11483,plain,
    ( ( one_one_int = hAPP_nat_int(semiri1621563631at_int,sK34(one_one_int)) )
    | ~ spl250_73
    | ~ spl250_516 ),
    inference(resolution,[],[f10776,f7640]) ).

tff(f7640,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),one_one_int))
    | ~ spl250_73 ),
    inference(avatar_component_clause,[],[f7638]) ).

tff(f10776,plain,
    ( ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
        | ( hAPP_nat_int(semiri1621563631at_int,sK34(X0)) = X0 ) )
    | ~ spl250_516 ),
    inference(avatar_component_clause,[],[f10775]) ).

tff(f16671,plain,
    ( spl250_911
    | ~ spl250_52
    | ~ spl250_516 ),
    inference(avatar_split_clause,[],[f11480,f10775,f7548,f16668]) ).

tff(f11480,plain,
    ( ( pls = hAPP_nat_int(semiri1621563631at_int,sK34(pls)) )
    | ~ spl250_52
    | ~ spl250_516 ),
    inference(resolution,[],[f10776,f7549]) ).

tff(f16666,plain,
    ( spl250_910
    | ~ spl250_371
    | ~ spl250_788 ),
    inference(avatar_split_clause,[],[f15362,f15359,f9695,f16664]) ).

tff(f16664,plain,
    ( spl250_910
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_eq_int,semiri1621563631at_int),X0),hAPP_nat_int(semiri1621563631at_int,X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_910])]) ).

tff(f9695,plain,
    ( spl250_371
  <=> ! [X2: nat,X0: fun_int_fun_int_bool,X1: fun_nat_int] : ( hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(X0,X1),X2) = hAPP_i1948725293t_bool(X0,hAPP_nat_int(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_371])]) ).

tff(f15359,plain,
    ( spl250_788
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_788])]) ).

tff(f15362,plain,
    ( ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_eq_int,semiri1621563631at_int),X0),hAPP_nat_int(semiri1621563631at_int,X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
    | ~ spl250_371
    | ~ spl250_788 ),
    inference(forward_demodulation,[],[f15360,f9696]) ).

tff(f9696,plain,
    ( ! [X2: nat,X0: fun_int_fun_int_bool,X1: fun_nat_int] : ( hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(X0,X1),X2) = hAPP_i1948725293t_bool(X0,hAPP_nat_int(X1,X2)) )
    | ~ spl250_371 ),
    inference(avatar_component_clause,[],[f9695]) ).

tff(f15360,plain,
    ( ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
    | ~ spl250_788 ),
    inference(avatar_component_clause,[],[f15359]) ).

tff(f16662,plain,
    ( spl250_909
    | ~ spl250_371
    | ~ spl250_787 ),
    inference(avatar_split_clause,[],[f15357,f15354,f9695,f16660]) ).

tff(f16660,plain,
    ( spl250_909
  <=> ! [X0: nat,X1: nat] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_eq_int,semiri1621563631at_int),X0),hAPP_nat_int(semiri1621563631at_int,X1)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_909])]) ).

tff(f15354,plain,
    ( spl250_787
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_787])]) ).

tff(f15357,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_eq_int,semiri1621563631at_int),X0),hAPP_nat_int(semiri1621563631at_int,X1)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
    | ~ spl250_371
    | ~ spl250_787 ),
    inference(forward_demodulation,[],[f15355,f9696]) ).

tff(f15355,plain,
    ( ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1))) )
    | ~ spl250_787 ),
    inference(avatar_component_clause,[],[f15354]) ).

tff(f16658,plain,
    ( spl250_908
    | ~ spl250_371
    | ~ spl250_785 ),
    inference(avatar_split_clause,[],[f15348,f15345,f9695,f16656]) ).

tff(f16656,plain,
    ( spl250_908
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_int,semiri1621563631at_int),X0),hAPP_nat_int(semiri1621563631at_int,X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_908])]) ).

tff(f15345,plain,
    ( spl250_785
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_785])]) ).

tff(f15348,plain,
    ( ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_int,semiri1621563631at_int),X0),hAPP_nat_int(semiri1621563631at_int,X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) )
    | ~ spl250_371
    | ~ spl250_785 ),
    inference(forward_demodulation,[],[f15346,f9696]) ).

tff(f15346,plain,
    ( ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) )
    | ~ spl250_785 ),
    inference(avatar_component_clause,[],[f15345]) ).

tff(f16654,plain,
    ( spl250_907
    | ~ spl250_371
    | ~ spl250_784 ),
    inference(avatar_split_clause,[],[f15343,f15340,f9695,f16652]) ).

tff(f16652,plain,
    ( spl250_907
  <=> ! [X0: nat,X1: nat] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_int,semiri1621563631at_int),X0),hAPP_nat_int(semiri1621563631at_int,X1)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_907])]) ).

tff(f15340,plain,
    ( spl250_784
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_784])]) ).

tff(f15343,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_int,semiri1621563631at_int),X0),hAPP_nat_int(semiri1621563631at_int,X1)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) )
    | ~ spl250_371
    | ~ spl250_784 ),
    inference(forward_demodulation,[],[f15341,f9696]) ).

tff(f15341,plain,
    ( ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1))) )
    | ~ spl250_784 ),
    inference(avatar_component_clause,[],[f15340]) ).

tff(f16564,plain,
    ( spl250_906
    | ~ spl250_73
    | ~ spl250_515 ),
    inference(avatar_split_clause,[],[f11470,f10771,f7638,f16561]) ).

tff(f16561,plain,
    ( spl250_906
  <=> ( one_one_int = hAPP_nat_int(semiri1621563631at_int,sK33(one_one_int)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_906])]) ).

tff(f10771,plain,
    ( spl250_515
  <=> ! [X0: int] :
        ( ( hAPP_nat_int(semiri1621563631at_int,sK33(X0)) = X0 )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_515])]) ).

tff(f11470,plain,
    ( ( one_one_int = hAPP_nat_int(semiri1621563631at_int,sK33(one_one_int)) )
    | ~ spl250_73
    | ~ spl250_515 ),
    inference(resolution,[],[f10772,f7640]) ).

tff(f10772,plain,
    ( ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
        | ( hAPP_nat_int(semiri1621563631at_int,sK33(X0)) = X0 ) )
    | ~ spl250_515 ),
    inference(avatar_component_clause,[],[f10771]) ).

tff(f16401,plain,
    ( spl250_905
    | ~ spl250_52
    | ~ spl250_515 ),
    inference(avatar_split_clause,[],[f11467,f10771,f7548,f16398]) ).

tff(f11467,plain,
    ( ( pls = hAPP_nat_int(semiri1621563631at_int,sK33(pls)) )
    | ~ spl250_52
    | ~ spl250_515 ),
    inference(resolution,[],[f10772,f7549]) ).

tff(f16291,plain,
    ( spl250_904
    | ~ spl250_73
    | ~ spl250_514 ),
    inference(avatar_split_clause,[],[f11457,f10767,f7638,f16288]) ).

tff(f16288,plain,
    ( spl250_904
  <=> ( one_one_int = hAPP_nat_int(semiri1621563631at_int,sK32(one_one_int)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_904])]) ).

tff(f10767,plain,
    ( spl250_514
  <=> ! [X0: int] :
        ( ( hAPP_nat_int(semiri1621563631at_int,sK32(X0)) = X0 )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_514])]) ).

tff(f11457,plain,
    ( ( one_one_int = hAPP_nat_int(semiri1621563631at_int,sK32(one_one_int)) )
    | ~ spl250_73
    | ~ spl250_514 ),
    inference(resolution,[],[f10768,f7640]) ).

tff(f10768,plain,
    ( ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
        | ( hAPP_nat_int(semiri1621563631at_int,sK32(X0)) = X0 ) )
    | ~ spl250_514 ),
    inference(avatar_component_clause,[],[f10767]) ).

tff(f16176,plain,
    ( spl250_903
    | ~ spl250_52
    | ~ spl250_514 ),
    inference(avatar_split_clause,[],[f11454,f10767,f7548,f16173]) ).

tff(f11454,plain,
    ( ( pls = hAPP_nat_int(semiri1621563631at_int,sK32(pls)) )
    | ~ spl250_52
    | ~ spl250_514 ),
    inference(resolution,[],[f10768,f7549]) ).

tff(f16020,plain,
    spl250_902,
    inference(avatar_split_clause,[],[f7186,f16018]) ).

tff(f16018,plain,
    ( spl250_902
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_902])]) ).

tff(f7186,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1))) ),
    inference(forward_demodulation,[],[f7185,f4588]) ).

tff(f7185,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) ),
    inference(forward_demodulation,[],[f7184,f4588]) ).

tff(f7184,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) ),
    inference(forward_demodulation,[],[f5637,f4588]) ).

tff(f5637,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) ),
    inference(cnf_transformation,[],[f4159]) ).

tff(f4159,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1))))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) )
      & ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))) ) ),
    inference(flattening,[],[f4158]) ).

tff(f4158,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1))))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) )
      & ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))) ) ),
    inference(nnf_transformation,[],[f2035]) ).

tff(f2035,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1))))
    <=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) ) ),
    inference(rectify,[],[f139]) ).

tff(f139,axiom,
    ! [X10: fun_nat_bool,X9: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X10),X9))))
    <=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X9)))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X10))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_finite__Collect__disjI) ).

tff(f16016,plain,
    ( spl250_901
    | ~ spl250_72
    | ~ spl250_513 ),
    inference(avatar_split_clause,[],[f11441,f10763,f7633,f16013]) ).

tff(f16013,plain,
    ( spl250_901
  <=> ( one_one_int = hAPP_nat_int(semiri1621563631at_int,sK31(one_one_int)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_901])]) ).

tff(f7633,plain,
    ( spl250_72
  <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),one_one_int)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_72])]) ).

tff(f10763,plain,
    ( spl250_513
  <=> ! [X0: int] :
        ( ( hAPP_nat_int(semiri1621563631at_int,sK31(X0)) = X0 )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_513])]) ).

tff(f11441,plain,
    ( ( one_one_int = hAPP_nat_int(semiri1621563631at_int,sK31(one_one_int)) )
    | ~ spl250_72
    | ~ spl250_513 ),
    inference(resolution,[],[f10764,f7635]) ).

tff(f7635,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),one_one_int))
    | ~ spl250_72 ),
    inference(avatar_component_clause,[],[f7633]) ).

tff(f10764,plain,
    ( ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
        | ( hAPP_nat_int(semiri1621563631at_int,sK31(X0)) = X0 ) )
    | ~ spl250_513 ),
    inference(avatar_component_clause,[],[f10763]) ).

tff(f16011,plain,
    spl250_900,
    inference(avatar_split_clause,[],[f7179,f16009]) ).

tff(f16009,plain,
    ( spl250_900
  <=> ! [X0: fun_int_bool,X1: fun_int_bool] :
        ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
        | hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_900])]) ).

tff(f7179,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1))) ),
    inference(forward_demodulation,[],[f7178,f4586]) ).

tff(f7178,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0))) ),
    inference(forward_demodulation,[],[f7177,f4586]) ).

tff(f7177,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0))) ),
    inference(forward_demodulation,[],[f5634,f4586]) ).

tff(f5634,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1))))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0))) ),
    inference(cnf_transformation,[],[f4157]) ).

tff(f4157,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1))))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0))) )
      & ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1)))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0))) )
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))) ) ),
    inference(flattening,[],[f4156]) ).

tff(f4156,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1))))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0))) )
      & ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1)))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0))) )
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))) ) ),
    inference(nnf_transformation,[],[f2034]) ).

tff(f2034,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1))))
    <=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1)))
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0))) ) ),
    inference(rectify,[],[f140]) ).

tff(f140,axiom,
    ! [X10: fun_int_bool,X9: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X10),X9))))
    <=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X9)))
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X10))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_finite__Collect__disjI) ).

tff(f16007,plain,
    spl250_899,
    inference(avatar_split_clause,[],[f7092,f16005]) ).

tff(f16005,plain,
    ( spl250_899
  <=> ! [X0: fun_nat_bool,X1: nat] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_n1699378549t_bool(fequal_nat,X1)))
        | ( hAPP_n1699378549t_bool(fequal_nat,X1) = X0 )
        | ( bot_bot_fun_nat_bool = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_899])]) ).

tff(f7092,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_n1699378549t_bool(fequal_nat,X1)))
      | ( hAPP_n1699378549t_bool(fequal_nat,X1) = X0 )
      | ( bot_bot_fun_nat_bool = X0 ) ),
    inference(forward_demodulation,[],[f7091,f6931]) ).

tff(f7091,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( ( hAPP_n1699378549t_bool(fequal_nat,X1) = X0 )
      | ( bot_bot_fun_nat_bool = X0 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))) ),
    inference(forward_demodulation,[],[f5392,f6931]) ).

tff(f5392,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool) = X0 )
      | ( bot_bot_fun_nat_bool = X0 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))) ),
    inference(cnf_transformation,[],[f3041]) ).

tff(f3041,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool) = X0 )
      | ( bot_bot_fun_nat_bool = X0 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))) ),
    inference(flattening,[],[f3040]) ).

tff(f3040,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool) = X0 )
      | ( bot_bot_fun_nat_bool = X0 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))) ),
    inference(ennf_transformation,[],[f1935]) ).

tff(f1935,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)))
     => ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool) = X0 )
        | ( bot_bot_fun_nat_bool = X0 ) ) ),
    inference(rectify,[],[f662]) ).

tff(f662,axiom,
    ! [X2: fun_nat_bool,X8: nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),bot_bot_fun_nat_bool)))
     => ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),bot_bot_fun_nat_bool) = X2 )
        | ( bot_bot_fun_nat_bool = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_661_subset__singletonD) ).

tff(f16003,plain,
    spl250_898,
    inference(avatar_split_clause,[],[f7089,f16001]) ).

tff(f16001,plain,
    ( spl250_898
  <=> ! [X0: fun_int_bool,X1: int] :
        ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_i1948725293t_bool(fequal_int,X1)))
        | ( hAPP_i1948725293t_bool(fequal_int,X1) = X0 )
        | ( bot_bot_fun_int_bool = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_898])]) ).

tff(f7089,plain,
    ! [X0: fun_int_bool,X1: int] :
      ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_i1948725293t_bool(fequal_int,X1)))
      | ( hAPP_i1948725293t_bool(fequal_int,X1) = X0 )
      | ( bot_bot_fun_int_bool = X0 ) ),
    inference(forward_demodulation,[],[f7088,f6930]) ).

tff(f7088,plain,
    ! [X0: fun_int_bool,X1: int] :
      ( ( hAPP_i1948725293t_bool(fequal_int,X1) = X0 )
      | ( bot_bot_fun_int_bool = X0 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))) ),
    inference(forward_demodulation,[],[f5390,f6930]) ).

tff(f5390,plain,
    ! [X0: fun_int_bool,X1: int] :
      ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool) = X0 )
      | ( bot_bot_fun_int_bool = X0 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))) ),
    inference(cnf_transformation,[],[f3038]) ).

tff(f3038,plain,
    ! [X0: fun_int_bool,X1: int] :
      ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool) = X0 )
      | ( bot_bot_fun_int_bool = X0 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))) ),
    inference(flattening,[],[f3037]) ).

tff(f3037,plain,
    ! [X0: fun_int_bool,X1: int] :
      ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool) = X0 )
      | ( bot_bot_fun_int_bool = X0 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))) ),
    inference(ennf_transformation,[],[f1933]) ).

tff(f1933,plain,
    ! [X0: fun_int_bool,X1: int] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)))
     => ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool) = X0 )
        | ( bot_bot_fun_int_bool = X0 ) ) ),
    inference(rectify,[],[f663]) ).

tff(f663,axiom,
    ! [X2: fun_int_bool,X8: int] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),bot_bot_fun_int_bool)))
     => ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),bot_bot_fun_int_bool) = X2 )
        | ( bot_bot_fun_int_bool = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_662_subset__singletonD) ).

tff(f15999,plain,
    spl250_897,
    inference(avatar_split_clause,[],[f7019,f15997]) ).

tff(f15997,plain,
    ( spl250_897
  <=> ! [X0: nat,X1: fun_nat_bool] :
        ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK89(X0,X1))))
        | ~ hBOOL(hAPP_nat_bool(X1,X0))
        | hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_897])]) ).

tff(f7019,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK89(X0,X1))))
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
    inference(forward_demodulation,[],[f5049,f4672]) ).

tff(f4672,plain,
    ! [X0: nat] : ( hAPP_nat_nat(suc,X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),one_one_nat) ),
    inference(cnf_transformation,[],[f1400]) ).

tff(f1400,plain,
    ! [X0: nat] : ( hAPP_nat_nat(suc,X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),one_one_nat) ),
    inference(rectify,[],[f851]) ).

tff(f851,axiom,
    ! [X11: nat] : ( hAPP_nat_nat(suc,X11) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X11),one_one_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_850_Suc__eq__plus1) ).

tff(f5049,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK89(X0,X1)),one_one_nat)))
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
    inference(cnf_transformation,[],[f3930]) ).

tff(f15995,plain,
    spl250_896,
    inference(avatar_split_clause,[],[f7005,f15993]) ).

tff(f15993,plain,
    ( spl250_896
  <=> ! [X0: nat,X1: int] :
        ( ~ hBOOL(hAPP_int_bool(nat_neg,X1))
        | ( hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_896])]) ).

tff(f7005,plain,
    ! [X0: nat,X1: int] :
      ( ~ hBOOL(hAPP_int_bool(nat_neg,X1))
      | ( hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X0)) ) ),
    inference(forward_demodulation,[],[f7004,f4587]) ).

tff(f7004,plain,
    ! [X0: nat,X1: int] :
      ( ( hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X0)) )
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ),
    inference(forward_demodulation,[],[f4966,f4671]) ).

tff(f4966,plain,
    ! [X0: nat,X1: int] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X0)) )
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ),
    inference(cnf_transformation,[],[f2621]) ).

tff(f2621,plain,
    ! [X0: nat,X1: int] :
      ( ( ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X0)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(succ(X1))),X0) )
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) )
      & ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X0)) )
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ) ),
    inference(ennf_transformation,[],[f1604]) ).

tff(f1604,plain,
    ! [X0: nat,X1: int] :
      ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1)))
       => ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X0)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(succ(X1))),X0) ) )
      & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1)))
       => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X0) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X0)) ) ) ),
    inference(rectify,[],[f1162]) ).

tff(f1162,axiom,
    ! [X11: nat,X130: int] :
      ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X130)))
       => ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X130)),X11)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(succ(X130))),X11) ) )
      & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X130)))
       => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X11) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X130)),X11)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1161_Suc__nat__number__of__add) ).

tff(f15991,plain,
    spl250_895,
    inference(avatar_split_clause,[],[f6979,f15989]) ).

tff(f15989,plain,
    ( spl250_895
  <=> ! [X0: nat,X1: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(fequal_nat,X0))),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_895])]) ).

tff(f6979,plain,
    ! [X0: nat,X1: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(fequal_nat,X0))),X1)) ),
    inference(forward_demodulation,[],[f6978,f4588]) ).

tff(f6978,plain,
    ! [X0: nat,X1: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),collect_nat(X1)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(fequal_nat,X0))),X1)) ),
    inference(forward_demodulation,[],[f4937,f6935]) ).

tff(f4937,plain,
    ! [X0: nat,X1: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),collect_nat(X1)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1)) ),
    inference(cnf_transformation,[],[f1585]) ).

tff(f1585,plain,
    ! [X0: nat,X1: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),collect_nat(X1)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0))),X1)) ),
    inference(rectify,[],[f376]) ).

tff(f376,axiom,
    ! [X5: nat,X10: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5),collect_nat(X10)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X5))),X10)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_375_insert__Collect) ).

tff(f15987,plain,
    spl250_894,
    inference(avatar_split_clause,[],[f6977,f15985]) ).

tff(f15985,plain,
    ( spl250_894
  <=> ! [X0: int,X1: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fimplies,cOMBB_bool_bool_int(fNot,hAPP_i1948725293t_bool(fequal_int,X0))),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_894])]) ).

tff(f6977,plain,
    ! [X0: int,X1: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fimplies,cOMBB_bool_bool_int(fNot,hAPP_i1948725293t_bool(fequal_int,X0))),X1)) ),
    inference(forward_demodulation,[],[f6976,f4586]) ).

tff(f6976,plain,
    ! [X0: int,X1: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),collect_int(X1)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fimplies,cOMBB_bool_bool_int(fNot,hAPP_i1948725293t_bool(fequal_int,X0))),X1)) ),
    inference(forward_demodulation,[],[f4936,f6933]) ).

tff(f4936,plain,
    ! [X0: int,X1: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),collect_int(X1)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fimplies,cOMBB_bool_bool_int(fNot,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X0))),X1)) ),
    inference(cnf_transformation,[],[f1584]) ).

tff(f1584,plain,
    ! [X0: int,X1: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),collect_int(X1)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fimplies,cOMBB_bool_bool_int(fNot,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X0))),X1)) ),
    inference(rectify,[],[f375]) ).

tff(f375,axiom,
    ! [X5: int,X10: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5),collect_int(X10)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fimplies,cOMBB_bool_bool_int(fNot,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X5))),X10)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_insert__Collect) ).

tff(f15982,plain,
    spl250_893,
    inference(avatar_split_clause,[],[f6963,f15980]) ).

tff(f6963,plain,
    ! [X0: int] :
      ( ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))
      | hBOOL(hAPP_int_bool(nat_neg,X0)) ),
    inference(forward_demodulation,[],[f6962,f4587]) ).

tff(f6962,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(nat_neg,X0))
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))) ),
    inference(forward_demodulation,[],[f6604,f4587]) ).

tff(f6604,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))) ),
    inference(definition_unfolding,[],[f4819,f4687]) ).

tff(f4819,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(X0)))) ),
    inference(cnf_transformation,[],[f3844]) ).

tff(f3844,plain,
    ! [X0: int] :
      ( ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(X0))))
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
      & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(X0)))) ) ),
    inference(nnf_transformation,[],[f1493]) ).

tff(f1493,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(X0))))
    <=> hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
    inference(rectify,[],[f1168]) ).

tff(f1168,axiom,
    ! [X136: int] :
      ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(X136))))
    <=> hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X136))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1167_neg__number__of__Bit1) ).

tff(f15977,plain,
    spl250_892,
    inference(avatar_split_clause,[],[f6961,f15975]) ).

tff(f6961,plain,
    ! [X0: int] :
      ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
      | hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0))) ),
    inference(forward_demodulation,[],[f6960,f4587]) ).

tff(f6960,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)))
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
    inference(forward_demodulation,[],[f6603,f4587]) ).

tff(f6603,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0))))
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
    inference(definition_unfolding,[],[f4820,f4687]) ).

tff(f4820,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(X0))))
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
    inference(cnf_transformation,[],[f3844]) ).

tff(f15972,plain,
    spl250_891,
    inference(avatar_split_clause,[],[f6942,f15970]) ).

tff(f6942,plain,
    ! [X0: int] :
      ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
      | ( zero_zero_nat = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)) ) ),
    inference(forward_demodulation,[],[f6586,f4587]) ).

tff(f6586,plain,
    ! [X0: int] :
      ( ( zero_zero_nat = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0)) )
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
    inference(definition_unfolding,[],[f4695,f4687]) ).

tff(f4695,plain,
    ! [X0: int] :
      ( ( zero_zero_nat = number_number_of_nat(bit1(X0)) )
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
    inference(cnf_transformation,[],[f2576]) ).

tff(f2576,plain,
    ! [X0: int] :
      ( ( ( number_number_of_nat(bit1(X0)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),number_number_of_nat(X0))) )
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
      & ( ( zero_zero_nat = number_number_of_nat(bit1(X0)) )
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) ),
    inference(ennf_transformation,[],[f1423]) ).

tff(f1423,plain,
    ! [X0: int] :
      ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
       => ( number_number_of_nat(bit1(X0)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X0)),number_number_of_nat(X0))) ) )
      & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
       => ( zero_zero_nat = number_number_of_nat(bit1(X0)) ) ) ),
    inference(rectify,[],[f1165]) ).

tff(f1165,axiom,
    ! [X132: int] :
      ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X132)))
       => ( number_number_of_nat(bit1(X132)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X132)),number_number_of_nat(X132))) ) )
      & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X132)))
       => ( zero_zero_nat = number_number_of_nat(bit1(X132)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1164_nat__number__of__Bit1) ).

tff(f15968,plain,
    ( spl250_890
    | ~ spl250_74
    | ~ spl250_506 ),
    inference(avatar_split_clause,[],[f11372,f10724,f7643,f15966]) ).

tff(f15966,plain,
    ( spl250_890
  <=> ! [X0: nat,X1: nat] : sP19(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_890])]) ).

tff(f7643,plain,
    ( spl250_74
  <=> ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_74])]) ).

tff(f10724,plain,
    ( spl250_506
  <=> ! [X2: nat,X0: fun_nat_bool,X1: nat] :
        ( sP19(X0,X1,X2)
        | ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_506])]) ).

tff(f11372,plain,
    ( ! [X0: nat,X1: nat] : sP19(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0,X1)
    | ~ spl250_74
    | ~ spl250_506 ),
    inference(resolution,[],[f10725,f7644]) ).

tff(f7644,plain,
    ( ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0))
    | ~ spl250_74 ),
    inference(avatar_component_clause,[],[f7643]) ).

tff(f10725,plain,
    ( ! [X2: nat,X0: fun_nat_bool,X1: nat] :
        ( ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
        | sP19(X0,X1,X2) )
    | ~ spl250_506 ),
    inference(avatar_component_clause,[],[f10724]) ).

tff(f15964,plain,
    spl250_889,
    inference(avatar_split_clause,[],[f6649,f15962]) ).

tff(f15962,plain,
    ( spl250_889
  <=> ! [X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_889])]) ).

tff(f6649,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),pls))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(definition_unfolding,[],[f5510,f4550]) ).

tff(f5510,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4072]) ).

tff(f4072,plain,
    ! [X0: int,X1: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),zero_zero_int)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),zero_zero_int))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
    inference(nnf_transformation,[],[f1988]) ).

tff(f1988,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),zero_zero_int)) ),
    inference(rectify,[],[f1038]) ).

tff(f1038,axiom,
    ! [X13: int,X131: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),X131))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X13),X131)),zero_zero_int)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1037_less__bin__lemma) ).

tff(f15960,plain,
    spl250_888,
    inference(avatar_split_clause,[],[f6648,f15958]) ).

tff(f15958,plain,
    ( spl250_888
  <=> ! [X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),pls)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_888])]) ).

tff(f6648,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),pls)) ),
    inference(definition_unfolding,[],[f5511,f4550]) ).

tff(f5511,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),zero_zero_int)) ),
    inference(cnf_transformation,[],[f4072]) ).

tff(f15956,plain,
    spl250_887,
    inference(avatar_split_clause,[],[f6633,f15954]) ).

tff(f15954,plain,
    ( spl250_887
  <=> ! [X0: int,X1: int] :
        ( ( one_one_int = X1 )
        | ( one_one_int != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0) )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_887])]) ).

tff(f6633,plain,
    ! [X0: int,X1: int] :
      ( ( one_one_int = X1 )
      | ( one_one_int != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
    inference(definition_unfolding,[],[f5293,f4550]) ).

tff(f5293,plain,
    ! [X0: int,X1: int] :
      ( ( one_one_int = X1 )
      | ( one_one_int != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
    inference(cnf_transformation,[],[f3982]) ).

tff(f3982,plain,
    ! [X0: int,X1: int] :
      ( ( ( ( one_one_int = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0) )
          | ( one_one_int != X0 )
          | ( one_one_int != X1 ) )
        & ( ( ( one_one_int = X0 )
            & ( one_one_int = X1 ) )
          | ( one_one_int != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0) ) ) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
    inference(flattening,[],[f3981]) ).

tff(f3981,plain,
    ! [X0: int,X1: int] :
      ( ( ( ( one_one_int = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0) )
          | ( one_one_int != X0 )
          | ( one_one_int != X1 ) )
        & ( ( ( one_one_int = X0 )
            & ( one_one_int = X1 ) )
          | ( one_one_int != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0) ) ) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
    inference(nnf_transformation,[],[f2913]) ).

tff(f2913,plain,
    ! [X0: int,X1: int] :
      ( ( ( one_one_int = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0) )
      <=> ( ( one_one_int = X0 )
          & ( one_one_int = X1 ) ) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
    inference(ennf_transformation,[],[f1848]) ).

tff(f1848,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
     => ( ( one_one_int = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0) )
      <=> ( ( one_one_int = X0 )
          & ( one_one_int = X1 ) ) ) ),
    inference(rectify,[],[f1032]) ).

tff(f1032,axiom,
    ! [X14: int,X22: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X22))
     => ( ( one_one_int = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X22),X14) )
      <=> ( ( one_one_int = X14 )
          & ( one_one_int = X22 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1031_pos__zmult__eq__1__iff) ).

tff(f15952,plain,
    spl250_886,
    inference(avatar_split_clause,[],[f6632,f15950]) ).

tff(f15950,plain,
    ( spl250_886
  <=> ! [X0: int,X1: int] :
        ( ( one_one_int = X0 )
        | ( one_one_int != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0) )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_886])]) ).

tff(f6632,plain,
    ! [X0: int,X1: int] :
      ( ( one_one_int = X0 )
      | ( one_one_int != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
    inference(definition_unfolding,[],[f5294,f4550]) ).

tff(f5294,plain,
    ! [X0: int,X1: int] :
      ( ( one_one_int = X0 )
      | ( one_one_int != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
    inference(cnf_transformation,[],[f3982]) ).

tff(f15948,plain,
    spl250_885,
    inference(avatar_split_clause,[],[f6592,f15946]) ).

tff(f15946,plain,
    ( spl250_885
  <=> ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_885])]) ).

tff(f6592,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(definition_unfolding,[],[f4725,f4550,f4550]) ).

tff(f4725,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
    inference(cnf_transformation,[],[f2597]) ).

tff(f2597,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
    inference(ennf_transformation,[],[f1448]) ).

tff(f1448,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0))) ),
    inference(rectify,[],[f1039]) ).

tff(f1039,axiom,
    ! [X95: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X95))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X95))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1038_le__imp__0__less) ).

tff(f15944,plain,
    spl250_884,
    inference(avatar_split_clause,[],[f6390,f15942]) ).

tff(f15942,plain,
    ( spl250_884
  <=> ! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_884])]) ).

tff(f6390,plain,
    ! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f4473]) ).

tff(f15940,plain,
    spl250_883,
    inference(avatar_split_clause,[],[f6389,f15938]) ).

tff(f15938,plain,
    ( spl250_883
  <=> ! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_883])]) ).

tff(f6389,plain,
    ! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f4473]) ).

tff(f15936,plain,
    spl250_882,
    inference(avatar_split_clause,[],[f6385,f15934]) ).

tff(f15934,plain,
    ( spl250_882
  <=> ! [X2: nat,X0: fun_nat_bool,X1: fun_nat_bool] :
        ( sP23(X0,X1,X2)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_882])]) ).

tff(f6385,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: fun_nat_bool] :
      ( sP23(X0,X1,X2)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ),
    inference(cnf_transformation,[],[f4470]) ).

tff(f15932,plain,
    spl250_881,
    inference(avatar_split_clause,[],[f6382,f15930]) ).

tff(f15930,plain,
    ( spl250_881
  <=> ! [X2: nat,X0: fun_nat_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
        | ~ sP23(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_881])]) ).

tff(f6382,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
      | ~ sP23(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4470]) ).

tff(f15928,plain,
    spl250_880,
    inference(avatar_split_clause,[],[f6373,f15926]) ).

tff(f15926,plain,
    ( spl250_880
  <=> ! [X2: fun_int_bool,X0: int,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_880])]) ).

tff(f6373,plain,
    ! [X2: fun_int_bool,X0: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f4463]) ).

tff(f15924,plain,
    ( spl250_879
    | ~ spl250_74
    | ~ spl250_504 ),
    inference(avatar_split_clause,[],[f11312,f10716,f7643,f15922]) ).

tff(f15922,plain,
    ( spl250_879
  <=> ! [X0: nat,X1: nat] : sP18(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_879])]) ).

tff(f10716,plain,
    ( spl250_504
  <=> ! [X2: nat,X0: fun_nat_bool,X1: nat] :
        ( sP18(X0,X1,X2)
        | ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_504])]) ).

tff(f11312,plain,
    ( ! [X0: nat,X1: nat] : sP18(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0,X1)
    | ~ spl250_74
    | ~ spl250_504 ),
    inference(resolution,[],[f10717,f7644]) ).

tff(f10717,plain,
    ( ! [X2: nat,X0: fun_nat_bool,X1: nat] :
        ( ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
        | sP18(X0,X1,X2) )
    | ~ spl250_504 ),
    inference(avatar_component_clause,[],[f10716]) ).

tff(f15920,plain,
    spl250_878,
    inference(avatar_split_clause,[],[f6372,f15918]) ).

tff(f15918,plain,
    ( spl250_878
  <=> ! [X2: fun_int_bool,X0: int,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_878])]) ).

tff(f6372,plain,
    ! [X2: fun_int_bool,X0: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f4463]) ).

tff(f15916,plain,
    spl250_877,
    inference(avatar_split_clause,[],[f6368,f15914]) ).

tff(f15914,plain,
    ( spl250_877
  <=> ! [X2: int,X0: fun_int_bool,X1: fun_int_bool] :
        ( sP22(X0,X1,X2)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_877])]) ).

tff(f6368,plain,
    ! [X2: int,X0: fun_int_bool,X1: fun_int_bool] :
      ( sP22(X0,X1,X2)
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ),
    inference(cnf_transformation,[],[f4460]) ).

tff(f15912,plain,
    spl250_876,
    inference(avatar_split_clause,[],[f6365,f15910]) ).

tff(f15910,plain,
    ( spl250_876
  <=> ! [X2: int,X0: fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
        | ~ sP22(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_876])]) ).

tff(f6365,plain,
    ! [X2: int,X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
      | ~ sP22(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4460]) ).

tff(f15908,plain,
    spl250_875,
    inference(avatar_split_clause,[],[f6356,f15906]) ).

tff(f15906,plain,
    ( spl250_875
  <=> ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_875])]) ).

tff(f6356,plain,
    ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f4453]) ).

tff(f15904,plain,
    spl250_874,
    inference(avatar_split_clause,[],[f6355,f15902]) ).

tff(f15902,plain,
    ( spl250_874
  <=> ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_874])]) ).

tff(f6355,plain,
    ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f4453]) ).

tff(f15900,plain,
    spl250_873,
    inference(avatar_split_clause,[],[f6351,f15898]) ).

tff(f15898,plain,
    ( spl250_873
  <=> ! [X2: x_a,X0: fun_a_bool,X1: fun_a_bool] :
        ( sP21(X0,X1,X2)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_873])]) ).

tff(f6351,plain,
    ! [X2: x_a,X0: fun_a_bool,X1: fun_a_bool] :
      ( sP21(X0,X1,X2)
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ),
    inference(cnf_transformation,[],[f4450]) ).

tff(f4450,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool,X2: x_a] :
      ( ( sP21(X0,X1,X2)
        | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) )
        | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))),X0))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ) )
      & ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
            | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) )
          & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))),X0))
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ) )
        | ~ sP21(X0,X1,X2) ) ),
    inference(rectify,[],[f4449]) ).

tff(f4449,plain,
    ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
      ( ( sP21(X2,X0,X1)
        | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X2))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) )
        | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))),X2))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) ) )
      & ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X2))
            | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) )
          & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))),X2))
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) ) )
        | ~ sP21(X2,X0,X1) ) ),
    inference(flattening,[],[f4448]) ).

tff(f4448,plain,
    ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
      ( ( sP21(X2,X0,X1)
        | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X2))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) )
        | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))),X2))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) ) )
      & ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X2))
            | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) )
          & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))),X2))
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) ) )
        | ~ sP21(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f3725]) ).

tff(f3725,plain,
    ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
      ( sP21(X2,X0,X1)
    <=> ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X2))
          | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) )
        & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))),X2))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP21])]) ).

tff(f15896,plain,
    spl250_872,
    inference(avatar_split_clause,[],[f6348,f15894]) ).

tff(f15894,plain,
    ( spl250_872
  <=> ! [X2: x_a,X0: fun_a_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
        | ~ sP21(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_872])]) ).

tff(f6348,plain,
    ! [X2: x_a,X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
      | ~ sP21(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4450]) ).

tff(f15892,plain,
    spl250_871,
    inference(avatar_split_clause,[],[f6339,f15890]) ).

tff(f15890,plain,
    ( spl250_871
  <=> ! [X2: fun_pname_bool,X0: pname,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_871])]) ).

tff(f6339,plain,
    ! [X2: fun_pname_bool,X0: pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f4443]) ).

tff(f15888,plain,
    spl250_870,
    inference(avatar_split_clause,[],[f6338,f15886]) ).

tff(f15886,plain,
    ( spl250_870
  <=> ! [X2: fun_pname_bool,X0: pname,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_870])]) ).

tff(f6338,plain,
    ! [X2: fun_pname_bool,X0: pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f4443]) ).

tff(f15884,plain,
    spl250_869,
    inference(avatar_split_clause,[],[f6328,f15882]) ).

tff(f15882,plain,
    ( spl250_869
  <=> ! [X2: pname,X0: fun_pname_bool,X1: fun_pname_bool] :
        ( sP20(X0,X1,X2)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_869])]) ).

tff(f6328,plain,
    ! [X2: pname,X0: fun_pname_bool,X1: fun_pname_bool] :
      ( sP20(X0,X1,X2)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ),
    inference(cnf_transformation,[],[f4436]) ).

tff(f4436,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool,X2: pname] :
      ( ( sP20(X0,X1,X2)
        | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) )
        | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool))),X0))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ) )
      & ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
            | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) )
          & ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool))),X0))
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ) )
        | ~ sP20(X0,X1,X2) ) ),
    inference(rectify,[],[f4435]) ).

tff(f4435,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
      ( ( sP20(X2,X0,X1)
        | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X2))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) )
        | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool))),X2))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) ) )
      & ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X2))
            | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) )
          & ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool))),X2))
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) ) )
        | ~ sP20(X2,X0,X1) ) ),
    inference(flattening,[],[f4434]) ).

tff(f4434,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
      ( ( sP20(X2,X0,X1)
        | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X2))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) )
        | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool))),X2))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) ) )
      & ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X2))
            | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) )
          & ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool))),X2))
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) ) )
        | ~ sP20(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f3723]) ).

tff(f3723,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
      ( sP20(X2,X0,X1)
    <=> ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X2))
          | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool))),X2))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP20])]) ).

tff(f15877,plain,
    spl250_868,
    inference(avatar_split_clause,[],[f6325,f15875]) ).

tff(f15875,plain,
    ( spl250_868
  <=> ! [X2: pname,X0: fun_pname_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
        | ~ sP20(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_868])]) ).

tff(f6325,plain,
    ! [X2: pname,X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
      | ~ sP20(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4436]) ).

tff(f15873,plain,
    spl250_867,
    inference(avatar_split_clause,[],[f6304,f15871]) ).

tff(f15871,plain,
    ( spl250_867
  <=> ! [X2: fun_nat_bool,X0: fun_int_bool,X1: fun_nat_int] :
        ( ( image_nat_int(X1,sK245(X0,X1,X2)) = X0 )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_867])]) ).

tff(f6304,plain,
    ! [X2: fun_nat_bool,X0: fun_int_bool,X1: fun_nat_int] :
      ( ( image_nat_int(X1,sK245(X0,X1,X2)) = X0 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2))) ),
    inference(cnf_transformation,[],[f4420]) ).

tff(f15869,plain,
    spl250_866,
    inference(avatar_split_clause,[],[f6301,f15867]) ).

tff(f15867,plain,
    ( spl250_866
  <=> ! [X2: fun_nat_bool,X0: int,X1: fun_nat_int] :
        ( ( hAPP_nat_int(X1,sK244(X0,X1,X2)) = X0 )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_866])]) ).

tff(f6301,plain,
    ! [X2: fun_nat_bool,X0: int,X1: fun_nat_int] :
      ( ( hAPP_nat_int(X1,sK244(X0,X1,X2)) = X0 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ),
    inference(cnf_transformation,[],[f4416]) ).

tff(f15865,plain,
    spl250_865,
    inference(avatar_split_clause,[],[f6298,f15863]) ).

tff(f15863,plain,
    ( spl250_865
  <=> ! [X2: fun_pname_bool,X0: fun_a_bool,X1: fun_pname_a] :
        ( ( image_pname_a(X1,sK243(X0,X1,X2)) = X0 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_865])]) ).

tff(f6298,plain,
    ! [X2: fun_pname_bool,X0: fun_a_bool,X1: fun_pname_a] :
      ( ( image_pname_a(X1,sK243(X0,X1,X2)) = X0 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2))) ),
    inference(cnf_transformation,[],[f4412]) ).

tff(f15861,plain,
    spl250_864,
    inference(avatar_split_clause,[],[f6295,f15859]) ).

tff(f15859,plain,
    ( spl250_864
  <=> ! [X2: fun_pname_bool,X0: x_a,X1: fun_pname_a] :
        ( ( hAPP_pname_a(X1,sK242(X0,X1,X2)) = X0 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_864])]) ).

tff(f6295,plain,
    ! [X2: fun_pname_bool,X0: x_a,X1: fun_pname_a] :
      ( ( hAPP_pname_a(X1,sK242(X0,X1,X2)) = X0 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ),
    inference(cnf_transformation,[],[f4408]) ).

tff(f15857,plain,
    spl250_863,
    inference(avatar_split_clause,[],[f6221,f15855]) ).

tff(f15855,plain,
    ( spl250_863
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_863])]) ).

tff(f6221,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f3532]) ).

tff(f3532,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2)) ),
    inference(ennf_transformation,[],[f2432]) ).

tff(f2432,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(rectify,[],[f831]) ).

tff(f831,axiom,
    ! [X12: nat,X19: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X12),X19)),X11))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X19),X11)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_830_add__leD2) ).

tff(f15853,plain,
    spl250_862,
    inference(avatar_split_clause,[],[f6220,f15851]) ).

tff(f15851,plain,
    ( spl250_862
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_862])]) ).

tff(f6220,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f3531]) ).

tff(f3531,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2)) ),
    inference(ennf_transformation,[],[f2431]) ).

tff(f2431,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X2)) ),
    inference(rectify,[],[f832]) ).

tff(f832,axiom,
    ! [X12: nat,X19: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X12),X19)),X11))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X11)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_831_add__leD1) ).

tff(f15849,plain,
    spl250_861,
    inference(avatar_split_clause,[],[f6219,f15847]) ).

tff(f15847,plain,
    ( spl250_861
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_861])]) ).

tff(f6219,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2)) ),
    inference(cnf_transformation,[],[f3530]) ).

tff(f3530,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2)) ),
    inference(ennf_transformation,[],[f2430]) ).

tff(f2430,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2)) ),
    inference(rectify,[],[f885]) ).

tff(f885,axiom,
    ! [X20: nat,X21: nat,X19: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X20),X21)),X19))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X20),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_884_add__lessD1) ).

tff(f15845,plain,
    spl250_860,
    inference(avatar_split_clause,[],[f6215,f15843]) ).

tff(f15843,plain,
    ( spl250_860
  <=> ! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_860])]) ).

tff(f6215,plain,
    ! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2))) ),
    inference(cnf_transformation,[],[f3526]) ).

tff(f3526,plain,
    ! [X0: nat,X1: fun_nat_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2))) ),
    inference(ennf_transformation,[],[f2427]) ).

tff(f2427,plain,
    ! [X0: nat,X1: fun_nat_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2)))
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ),
    inference(rectify,[],[f718]) ).

tff(f718,axiom,
    ! [X29: nat,X2: fun_nat_bool,X7: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X7)))
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_717_DiffD1) ).

tff(f15841,plain,
    spl250_859,
    inference(avatar_split_clause,[],[f6214,f15839]) ).

tff(f15839,plain,
    ( spl250_859
  <=> ! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_859])]) ).

tff(f6214,plain,
    ! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2))) ),
    inference(cnf_transformation,[],[f3525]) ).

tff(f3525,plain,
    ! [X0: nat,X1: fun_nat_bool,X2: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2))) ),
    inference(ennf_transformation,[],[f2426]) ).

tff(f2426,plain,
    ! [X0: nat,X1: fun_nat_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2)))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X2)) ),
    inference(rectify,[],[f714]) ).

tff(f714,axiom,
    ! [X29: nat,X2: fun_nat_bool,X7: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X7)))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X29),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_713_DiffD2) ).

tff(f15645,plain,
    spl250_858,
    inference(avatar_split_clause,[],[f6210,f15643]) ).

tff(f15643,plain,
    ( spl250_858
  <=> ! [X2: fun_int_bool,X0: int,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_858])]) ).

tff(f6210,plain,
    ! [X2: fun_int_bool,X0: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X2))) ),
    inference(cnf_transformation,[],[f3521]) ).

tff(f3521,plain,
    ! [X0: int,X1: fun_int_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X2))) ),
    inference(ennf_transformation,[],[f2423]) ).

tff(f2423,plain,
    ! [X0: int,X1: fun_int_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X2)))
     => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ),
    inference(rectify,[],[f717]) ).

tff(f717,axiom,
    ! [X29: int,X2: fun_int_bool,X7: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X29),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X7)))
     => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X29),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_716_DiffD1) ).

tff(f15641,plain,
    spl250_857,
    inference(avatar_split_clause,[],[f6209,f15639]) ).

tff(f15639,plain,
    ( spl250_857
  <=> ! [X2: fun_int_bool,X0: int,X1: fun_int_bool] :
        ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_857])]) ).

tff(f6209,plain,
    ! [X2: fun_int_bool,X0: int,X1: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X2))) ),
    inference(cnf_transformation,[],[f3520]) ).

tff(f3520,plain,
    ! [X0: int,X1: fun_int_bool,X2: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X2))) ),
    inference(ennf_transformation,[],[f2422]) ).

tff(f2422,plain,
    ! [X0: int,X1: fun_int_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X2)))
     => ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X2)) ),
    inference(rectify,[],[f713]) ).

tff(f713,axiom,
    ! [X29: int,X2: fun_int_bool,X7: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X29),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X7)))
     => ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X29),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_712_DiffD2) ).

tff(f15637,plain,
    spl250_856,
    inference(avatar_split_clause,[],[f6205,f15635]) ).

tff(f15635,plain,
    ( spl250_856
  <=> ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_856])]) ).

tff(f6205,plain,
    ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X2))) ),
    inference(cnf_transformation,[],[f3516]) ).

tff(f3516,plain,
    ! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X2))) ),
    inference(ennf_transformation,[],[f2419]) ).

tff(f2419,plain,
    ! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X2)))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ),
    inference(rectify,[],[f719]) ).

tff(f719,axiom,
    ! [X29: x_a,X2: fun_a_bool,X7: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X29),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X7)))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X29),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_718_DiffD1) ).

tff(f15633,plain,
    spl250_855,
    inference(avatar_split_clause,[],[f6204,f15631]) ).

tff(f15631,plain,
    ( spl250_855
  <=> ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_855])]) ).

tff(f6204,plain,
    ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X2))) ),
    inference(cnf_transformation,[],[f3515]) ).

tff(f3515,plain,
    ! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X2))) ),
    inference(ennf_transformation,[],[f2418]) ).

tff(f2418,plain,
    ! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X2)))
     => ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X2)) ),
    inference(rectify,[],[f715]) ).

tff(f715,axiom,
    ! [X29: x_a,X2: fun_a_bool,X7: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X29),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X7)))
     => ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X29),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_714_DiffD2) ).

tff(f15629,plain,
    spl250_854,
    inference(avatar_split_clause,[],[f6200,f15627]) ).

tff(f15627,plain,
    ( spl250_854
  <=> ! [X2: fun_pname_bool,X0: pname,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_854])]) ).

tff(f6200,plain,
    ! [X2: fun_pname_bool,X0: pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2))) ),
    inference(cnf_transformation,[],[f3511]) ).

tff(f3511,plain,
    ! [X0: pname,X1: fun_pname_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2))) ),
    inference(ennf_transformation,[],[f2415]) ).

tff(f2415,plain,
    ! [X0: pname,X1: fun_pname_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2)))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ),
    inference(rectify,[],[f720]) ).

tff(f720,axiom,
    ! [X29: pname,X2: fun_pname_bool,X7: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X29),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X7)))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X29),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_719_DiffD1) ).

tff(f15625,plain,
    spl250_853,
    inference(avatar_split_clause,[],[f6199,f15623]) ).

tff(f15623,plain,
    ( spl250_853
  <=> ! [X2: fun_pname_bool,X0: pname,X1: fun_pname_bool] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_853])]) ).

tff(f6199,plain,
    ! [X2: fun_pname_bool,X0: pname,X1: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2))) ),
    inference(cnf_transformation,[],[f3510]) ).

tff(f3510,plain,
    ! [X0: pname,X1: fun_pname_bool,X2: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2))) ),
    inference(ennf_transformation,[],[f2414]) ).

tff(f2414,plain,
    ! [X0: pname,X1: fun_pname_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2)))
     => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X2)) ),
    inference(rectify,[],[f716]) ).

tff(f716,axiom,
    ! [X29: pname,X2: fun_pname_bool,X7: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X29),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X7)))
     => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X29),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_715_DiffD2) ).

tff(f15621,plain,
    spl250_852,
    inference(avatar_split_clause,[],[f6197,f15619]) ).

tff(f15619,plain,
    ( spl250_852
  <=> ! [X2: fun_nat_bool,X0: int,X1: fun_nat_int] :
        ( ( hAPP_nat_int(X1,sK224(X0,X1,X2)) = X0 )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_852])]) ).

tff(f6197,plain,
    ! [X2: fun_nat_bool,X0: int,X1: fun_nat_int] :
      ( ( hAPP_nat_int(X1,sK224(X0,X1,X2)) = X0 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),image_nat_int(X1,X2))) ),
    inference(cnf_transformation,[],[f4360]) ).

tff(f15617,plain,
    spl250_851,
    inference(avatar_split_clause,[],[f6195,f15615]) ).

tff(f15615,plain,
    ( spl250_851
  <=> ! [X2: fun_pname_bool,X0: x_a,X1: fun_pname_a] :
        ( ( hAPP_pname_a(X1,sK223(X0,X1,X2)) = X0 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_851])]) ).

tff(f6195,plain,
    ! [X2: fun_pname_bool,X0: x_a,X1: fun_pname_a] :
      ( ( hAPP_pname_a(X1,sK223(X0,X1,X2)) = X0 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),image_pname_a(X1,X2))) ),
    inference(cnf_transformation,[],[f4358]) ).

tff(f15613,plain,
    spl250_850,
    inference(avatar_split_clause,[],[f6159,f15611]) ).

tff(f15611,plain,
    ( spl250_850
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_850])]) ).

tff(f6159,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f3469]) ).

tff(f3469,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f2383]) ).

tff(f2383,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2))) ),
    inference(rectify,[],[f828]) ).

tff(f828,axiom,
    ! [X12: nat,X20: nat,X21: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X20),X21))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X20),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X12),X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_827_trans__le__add2) ).

tff(f15609,plain,
    spl250_849,
    inference(avatar_split_clause,[],[f6157,f15607]) ).

tff(f15607,plain,
    ( spl250_849
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_849])]) ).

tff(f6157,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f3467]) ).

tff(f3467,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f2381]) ).

tff(f2381,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0))) ),
    inference(rectify,[],[f855]) ).

tff(f855,axiom,
    ! [X95: nat,X15: nat,X16: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X16))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X16),X95))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_854_termination__basic__simps_I3_J) ).

tff(f15602,plain,
    spl250_848,
    inference(avatar_split_clause,[],[f6150,f15600]) ).

tff(f15600,plain,
    ( spl250_848
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)),X2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_848])]) ).

tff(f6150,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f3455]) ).

tff(f3455,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)),X2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f2374]) ).

tff(f2374,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X0)),X2)) ),
    inference(rectify,[],[f894]) ).

tff(f894,axiom,
    ! [X11: nat,X21: nat,X19: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X21),X19))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X21),X11)),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_893_less__imp__diff__less) ).

tff(f15598,plain,
    spl250_847,
    inference(avatar_split_clause,[],[f6147,f15596]) ).

tff(f15596,plain,
    ( spl250_847
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_847])]) ).

tff(f6147,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f3452]) ).

tff(f3452,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f2371]) ).

tff(f2371,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X0))) ),
    inference(rectify,[],[f886]) ).

tff(f886,axiom,
    ! [X95: nat,X15: nat,X16: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X16))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X16),X95))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_885_termination__basic__simps_I1_J) ).

tff(f15594,plain,
    spl250_846,
    inference(avatar_split_clause,[],[f6146,f15592]) ).

tff(f15592,plain,
    ( spl250_846
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_846])]) ).

tff(f6146,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f3451]) ).

tff(f3451,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f2370]) ).

tff(f2370,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2))) ),
    inference(rectify,[],[f887]) ).

tff(f887,axiom,
    ! [X16: nat,X15: nat,X95: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X95))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X16),X95))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_886_termination__basic__simps_I2_J) ).

tff(f15590,plain,
    spl250_845,
    inference(avatar_split_clause,[],[f6112,f15588]) ).

tff(f15588,plain,
    ( spl250_845
  <=> ! [X2: fun_nat_bool,X0: fun_nat_int,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X0,X1)),image_nat_int(X0,X2)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_845])]) ).

tff(f6112,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_int,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X0,X1)),image_nat_int(X0,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
    inference(cnf_transformation,[],[f3405]) ).

tff(f3405,plain,
    ! [X0: fun_nat_int,X1: fun_nat_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X0,X1)),image_nat_int(X0,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
    inference(ennf_transformation,[],[f2344]) ).

tff(f2344,plain,
    ! [X0: fun_nat_int,X1: fun_nat_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
     => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X0,X1)),image_nat_int(X0,X2))) ),
    inference(rectify,[],[f474]) ).

tff(f474,axiom,
    ! [X6: fun_nat_int,X2: fun_nat_bool,X7: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X7))
     => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X6,X2)),image_nat_int(X6,X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_image__mono) ).

tff(f15586,plain,
    spl250_844,
    inference(avatar_split_clause,[],[f6109,f15584]) ).

tff(f15584,plain,
    ( spl250_844
  <=> ! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_844])]) ).

tff(f6109,plain,
    ! [X2: fun_nat_bool,X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
    inference(cnf_transformation,[],[f3402]) ).

tff(f3402,plain,
    ! [X0: nat,X1: fun_nat_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
    inference(ennf_transformation,[],[f2341]) ).

tff(f2341,plain,
    ! [X0: nat,X1: fun_nat_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2))) ),
    inference(rectify,[],[f464]) ).

tff(f464,axiom,
    ! [X28: nat,X2: fun_nat_bool,X7: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X7))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X28),X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_463_subset__insertI2) ).

tff(f15582,plain,
    spl250_843,
    inference(avatar_split_clause,[],[f6104,f15580]) ).

tff(f15580,plain,
    ( spl250_843
  <=> ! [X2: fun_nat_bool,X0: fun_nat_int,X1: nat] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X0,X1)),image_nat_int(X0,X2)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_843])]) ).

tff(f6104,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_int,X1: nat] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X0,X1)),image_nat_int(X0,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f3395]) ).

tff(f3395,plain,
    ! [X0: fun_nat_int,X1: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X0,X1)),image_nat_int(X0,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f2336]) ).

tff(f2336,plain,
    ! [X0: fun_nat_int,X1: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
     => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X0,X1)),image_nat_int(X0,X2))) ),
    inference(rectify,[],[f434]) ).

tff(f434,axiom,
    ! [X6: fun_nat_int,X8: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X2))
     => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X6,X8)),image_nat_int(X6,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_433_imageI) ).

tff(f15578,plain,
    spl250_842,
    inference(avatar_split_clause,[],[f6103,f15576]) ).

tff(f15576,plain,
    ( spl250_842
  <=> ! [X2: fun_nat_bool,X0: nat,X1: nat] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_842])]) ).

tff(f6103,plain,
    ! [X2: fun_nat_bool,X0: nat,X1: nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f3394]) ).

tff(f3394,plain,
    ! [X0: nat,X1: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f2335]) ).

tff(f2335,plain,
    ! [X0: nat,X1: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X2))) ),
    inference(rectify,[],[f396]) ).

tff(f396,axiom,
    ! [X28: nat,X5: nat,X7: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5),X7))
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X28),X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_395_insertI2) ).

tff(f15574,plain,
    spl250_841,
    inference(avatar_split_clause,[],[f6089,f15572]) ).

tff(f15572,plain,
    ( spl250_841
  <=> ! [X2: fun_int_bool,X0: int,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2)))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_841])]) ).

tff(f6089,plain,
    ! [X2: fun_int_bool,X0: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ),
    inference(cnf_transformation,[],[f3371]) ).

tff(f3371,plain,
    ! [X0: int,X1: fun_int_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ),
    inference(ennf_transformation,[],[f2321]) ).

tff(f2321,plain,
    ! [X0: int,X1: fun_int_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
     => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2))) ),
    inference(rectify,[],[f463]) ).

tff(f463,axiom,
    ! [X28: int,X2: fun_int_bool,X7: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X7))
     => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X28),X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_462_subset__insertI2) ).

tff(f15570,plain,
    spl250_840,
    inference(avatar_split_clause,[],[f6085,f15568]) ).

tff(f15568,plain,
    ( spl250_840
  <=> ! [X2: fun_int_bool,X0: int,X1: int] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2)))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_840])]) ).

tff(f6085,plain,
    ! [X2: fun_int_bool,X0: int,X1: int] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
    inference(cnf_transformation,[],[f3365]) ).

tff(f3365,plain,
    ! [X0: int,X1: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
    inference(ennf_transformation,[],[f2317]) ).

tff(f2317,plain,
    ! [X0: int,X1: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
     => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X2))) ),
    inference(rectify,[],[f395]) ).

tff(f395,axiom,
    ! [X28: int,X5: int,X7: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5),X7))
     => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X28),X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_394_insertI2) ).

tff(f15566,plain,
    spl250_839,
    inference(avatar_split_clause,[],[f6072,f15564]) ).

tff(f15564,plain,
    ( spl250_839
  <=> ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_839])]) ).

tff(f6072,plain,
    ! [X2: fun_a_bool,X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
    inference(cnf_transformation,[],[f3343]) ).

tff(f3343,plain,
    ! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
    inference(ennf_transformation,[],[f2304]) ).

tff(f2304,plain,
    ! [X0: x_a,X1: fun_a_bool,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2))) ),
    inference(rectify,[],[f462]) ).

tff(f462,axiom,
    ! [X28: x_a,X2: fun_a_bool,X7: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X28),X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_461_subset__insertI2) ).

tff(f15562,plain,
    spl250_838,
    inference(avatar_split_clause,[],[f6068,f15560]) ).

tff(f15560,plain,
    ( spl250_838
  <=> ! [X2: fun_a_bool,X0: x_a,X1: x_a] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_838])]) ).

tff(f6068,plain,
    ! [X2: fun_a_bool,X0: x_a,X1: x_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
    inference(cnf_transformation,[],[f3337]) ).

tff(f3337,plain,
    ! [X0: x_a,X1: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
    inference(ennf_transformation,[],[f2300]) ).

tff(f2300,plain,
    ! [X0: x_a,X1: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X2))) ),
    inference(rectify,[],[f394]) ).

tff(f394,axiom,
    ! [X28: x_a,X5: x_a,X7: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5),X7))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X28),X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_393_insertI2) ).

tff(f15558,plain,
    spl250_837,
    inference(avatar_split_clause,[],[f6063,f15556]) ).

tff(f6063,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_a,X1: pname] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
    inference(cnf_transformation,[],[f3330]) ).

tff(f3330,plain,
    ! [X0: fun_pname_a,X1: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
    inference(ennf_transformation,[],[f2295]) ).

tff(f2295,plain,
    ! [X0: fun_pname_a,X1: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X0,X1)),image_pname_a(X0,X2))) ),
    inference(rectify,[],[f435]) ).

tff(f435,axiom,
    ! [X6: fun_pname_a,X8: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X2))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X6,X8)),image_pname_a(X6,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_434_imageI) ).

tff(f15554,plain,
    spl250_836,
    inference(avatar_split_clause,[],[f6062,f15552]) ).

tff(f15552,plain,
    ( spl250_836
  <=> ! [X2: fun_pname_bool,X0: pname,X1: pname] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X2)))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_836])]) ).

tff(f6062,plain,
    ! [X2: fun_pname_bool,X0: pname,X1: pname] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
    inference(cnf_transformation,[],[f3329]) ).

tff(f3329,plain,
    ! [X0: pname,X1: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
    inference(ennf_transformation,[],[f2294]) ).

tff(f2294,plain,
    ! [X0: pname,X1: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X2))) ),
    inference(rectify,[],[f397]) ).

tff(f397,axiom,
    ! [X28: pname,X5: pname,X7: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5),X7))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X28),X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_396_insertI2) ).

tff(f15550,plain,
    spl250_835,
    inference(avatar_split_clause,[],[f6057,f15548]) ).

tff(f15548,plain,
    ( spl250_835
  <=> ! [X2: fun_pname_bool,X0: fun_pname_a,X1: fun_pname_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X1)),image_pname_a(X0,X2)))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_835])]) ).

tff(f6057,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_a,X1: fun_pname_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X1)),image_pname_a(X0,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
    inference(cnf_transformation,[],[f3321]) ).

tff(f3321,plain,
    ! [X0: fun_pname_a,X1: fun_pname_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X1)),image_pname_a(X0,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
    inference(ennf_transformation,[],[f2289]) ).

tff(f2289,plain,
    ! [X0: fun_pname_a,X1: fun_pname_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X0,X1)),image_pname_a(X0,X2))) ),
    inference(rectify,[],[f475]) ).

tff(f475,axiom,
    ! [X6: fun_pname_a,X2: fun_pname_bool,X7: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X7))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X6,X2)),image_pname_a(X6,X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_474_image__mono) ).

tff(f15546,plain,
    spl250_834,
    inference(avatar_split_clause,[],[f5983,f15544]) ).

tff(f15544,plain,
    ( spl250_834
  <=> ! [X2: fun_nat_bool,X0: fun_int_bool,X1: fun_nat_int] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_834])]) ).

tff(f5983,plain,
    ! [X2: fun_nat_bool,X0: fun_int_bool,X1: fun_nat_int] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f3264]) ).

tff(f3264,plain,
    ! [X0: fun_int_bool,X1: fun_nat_int,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(flattening,[],[f3263]) ).

tff(f3263,plain,
    ! [X0: fun_int_bool,X1: fun_nat_int,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(ennf_transformation,[],[f2254]) ).

tff(f2254,plain,
    ! [X0: fun_int_bool,X1: fun_nat_int,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_nat_int(X1,X2)))
       => hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
    inference(rectify,[],[f219]) ).

tff(f219,axiom,
    ! [X7: fun_int_bool,X6: fun_nat_int,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X7),image_nat_int(X6,X2)))
       => hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_finite__surj) ).

tff(f15542,plain,
    spl250_833,
    inference(avatar_split_clause,[],[f5982,f15540]) ).

tff(f15540,plain,
    ( spl250_833
  <=> ! [X2: fun_nat_bool,X0: fun_a_bool,X1: fun_nat_a] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_nat_a(X1,X2)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_833])]) ).

tff(f5982,plain,
    ! [X2: fun_nat_bool,X0: fun_a_bool,X1: fun_nat_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_nat_a(X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f3262]) ).

tff(f3262,plain,
    ! [X0: fun_a_bool,X1: fun_nat_a,X2: fun_nat_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_nat_a(X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(flattening,[],[f3261]) ).

tff(f3261,plain,
    ! [X0: fun_a_bool,X1: fun_nat_a,X2: fun_nat_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_nat_a(X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(ennf_transformation,[],[f2253]) ).

tff(f2253,plain,
    ! [X0: fun_a_bool,X1: fun_nat_a,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_nat_a(X1,X2)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
    inference(rectify,[],[f191]) ).

tff(f191,axiom,
    ! [X7: fun_a_bool,X6: fun_nat_a,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),image_nat_a(X6,X2)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_finite__surj) ).

tff(f15538,plain,
    spl250_832,
    inference(avatar_split_clause,[],[f5981,f15536]) ).

tff(f15536,plain,
    ( spl250_832
  <=> ! [X2: fun_nat_bool,X0: fun_pname_bool,X1: fun_nat_pname] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_nat_pname(X1,X2)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_832])]) ).

tff(f5981,plain,
    ! [X2: fun_nat_bool,X0: fun_pname_bool,X1: fun_nat_pname] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_nat_pname(X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f3260]) ).

tff(f3260,plain,
    ! [X0: fun_pname_bool,X1: fun_nat_pname,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_nat_pname(X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(flattening,[],[f3259]) ).

tff(f3259,plain,
    ! [X0: fun_pname_bool,X1: fun_nat_pname,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_nat_pname(X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(ennf_transformation,[],[f2252]) ).

tff(f2252,plain,
    ! [X0: fun_pname_bool,X1: fun_nat_pname,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_nat_pname(X1,X2)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
    inference(rectify,[],[f196]) ).

tff(f196,axiom,
    ! [X7: fun_pname_bool,X6: fun_nat_pname,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X7),image_nat_pname(X6,X2)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_finite__surj) ).

tff(f15534,plain,
    spl250_831,
    inference(avatar_split_clause,[],[f5980,f15532]) ).

tff(f15532,plain,
    ( spl250_831
  <=> ! [X2: fun_nat_bool,X0: fun_fu1430349052l_bool,X1: fun_na936072029e_bool] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_1655916159e_bool(X1,X2)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_831])]) ).

tff(f5980,plain,
    ! [X2: fun_nat_bool,X0: fun_fu1430349052l_bool,X1: fun_na936072029e_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_1655916159e_bool(X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f3258]) ).

tff(f3258,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_na936072029e_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_1655916159e_bool(X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(flattening,[],[f3257]) ).

tff(f3257,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_na936072029e_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_1655916159e_bool(X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(ennf_transformation,[],[f2251]) ).

tff(f2251,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_na936072029e_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_1655916159e_bool(X1,X2)))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ) ),
    inference(rectify,[],[f194]) ).

tff(f194,axiom,
    ! [X7: fun_fu1430349052l_bool,X6: fun_na936072029e_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X7),image_1655916159e_bool(X6,X2)))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_finite__surj) ).

tff(f15530,plain,
    spl250_830,
    inference(avatar_split_clause,[],[f5979,f15528]) ).

tff(f15528,plain,
    ( spl250_830
  <=> ! [X2: fun_nat_bool,X0: fun_fun_a_bool_bool,X1: fun_nat_fun_a_bool] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_nat_fun_a_bool(X1,X2)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_830])]) ).

tff(f5979,plain,
    ! [X2: fun_nat_bool,X0: fun_fun_a_bool_bool,X1: fun_nat_fun_a_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_nat_fun_a_bool(X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f3256]) ).

tff(f3256,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_nat_fun_a_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_nat_fun_a_bool(X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(flattening,[],[f3255]) ).

tff(f3255,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_nat_fun_a_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_nat_fun_a_bool(X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(ennf_transformation,[],[f2250]) ).

tff(f2250,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_nat_fun_a_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_nat_fun_a_bool(X1,X2)))
       => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ) ),
    inference(rectify,[],[f195]) ).

tff(f195,axiom,
    ! [X7: fun_fun_a_bool_bool,X6: fun_nat_fun_a_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X7),image_nat_fun_a_bool(X6,X2)))
       => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_finite__surj) ).

tff(f15526,plain,
    spl250_829,
    inference(avatar_split_clause,[],[f5978,f15524]) ).

tff(f15524,plain,
    ( spl250_829
  <=> ! [X2: fun_nat_bool,X0: fun_fu819804446l_bool,X1: fun_nat_fun_int_bool] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_1556378401t_bool(X1,X2)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_829])]) ).

tff(f5978,plain,
    ! [X2: fun_nat_bool,X0: fun_fu819804446l_bool,X1: fun_nat_fun_int_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_1556378401t_bool(X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f3254]) ).

tff(f3254,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_nat_fun_int_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_1556378401t_bool(X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(flattening,[],[f3253]) ).

tff(f3253,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_nat_fun_int_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_1556378401t_bool(X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(ennf_transformation,[],[f2249]) ).

tff(f2249,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_nat_fun_int_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_1556378401t_bool(X1,X2)))
       => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0)) ) ),
    inference(rectify,[],[f192]) ).

tff(f192,axiom,
    ! [X7: fun_fu819804446l_bool,X6: fun_nat_fun_int_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X7),image_1556378401t_bool(X6,X2)))
       => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_finite__surj) ).

tff(f15522,plain,
    spl250_828,
    inference(avatar_split_clause,[],[f5977,f15520]) ).

tff(f15520,plain,
    ( spl250_828
  <=> ! [X2: fun_nat_bool,X0: fun_fu425979586l_bool,X1: fun_nat_fun_nat_bool] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_26036933t_bool(X1,X2)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_828])]) ).

tff(f5977,plain,
    ! [X2: fun_nat_bool,X0: fun_fu425979586l_bool,X1: fun_nat_fun_nat_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_26036933t_bool(X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(cnf_transformation,[],[f3252]) ).

tff(f3252,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_fun_nat_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_26036933t_bool(X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(flattening,[],[f3251]) ).

tff(f3251,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_fun_nat_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_26036933t_bool(X1,X2)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    inference(ennf_transformation,[],[f2248]) ).

tff(f2248,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_fun_nat_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_26036933t_bool(X1,X2)))
       => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ) ),
    inference(rectify,[],[f193]) ).

tff(f193,axiom,
    ! [X7: fun_fu425979586l_bool,X6: fun_nat_fun_nat_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X7),image_26036933t_bool(X6,X2)))
       => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_finite__surj) ).

tff(f15518,plain,
    spl250_827,
    inference(avatar_split_clause,[],[f5948,f15516]) ).

tff(f15516,plain,
    ( spl250_827
  <=> ! [X2: fun_int_bool,X0: fun_a_bool,X1: fun_int_a] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_int_a(X1,X2)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_827])]) ).

tff(f5948,plain,
    ! [X2: fun_int_bool,X0: fun_a_bool,X1: fun_int_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_int_a(X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f3232]) ).

tff(f3232,plain,
    ! [X0: fun_a_bool,X1: fun_int_a,X2: fun_int_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_int_a(X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(flattening,[],[f3231]) ).

tff(f3231,plain,
    ! [X0: fun_a_bool,X1: fun_int_a,X2: fun_int_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_int_a(X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(ennf_transformation,[],[f2238]) ).

tff(f2238,plain,
    ! [X0: fun_a_bool,X1: fun_int_a,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_int_a(X1,X2)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
    inference(rectify,[],[f197]) ).

tff(f197,axiom,
    ! [X7: fun_a_bool,X6: fun_int_a,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),image_int_a(X6,X2)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_finite__surj) ).

tff(f15514,plain,
    spl250_826,
    inference(avatar_split_clause,[],[f5947,f15512]) ).

tff(f15512,plain,
    ( spl250_826
  <=> ! [X2: fun_int_bool,X0: fun_pname_bool,X1: fun_int_pname] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_int_pname(X1,X2)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_826])]) ).

tff(f5947,plain,
    ! [X2: fun_int_bool,X0: fun_pname_bool,X1: fun_int_pname] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_int_pname(X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f3230]) ).

tff(f3230,plain,
    ! [X0: fun_pname_bool,X1: fun_int_pname,X2: fun_int_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_int_pname(X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(flattening,[],[f3229]) ).

tff(f3229,plain,
    ! [X0: fun_pname_bool,X1: fun_int_pname,X2: fun_int_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_int_pname(X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(ennf_transformation,[],[f2237]) ).

tff(f2237,plain,
    ! [X0: fun_pname_bool,X1: fun_int_pname,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_int_pname(X1,X2)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
    inference(rectify,[],[f202]) ).

tff(f202,axiom,
    ! [X7: fun_pname_bool,X6: fun_int_pname,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X7),image_int_pname(X6,X2)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_finite__surj) ).

tff(f15510,plain,
    spl250_825,
    inference(avatar_split_clause,[],[f5946,f15508]) ).

tff(f15508,plain,
    ( spl250_825
  <=> ! [X2: fun_int_bool,X0: fun_fun_a_bool_bool,X1: fun_int_fun_a_bool] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_int_fun_a_bool(X1,X2)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_825])]) ).

tff(f5946,plain,
    ! [X2: fun_int_bool,X0: fun_fun_a_bool_bool,X1: fun_int_fun_a_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_int_fun_a_bool(X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f3228]) ).

tff(f3228,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_int_fun_a_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_int_fun_a_bool(X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(flattening,[],[f3227]) ).

tff(f3227,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_int_fun_a_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_int_fun_a_bool(X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(ennf_transformation,[],[f2236]) ).

tff(f2236,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_int_fun_a_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_int_fun_a_bool(X1,X2)))
       => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ) ),
    inference(rectify,[],[f201]) ).

tff(f201,axiom,
    ! [X7: fun_fun_a_bool_bool,X6: fun_int_fun_a_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X7),image_int_fun_a_bool(X6,X2)))
       => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_finite__surj) ).

tff(f15506,plain,
    spl250_824,
    inference(avatar_split_clause,[],[f5945,f15504]) ).

tff(f15504,plain,
    ( spl250_824
  <=> ! [X2: fun_int_bool,X0: fun_fu1430349052l_bool,X1: fun_in2065004473e_bool] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_637364955e_bool(X1,X2)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_824])]) ).

tff(f5945,plain,
    ! [X2: fun_int_bool,X0: fun_fu1430349052l_bool,X1: fun_in2065004473e_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_637364955e_bool(X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f3226]) ).

tff(f3226,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_in2065004473e_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_637364955e_bool(X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(flattening,[],[f3225]) ).

tff(f3225,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_in2065004473e_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_637364955e_bool(X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(ennf_transformation,[],[f2235]) ).

tff(f2235,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_in2065004473e_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_637364955e_bool(X1,X2)))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ) ),
    inference(rectify,[],[f200]) ).

tff(f200,axiom,
    ! [X7: fun_fu1430349052l_bool,X6: fun_in2065004473e_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X7),image_637364955e_bool(X6,X2)))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_finite__surj) ).

tff(f15502,plain,
    spl250_823,
    inference(avatar_split_clause,[],[f5944,f15500]) ).

tff(f15500,plain,
    ( spl250_823
  <=> ! [X2: fun_int_bool,X0: fun_fu819804446l_bool,X1: fun_int_fun_int_bool] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_275383677t_bool(X1,X2)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_823])]) ).

tff(f5944,plain,
    ! [X2: fun_int_bool,X0: fun_fu819804446l_bool,X1: fun_int_fun_int_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_275383677t_bool(X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f3224]) ).

tff(f3224,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_fun_int_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_275383677t_bool(X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(flattening,[],[f3223]) ).

tff(f3223,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_fun_int_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_275383677t_bool(X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(ennf_transformation,[],[f2234]) ).

tff(f2234,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_fun_int_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_275383677t_bool(X1,X2)))
       => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0)) ) ),
    inference(rectify,[],[f198]) ).

tff(f198,axiom,
    ! [X7: fun_fu819804446l_bool,X6: fun_int_fun_int_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X7),image_275383677t_bool(X6,X2)))
       => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_finite__surj) ).

tff(f15498,plain,
    spl250_822,
    inference(avatar_split_clause,[],[f5943,f15496]) ).

tff(f15496,plain,
    ( spl250_822
  <=> ! [X2: fun_int_bool,X0: fun_fu425979586l_bool,X1: fun_int_fun_nat_bool] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_892525857t_bool(X1,X2)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_822])]) ).

tff(f5943,plain,
    ! [X2: fun_int_bool,X0: fun_fu425979586l_bool,X1: fun_int_fun_nat_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_892525857t_bool(X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(cnf_transformation,[],[f3222]) ).

tff(f3222,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_int_fun_nat_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_892525857t_bool(X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(flattening,[],[f3221]) ).

tff(f3221,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_int_fun_nat_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_892525857t_bool(X1,X2)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    inference(ennf_transformation,[],[f2233]) ).

tff(f2233,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_int_fun_nat_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_892525857t_bool(X1,X2)))
       => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ) ),
    inference(rectify,[],[f199]) ).

tff(f199,axiom,
    ! [X7: fun_fu425979586l_bool,X6: fun_int_fun_nat_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X7),image_892525857t_bool(X6,X2)))
       => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_finite__surj) ).

tff(f15494,plain,
    spl250_821,
    inference(avatar_split_clause,[],[f5935,f15492]) ).

tff(f15492,plain,
    ( spl250_821
  <=> ! [X2: fun_a_bool,X0: fun_nat_bool,X1: fun_a_nat] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_a_nat(X1,X2)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_821])]) ).

tff(f5935,plain,
    ! [X2: fun_a_bool,X0: fun_nat_bool,X1: fun_a_nat] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_a_nat(X1,X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f3216]) ).

tff(f3216,plain,
    ! [X0: fun_nat_bool,X1: fun_a_nat,X2: fun_a_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_a_nat(X1,X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(flattening,[],[f3215]) ).

tff(f3215,plain,
    ! [X0: fun_nat_bool,X1: fun_a_nat,X2: fun_a_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_a_nat(X1,X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(ennf_transformation,[],[f2230]) ).

tff(f2230,plain,
    ! [X0: fun_nat_bool,X1: fun_a_nat,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_a_nat(X1,X2)))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    inference(rectify,[],[f208]) ).

tff(f208,axiom,
    ! [X7: fun_nat_bool,X6: fun_a_nat,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7),image_a_nat(X6,X2)))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_finite__surj) ).

tff(f15490,plain,
    spl250_820,
    inference(avatar_split_clause,[],[f5934,f15488]) ).

tff(f15488,plain,
    ( spl250_820
  <=> ! [X2: fun_a_bool,X0: fun_int_bool,X1: fun_a_int] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_a_int(X1,X2)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_820])]) ).

tff(f5934,plain,
    ! [X2: fun_a_bool,X0: fun_int_bool,X1: fun_a_int] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_a_int(X1,X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f3214]) ).

tff(f3214,plain,
    ! [X0: fun_int_bool,X1: fun_a_int,X2: fun_a_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_a_int(X1,X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(flattening,[],[f3213]) ).

tff(f3213,plain,
    ! [X0: fun_int_bool,X1: fun_a_int,X2: fun_a_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_a_int(X1,X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(ennf_transformation,[],[f2229]) ).

tff(f2229,plain,
    ! [X0: fun_int_bool,X1: fun_a_int,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_a_int(X1,X2)))
       => hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
    inference(rectify,[],[f213]) ).

tff(f213,axiom,
    ! [X7: fun_int_bool,X6: fun_a_int,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X7),image_a_int(X6,X2)))
       => hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_finite__surj) ).

tff(f15486,plain,
    spl250_819,
    inference(avatar_split_clause,[],[f5909,f15484]) ).

tff(f15484,plain,
    ( spl250_819
  <=> ! [X2: fun_a_bool,X0: fun_a_bool,X1: fun_a_a] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_a_a(X1,X2)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_819])]) ).

tff(f5909,plain,
    ! [X2: fun_a_bool,X0: fun_a_bool,X1: fun_a_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_a_a(X1,X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f3196]) ).

tff(f3196,plain,
    ! [X0: fun_a_bool,X1: fun_a_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_a_a(X1,X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(flattening,[],[f3195]) ).

tff(f3195,plain,
    ! [X0: fun_a_bool,X1: fun_a_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_a_a(X1,X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(ennf_transformation,[],[f2220]) ).

tff(f2220,plain,
    ! [X0: fun_a_bool,X1: fun_a_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_a_a(X1,X2)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
    inference(rectify,[],[f181]) ).

tff(f181,axiom,
    ! [X7: fun_a_bool,X6: fun_a_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),image_a_a(X6,X2)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_finite__surj) ).

tff(f15482,plain,
    spl250_818,
    inference(avatar_split_clause,[],[f5908,f15480]) ).

tff(f15480,plain,
    ( spl250_818
  <=> ! [X2: fun_a_bool,X0: fun_pname_bool,X1: fun_a_pname] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_a_pname(X1,X2)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_818])]) ).

tff(f5908,plain,
    ! [X2: fun_a_bool,X0: fun_pname_bool,X1: fun_a_pname] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_a_pname(X1,X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(cnf_transformation,[],[f3194]) ).

tff(f3194,plain,
    ! [X0: fun_pname_bool,X1: fun_a_pname,X2: fun_a_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_a_pname(X1,X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(flattening,[],[f3193]) ).

tff(f3193,plain,
    ! [X0: fun_pname_bool,X1: fun_a_pname,X2: fun_a_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_a_pname(X1,X2)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    inference(ennf_transformation,[],[f2219]) ).

tff(f2219,plain,
    ! [X0: fun_pname_bool,X1: fun_a_pname,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_a_pname(X1,X2)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
    inference(rectify,[],[f203]) ).

tff(f203,axiom,
    ! [X7: fun_pname_bool,X6: fun_a_pname,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X7),image_a_pname(X6,X2)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_finite__surj) ).

tff(f15478,plain,
    spl250_817,
    inference(avatar_split_clause,[],[f5900,f15476]) ).

tff(f5900,plain,
    ! [X2: fun_pname_bool,X0: fun_a_bool,X1: fun_pname_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f3188]) ).

tff(f3188,plain,
    ! [X0: fun_a_bool,X1: fun_pname_a,X2: fun_pname_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(flattening,[],[f3187]) ).

tff(f3187,plain,
    ! [X0: fun_a_bool,X1: fun_pname_a,X2: fun_pname_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(ennf_transformation,[],[f2216]) ).

tff(f2216,plain,
    ! [X0: fun_a_bool,X1: fun_pname_a,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_pname_a(X1,X2)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
    inference(rectify,[],[f218]) ).

tff(f218,axiom,
    ! [X7: fun_a_bool,X6: fun_pname_a,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),image_pname_a(X6,X2)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_finite__surj) ).

tff(f15474,plain,
    spl250_816,
    inference(avatar_split_clause,[],[f5875,f15472]) ).

tff(f15472,plain,
    ( spl250_816
  <=> ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: fun_pname_pname] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_pname_pname(X1,X2)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_816])]) ).

tff(f5875,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: fun_pname_pname] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_pname_pname(X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f3170]) ).

tff(f3170,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_pname_pname(X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(flattening,[],[f3169]) ).

tff(f3169,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_pname_pname(X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(ennf_transformation,[],[f2207]) ).

tff(f2207,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_pname_pname(X1,X2)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
    inference(rectify,[],[f190]) ).

tff(f190,axiom,
    ! [X7: fun_pname_bool,X6: fun_pname_pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X7),image_pname_pname(X6,X2)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_finite__surj) ).

tff(f15470,plain,
    spl250_815,
    inference(avatar_split_clause,[],[f5874,f15468]) ).

tff(f15468,plain,
    ( spl250_815
  <=> ! [X2: fun_pname_bool,X0: fun_fun_a_bool_bool,X1: fun_pname_fun_a_bool] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_112932426a_bool(X1,X2)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_815])]) ).

tff(f5874,plain,
    ! [X2: fun_pname_bool,X0: fun_fun_a_bool_bool,X1: fun_pname_fun_a_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_112932426a_bool(X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f3168]) ).

tff(f3168,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_pname_fun_a_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_112932426a_bool(X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(flattening,[],[f3167]) ).

tff(f3167,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_pname_fun_a_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_112932426a_bool(X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(ennf_transformation,[],[f2206]) ).

tff(f2206,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_pname_fun_a_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),image_112932426a_bool(X1,X2)))
       => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ) ),
    inference(rectify,[],[f189]) ).

tff(f189,axiom,
    ! [X7: fun_fun_a_bool_bool,X6: fun_pname_fun_a_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X7),image_112932426a_bool(X6,X2)))
       => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_finite__surj) ).

tff(f15466,plain,
    spl250_814,
    inference(avatar_split_clause,[],[f5873,f15464]) ).

tff(f15464,plain,
    ( spl250_814
  <=> ! [X2: fun_pname_bool,X0: fun_fu819804446l_bool,X1: fun_pn665169337t_bool] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_1512837979t_bool(X1,X2)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_814])]) ).

tff(f5873,plain,
    ! [X2: fun_pname_bool,X0: fun_fu819804446l_bool,X1: fun_pn665169337t_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_1512837979t_bool(X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f3166]) ).

tff(f3166,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_pn665169337t_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_1512837979t_bool(X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(flattening,[],[f3165]) ).

tff(f3165,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_pn665169337t_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_1512837979t_bool(X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(ennf_transformation,[],[f2205]) ).

tff(f2205,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_pn665169337t_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),image_1512837979t_bool(X1,X2)))
       => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0)) ) ),
    inference(rectify,[],[f186]) ).

tff(f186,axiom,
    ! [X7: fun_fu819804446l_bool,X6: fun_pn665169337t_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X7),image_1512837979t_bool(X6,X2)))
       => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_finite__surj) ).

tff(f15462,plain,
    spl250_813,
    inference(avatar_split_clause,[],[f5872,f15460]) ).

tff(f15460,plain,
    ( spl250_813
  <=> ! [X2: fun_pname_bool,X0: fun_fu425979586l_bool,X1: fun_pn406123357t_bool] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_2129980159t_bool(X1,X2)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_813])]) ).

tff(f5872,plain,
    ! [X2: fun_pname_bool,X0: fun_fu425979586l_bool,X1: fun_pn406123357t_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_2129980159t_bool(X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f3164]) ).

tff(f3164,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_pn406123357t_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_2129980159t_bool(X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(flattening,[],[f3163]) ).

tff(f3163,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_pn406123357t_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_2129980159t_bool(X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(ennf_transformation,[],[f2204]) ).

tff(f2204,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_pn406123357t_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),image_2129980159t_bool(X1,X2)))
       => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ) ),
    inference(rectify,[],[f187]) ).

tff(f187,axiom,
    ! [X7: fun_fu425979586l_bool,X6: fun_pn406123357t_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X7),image_2129980159t_bool(X6,X2)))
       => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_finite__surj) ).

tff(f15458,plain,
    spl250_812,
    inference(avatar_split_clause,[],[f5871,f15456]) ).

tff(f15456,plain,
    ( spl250_812
  <=> ! [X2: fun_pname_bool,X0: fun_fu1430349052l_bool,X1: fun_pn800050071e_bool] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_47868345e_bool(X1,X2)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_812])]) ).

tff(f5871,plain,
    ! [X2: fun_pname_bool,X0: fun_fu1430349052l_bool,X1: fun_pn800050071e_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_47868345e_bool(X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(cnf_transformation,[],[f3162]) ).

tff(f3162,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pn800050071e_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_47868345e_bool(X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(flattening,[],[f3161]) ).

tff(f3161,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pn800050071e_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_47868345e_bool(X1,X2)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    inference(ennf_transformation,[],[f2203]) ).

tff(f2203,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pn800050071e_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),image_47868345e_bool(X1,X2)))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ) ),
    inference(rectify,[],[f188]) ).

tff(f188,axiom,
    ! [X7: fun_fu1430349052l_bool,X6: fun_pn800050071e_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X7),image_47868345e_bool(X6,X2)))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_finite__surj) ).

tff(f15454,plain,
    spl250_811,
    inference(avatar_split_clause,[],[f5863,f15452]) ).

tff(f15452,plain,
    ( spl250_811
  <=> ! [X2: fun_fu425979586l_bool,X0: fun_nat_bool,X1: fun_fun_nat_bool_nat] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_496248727ol_nat(X1,X2)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_811])]) ).

tff(f5863,plain,
    ! [X2: fun_fu425979586l_bool,X0: fun_nat_bool,X1: fun_fun_nat_bool_nat] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_496248727ol_nat(X1,X2)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(cnf_transformation,[],[f3156]) ).

tff(f3156,plain,
    ! [X0: fun_nat_bool,X1: fun_fun_nat_bool_nat,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_496248727ol_nat(X1,X2)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(flattening,[],[f3155]) ).

tff(f3155,plain,
    ! [X0: fun_nat_bool,X1: fun_fun_nat_bool_nat,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_496248727ol_nat(X1,X2)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(ennf_transformation,[],[f2200]) ).

tff(f2200,plain,
    ! [X0: fun_nat_bool,X1: fun_fun_nat_bool_nat,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_496248727ol_nat(X1,X2)))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    inference(rectify,[],[f210]) ).

tff(f210,axiom,
    ! [X7: fun_nat_bool,X6: fun_fun_nat_bool_nat,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7),image_496248727ol_nat(X6,X2)))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_finite__surj) ).

tff(f15450,plain,
    spl250_810,
    inference(avatar_split_clause,[],[f5862,f15448]) ).

tff(f15448,plain,
    ( spl250_810
  <=> ! [X2: fun_fun_a_bool_bool,X0: fun_nat_bool,X1: fun_fun_a_bool_nat] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_fun_a_bool_nat(X1,X2)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_810])]) ).

tff(f5862,plain,
    ! [X2: fun_fun_a_bool_bool,X0: fun_nat_bool,X1: fun_fun_a_bool_nat] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_fun_a_bool_nat(X1,X2)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(cnf_transformation,[],[f3154]) ).

tff(f3154,plain,
    ! [X0: fun_nat_bool,X1: fun_fun_a_bool_nat,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_fun_a_bool_nat(X1,X2)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(flattening,[],[f3153]) ).

tff(f3153,plain,
    ! [X0: fun_nat_bool,X1: fun_fun_a_bool_nat,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_fun_a_bool_nat(X1,X2)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(ennf_transformation,[],[f2199]) ).

tff(f2199,plain,
    ! [X0: fun_nat_bool,X1: fun_fun_a_bool_nat,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_fun_a_bool_nat(X1,X2)))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    inference(rectify,[],[f212]) ).

tff(f212,axiom,
    ! [X7: fun_nat_bool,X6: fun_fun_a_bool_nat,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7),image_fun_a_bool_nat(X6,X2)))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_finite__surj) ).

tff(f15446,plain,
    spl250_809,
    inference(avatar_split_clause,[],[f5861,f15444]) ).

tff(f15444,plain,
    ( spl250_809
  <=> ! [X2: fun_fu1430349052l_bool,X0: fun_nat_bool,X1: fun_fu1668467777ol_nat] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_1551609309ol_nat(X1,X2)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_809])]) ).

tff(f5861,plain,
    ! [X2: fun_fu1430349052l_bool,X0: fun_nat_bool,X1: fun_fu1668467777ol_nat] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_1551609309ol_nat(X1,X2)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(cnf_transformation,[],[f3152]) ).

tff(f3152,plain,
    ! [X0: fun_nat_bool,X1: fun_fu1668467777ol_nat,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_1551609309ol_nat(X1,X2)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(flattening,[],[f3151]) ).

tff(f3151,plain,
    ! [X0: fun_nat_bool,X1: fun_fu1668467777ol_nat,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_1551609309ol_nat(X1,X2)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(ennf_transformation,[],[f2198]) ).

tff(f2198,plain,
    ! [X0: fun_nat_bool,X1: fun_fu1668467777ol_nat,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_1551609309ol_nat(X1,X2)))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    inference(rectify,[],[f211]) ).

tff(f211,axiom,
    ! [X7: fun_nat_bool,X6: fun_fu1668467777ol_nat,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7),image_1551609309ol_nat(X6,X2)))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_finite__surj) ).

tff(f15442,plain,
    ( spl250_808
    | ~ spl250_48
    | ~ spl250_721 ),
    inference(avatar_split_clause,[],[f14869,f14231,f7532,f15440]) ).

tff(f15440,plain,
    ( spl250_808
  <=> ! [X0: fun_nat_bool] : ~ sP11(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_808])]) ).

tff(f7532,plain,
    ( spl250_48
  <=> ! [X0: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_48])]) ).

tff(f14231,plain,
    ( spl250_721
  <=> ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
        ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK189(X0,X1)),sK190(X0,X1))))
        | ~ sP11(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_721])]) ).

tff(f14869,plain,
    ( ! [X0: fun_nat_bool] : ~ sP11(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X0)
    | ~ spl250_48
    | ~ spl250_721 ),
    inference(resolution,[],[f14232,f7533]) ).

tff(f7533,plain,
    ( ! [X0: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X0))
    | ~ spl250_48 ),
    inference(avatar_component_clause,[],[f7532]) ).

tff(f14232,plain,
    ( ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
        ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK189(X0,X1)),sK190(X0,X1))))
        | ~ sP11(X0,X1) )
    | ~ spl250_721 ),
    inference(avatar_component_clause,[],[f14231]) ).

tff(f15438,plain,
    spl250_807,
    inference(avatar_split_clause,[],[f5860,f15436]) ).

tff(f15436,plain,
    ( spl250_807
  <=> ! [X2: fun_fu819804446l_bool,X0: fun_nat_bool,X1: fun_fun_int_bool_nat] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_1431733819ol_nat(X1,X2)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_807])]) ).

tff(f5860,plain,
    ! [X2: fun_fu819804446l_bool,X0: fun_nat_bool,X1: fun_fun_int_bool_nat] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_1431733819ol_nat(X1,X2)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(cnf_transformation,[],[f3150]) ).

tff(f3150,plain,
    ! [X0: fun_nat_bool,X1: fun_fun_int_bool_nat,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_1431733819ol_nat(X1,X2)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(flattening,[],[f3149]) ).

tff(f3149,plain,
    ! [X0: fun_nat_bool,X1: fun_fun_int_bool_nat,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_1431733819ol_nat(X1,X2)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(ennf_transformation,[],[f2197]) ).

tff(f2197,plain,
    ! [X0: fun_nat_bool,X1: fun_fun_int_bool_nat,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),image_1431733819ol_nat(X1,X2)))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    inference(rectify,[],[f209]) ).

tff(f209,axiom,
    ! [X7: fun_nat_bool,X6: fun_fun_int_bool_nat,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7),image_1431733819ol_nat(X6,X2)))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_finite__surj) ).

tff(f15434,plain,
    spl250_806,
    inference(avatar_split_clause,[],[f5859,f15432]) ).

tff(f15432,plain,
    ( spl250_806
  <=> ! [X2: fun_fu1430349052l_bool,X0: fun_int_bool,X1: fun_fu1830380701ol_int] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_41399353ol_int(X1,X2)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_806])]) ).

tff(f5859,plain,
    ! [X2: fun_fu1430349052l_bool,X0: fun_int_bool,X1: fun_fu1830380701ol_int] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_41399353ol_int(X1,X2)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(cnf_transformation,[],[f3148]) ).

tff(f3148,plain,
    ! [X0: fun_int_bool,X1: fun_fu1830380701ol_int,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_41399353ol_int(X1,X2)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(flattening,[],[f3147]) ).

tff(f3147,plain,
    ! [X0: fun_int_bool,X1: fun_fu1830380701ol_int,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_41399353ol_int(X1,X2)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(ennf_transformation,[],[f2196]) ).

tff(f2196,plain,
    ! [X0: fun_int_bool,X1: fun_fu1830380701ol_int,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_41399353ol_int(X1,X2)))
       => hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
    inference(rectify,[],[f216]) ).

tff(f216,axiom,
    ! [X7: fun_int_bool,X6: fun_fu1830380701ol_int,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X7),image_41399353ol_int(X6,X2)))
       => hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_finite__surj) ).

tff(f15430,plain,
    spl250_805,
    inference(avatar_split_clause,[],[f5858,f15428]) ).

tff(f15428,plain,
    ( spl250_805
  <=> ! [X2: fun_fu819804446l_bool,X0: fun_int_bool,X1: fun_fun_int_bool_int] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_2069007511ol_int(X1,X2)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_805])]) ).

tff(f5858,plain,
    ! [X2: fun_fu819804446l_bool,X0: fun_int_bool,X1: fun_fun_int_bool_int] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_2069007511ol_int(X1,X2)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(cnf_transformation,[],[f3146]) ).

tff(f3146,plain,
    ! [X0: fun_int_bool,X1: fun_fun_int_bool_int,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_2069007511ol_int(X1,X2)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(flattening,[],[f3145]) ).

tff(f3145,plain,
    ! [X0: fun_int_bool,X1: fun_fun_int_bool_int,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_2069007511ol_int(X1,X2)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(ennf_transformation,[],[f2195]) ).

tff(f2195,plain,
    ! [X0: fun_int_bool,X1: fun_fun_int_bool_int,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_2069007511ol_int(X1,X2)))
       => hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
    inference(rectify,[],[f214]) ).

tff(f214,axiom,
    ! [X7: fun_int_bool,X6: fun_fun_int_bool_int,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X7),image_2069007511ol_int(X6,X2)))
       => hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_finite__surj) ).

tff(f15426,plain,
    spl250_804,
    inference(avatar_split_clause,[],[f5857,f15424]) ).

tff(f15424,plain,
    ( spl250_804
  <=> ! [X2: fun_fu425979586l_bool,X0: fun_int_bool,X1: fun_fun_nat_bool_int] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_1133522419ol_int(X1,X2)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_804])]) ).

tff(f5857,plain,
    ! [X2: fun_fu425979586l_bool,X0: fun_int_bool,X1: fun_fun_nat_bool_int] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_1133522419ol_int(X1,X2)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(cnf_transformation,[],[f3144]) ).

tff(f3144,plain,
    ! [X0: fun_int_bool,X1: fun_fun_nat_bool_int,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_1133522419ol_int(X1,X2)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(flattening,[],[f3143]) ).

tff(f3143,plain,
    ! [X0: fun_int_bool,X1: fun_fun_nat_bool_int,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_1133522419ol_int(X1,X2)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(ennf_transformation,[],[f2194]) ).

tff(f2194,plain,
    ! [X0: fun_int_bool,X1: fun_fun_nat_bool_int,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_1133522419ol_int(X1,X2)))
       => hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
    inference(rectify,[],[f215]) ).

tff(f215,axiom,
    ! [X7: fun_int_bool,X6: fun_fun_nat_bool_int,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X7),image_1133522419ol_int(X6,X2)))
       => hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_finite__surj) ).

tff(f15422,plain,
    spl250_803,
    inference(avatar_split_clause,[],[f5856,f15420]) ).

tff(f15420,plain,
    ( spl250_803
  <=> ! [X2: fun_fun_a_bool_bool,X0: fun_int_bool,X1: fun_fun_a_bool_int] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_fun_a_bool_int(X1,X2)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_803])]) ).

tff(f5856,plain,
    ! [X2: fun_fun_a_bool_bool,X0: fun_int_bool,X1: fun_fun_a_bool_int] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_fun_a_bool_int(X1,X2)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(cnf_transformation,[],[f3142]) ).

tff(f3142,plain,
    ! [X0: fun_int_bool,X1: fun_fun_a_bool_int,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_fun_a_bool_int(X1,X2)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(flattening,[],[f3141]) ).

tff(f3141,plain,
    ! [X0: fun_int_bool,X1: fun_fun_a_bool_int,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_fun_a_bool_int(X1,X2)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(ennf_transformation,[],[f2193]) ).

tff(f2193,plain,
    ! [X0: fun_int_bool,X1: fun_fun_a_bool_int,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),image_fun_a_bool_int(X1,X2)))
       => hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
    inference(rectify,[],[f217]) ).

tff(f217,axiom,
    ! [X7: fun_int_bool,X6: fun_fun_a_bool_int,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X7),image_fun_a_bool_int(X6,X2)))
       => hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_finite__surj) ).

tff(f15418,plain,
    spl250_802,
    inference(avatar_split_clause,[],[f5855,f15416]) ).

tff(f15416,plain,
    ( spl250_802
  <=> ! [X2: fun_fu819804446l_bool,X0: fun_a_bool,X1: fun_fun_int_bool_a] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_int_bool_a(X1,X2)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_802])]) ).

tff(f5855,plain,
    ! [X2: fun_fu819804446l_bool,X0: fun_a_bool,X1: fun_fun_int_bool_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_int_bool_a(X1,X2)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(cnf_transformation,[],[f3140]) ).

tff(f3140,plain,
    ! [X0: fun_a_bool,X1: fun_fun_int_bool_a,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_int_bool_a(X1,X2)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(flattening,[],[f3139]) ).

tff(f3139,plain,
    ! [X0: fun_a_bool,X1: fun_fun_int_bool_a,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_int_bool_a(X1,X2)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(ennf_transformation,[],[f2192]) ).

tff(f2192,plain,
    ! [X0: fun_a_bool,X1: fun_fun_int_bool_a,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_int_bool_a(X1,X2)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
    inference(rectify,[],[f182]) ).

tff(f182,axiom,
    ! [X7: fun_a_bool,X6: fun_fun_int_bool_a,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),image_fun_int_bool_a(X6,X2)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_finite__surj) ).

tff(f15414,plain,
    spl250_801,
    inference(avatar_split_clause,[],[f5854,f15412]) ).

tff(f15412,plain,
    ( spl250_801
  <=> ! [X2: fun_fun_a_bool_bool,X0: fun_a_bool,X1: fun_fun_a_bool_a] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_a_bool_a(X1,X2)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_801])]) ).

tff(f5854,plain,
    ! [X2: fun_fun_a_bool_bool,X0: fun_a_bool,X1: fun_fun_a_bool_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_a_bool_a(X1,X2)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(cnf_transformation,[],[f3138]) ).

tff(f3138,plain,
    ! [X0: fun_a_bool,X1: fun_fun_a_bool_a,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_a_bool_a(X1,X2)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(flattening,[],[f3137]) ).

tff(f3137,plain,
    ! [X0: fun_a_bool,X1: fun_fun_a_bool_a,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_a_bool_a(X1,X2)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(ennf_transformation,[],[f2191]) ).

tff(f2191,plain,
    ! [X0: fun_a_bool,X1: fun_fun_a_bool_a,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_a_bool_a(X1,X2)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
    inference(rectify,[],[f185]) ).

tff(f185,axiom,
    ! [X7: fun_a_bool,X6: fun_fun_a_bool_a,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),image_fun_a_bool_a(X6,X2)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_finite__surj) ).

tff(f15410,plain,
    spl250_800,
    inference(avatar_split_clause,[],[f5853,f15408]) ).

tff(f15408,plain,
    ( spl250_800
  <=> ! [X2: fun_fu425979586l_bool,X0: fun_a_bool,X1: fun_fun_nat_bool_a] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_nat_bool_a(X1,X2)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_800])]) ).

tff(f5853,plain,
    ! [X2: fun_fu425979586l_bool,X0: fun_a_bool,X1: fun_fun_nat_bool_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_nat_bool_a(X1,X2)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(cnf_transformation,[],[f3136]) ).

tff(f3136,plain,
    ! [X0: fun_a_bool,X1: fun_fun_nat_bool_a,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_nat_bool_a(X1,X2)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(flattening,[],[f3135]) ).

tff(f3135,plain,
    ! [X0: fun_a_bool,X1: fun_fun_nat_bool_a,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_nat_bool_a(X1,X2)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(ennf_transformation,[],[f2190]) ).

tff(f2190,plain,
    ! [X0: fun_a_bool,X1: fun_fun_nat_bool_a,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_fun_nat_bool_a(X1,X2)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
    inference(rectify,[],[f183]) ).

tff(f183,axiom,
    ! [X7: fun_a_bool,X6: fun_fun_nat_bool_a,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),image_fun_nat_bool_a(X6,X2)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_finite__surj) ).

tff(f15406,plain,
    spl250_799,
    inference(avatar_split_clause,[],[f5852,f15404]) ).

tff(f15404,plain,
    ( spl250_799
  <=> ! [X2: fun_fu1430349052l_bool,X0: fun_a_bool,X1: fun_fun_pname_bool_a] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_876012084bool_a(X1,X2)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_799])]) ).

tff(f5852,plain,
    ! [X2: fun_fu1430349052l_bool,X0: fun_a_bool,X1: fun_fun_pname_bool_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_876012084bool_a(X1,X2)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(cnf_transformation,[],[f3134]) ).

tff(f3134,plain,
    ! [X0: fun_a_bool,X1: fun_fun_pname_bool_a,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_876012084bool_a(X1,X2)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(flattening,[],[f3133]) ).

tff(f3133,plain,
    ! [X0: fun_a_bool,X1: fun_fun_pname_bool_a,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_876012084bool_a(X1,X2)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(ennf_transformation,[],[f2189]) ).

tff(f2189,plain,
    ! [X0: fun_a_bool,X1: fun_fun_pname_bool_a,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),image_876012084bool_a(X1,X2)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
    inference(rectify,[],[f184]) ).

tff(f184,axiom,
    ! [X7: fun_a_bool,X6: fun_fun_pname_bool_a,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),image_876012084bool_a(X6,X2)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_finite__surj) ).

tff(f15402,plain,
    spl250_798,
    inference(avatar_split_clause,[],[f5851,f15400]) ).

tff(f15400,plain,
    ( spl250_798
  <=> ! [X2: fun_fun_a_bool_bool,X0: fun_pname_bool,X1: fun_fun_a_bool_pname] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1854862208_pname(X1,X2)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_798])]) ).

tff(f5851,plain,
    ! [X2: fun_fun_a_bool_bool,X0: fun_pname_bool,X1: fun_fun_a_bool_pname] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1854862208_pname(X1,X2)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(cnf_transformation,[],[f3132]) ).

tff(f3132,plain,
    ! [X0: fun_pname_bool,X1: fun_fun_a_bool_pname,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1854862208_pname(X1,X2)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(flattening,[],[f3131]) ).

tff(f3131,plain,
    ! [X0: fun_pname_bool,X1: fun_fun_a_bool_pname,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1854862208_pname(X1,X2)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    inference(ennf_transformation,[],[f2188]) ).

tff(f2188,plain,
    ! [X0: fun_pname_bool,X1: fun_fun_a_bool_pname,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1854862208_pname(X1,X2)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
    inference(rectify,[],[f207]) ).

tff(f207,axiom,
    ! [X7: fun_pname_bool,X6: fun_fun_a_bool_pname,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X7),image_1854862208_pname(X6,X2)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_finite__surj) ).

tff(f15398,plain,
    ( spl250_797
    | ~ spl250_47
    | ~ spl250_720 ),
    inference(avatar_split_clause,[],[f14861,f14227,f7528,f15396]) ).

tff(f15396,plain,
    ( spl250_797
  <=> ! [X0: fun_int_bool] : ~ sP10(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_797])]) ).

tff(f7528,plain,
    ( spl250_47
  <=> ! [X0: fun_int_bool] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_47])]) ).

tff(f14227,plain,
    ( spl250_720
  <=> ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
        ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK180(X0,X1)),sK181(X0,X1))))
        | ~ sP10(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_720])]) ).

tff(f14861,plain,
    ( ! [X0: fun_int_bool] : ~ sP10(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),X0)
    | ~ spl250_47
    | ~ spl250_720 ),
    inference(resolution,[],[f14228,f7529]) ).

tff(f7529,plain,
    ( ! [X0: fun_int_bool] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),X0))
    | ~ spl250_47 ),
    inference(avatar_component_clause,[],[f7528]) ).

tff(f14228,plain,
    ( ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
        ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK180(X0,X1)),sK181(X0,X1))))
        | ~ sP10(X0,X1) )
    | ~ spl250_720 ),
    inference(avatar_component_clause,[],[f14227]) ).

tff(f15394,plain,
    spl250_796,
    inference(avatar_split_clause,[],[f5850,f15392]) ).

tff(f15392,plain,
    ( spl250_796
  <=> ! [X2: fun_fu819804446l_bool,X0: fun_pname_bool,X1: fun_fu953875929_pname] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_62782965_pname(X1,X2)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_796])]) ).

tff(f5850,plain,
    ! [X2: fun_fu819804446l_bool,X0: fun_pname_bool,X1: fun_fu953875929_pname] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_62782965_pname(X1,X2)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(cnf_transformation,[],[f3130]) ).

tff(f3130,plain,
    ! [X0: fun_pname_bool,X1: fun_fu953875929_pname,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_62782965_pname(X1,X2)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(flattening,[],[f3129]) ).

tff(f3129,plain,
    ! [X0: fun_pname_bool,X1: fun_fu953875929_pname,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_62782965_pname(X1,X2)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    inference(ennf_transformation,[],[f2187]) ).

tff(f2187,plain,
    ! [X0: fun_pname_bool,X1: fun_fu953875929_pname,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_62782965_pname(X1,X2)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
    inference(rectify,[],[f204]) ).

tff(f204,axiom,
    ! [X7: fun_pname_bool,X6: fun_fu953875929_pname,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X7),image_62782965_pname(X6,X2)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_finite__surj) ).

tff(f15390,plain,
    spl250_795,
    inference(avatar_split_clause,[],[f5849,f15388]) ).

tff(f15388,plain,
    ( spl250_795
  <=> ! [X2: fun_fu1430349052l_bool,X0: fun_pname_bool,X1: fun_fu1499449723_pname] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1283814551_pname(X1,X2)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_795])]) ).

tff(f5849,plain,
    ! [X2: fun_fu1430349052l_bool,X0: fun_pname_bool,X1: fun_fu1499449723_pname] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1283814551_pname(X1,X2)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(cnf_transformation,[],[f3128]) ).

tff(f3128,plain,
    ! [X0: fun_pname_bool,X1: fun_fu1499449723_pname,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1283814551_pname(X1,X2)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(flattening,[],[f3127]) ).

tff(f3127,plain,
    ! [X0: fun_pname_bool,X1: fun_fu1499449723_pname,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1283814551_pname(X1,X2)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    inference(ennf_transformation,[],[f2186]) ).

tff(f2186,plain,
    ! [X0: fun_pname_bool,X1: fun_fu1499449723_pname,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1283814551_pname(X1,X2)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
    inference(rectify,[],[f206]) ).

tff(f206,axiom,
    ! [X7: fun_pname_bool,X6: fun_fu1499449723_pname,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X7),image_1283814551_pname(X6,X2)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_finite__surj) ).

tff(f15386,plain,
    spl250_794,
    inference(avatar_split_clause,[],[f5848,f15384]) ).

tff(f15384,plain,
    ( spl250_794
  <=> ! [X2: fun_fu425979586l_bool,X0: fun_pname_bool,X1: fun_fu665170229_pname] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1921560913_pname(X1,X2)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_794])]) ).

tff(f5848,plain,
    ! [X2: fun_fu425979586l_bool,X0: fun_pname_bool,X1: fun_fu665170229_pname] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1921560913_pname(X1,X2)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(cnf_transformation,[],[f3126]) ).

tff(f3126,plain,
    ! [X0: fun_pname_bool,X1: fun_fu665170229_pname,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1921560913_pname(X1,X2)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(flattening,[],[f3125]) ).

tff(f3125,plain,
    ! [X0: fun_pname_bool,X1: fun_fu665170229_pname,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1921560913_pname(X1,X2)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    inference(ennf_transformation,[],[f2185]) ).

tff(f2185,plain,
    ! [X0: fun_pname_bool,X1: fun_fu665170229_pname,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),image_1921560913_pname(X1,X2)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
    inference(rectify,[],[f205]) ).

tff(f205,axiom,
    ! [X7: fun_pname_bool,X6: fun_fu665170229_pname,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X7),image_1921560913_pname(X6,X2)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_finite__surj) ).

tff(f15382,plain,
    spl250_793,
    inference(avatar_split_clause,[],[f5667,f15380]) ).

tff(f15380,plain,
    ( spl250_793
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_793])]) ).

tff(f5667,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0)) ),
    inference(cnf_transformation,[],[f4175]) ).

tff(f4175,plain,
    ! [X0: nat,X1: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1))) ) ),
    inference(nnf_transformation,[],[f2049]) ).

tff(f2049,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0)) ),
    inference(rectify,[],[f953]) ).

tff(f953,axiom,
    ! [X14: nat,X22: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),X22)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X14)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_952_zero__less__diff) ).

tff(f15378,plain,
    spl250_792,
    inference(avatar_split_clause,[],[f5666,f15376]) ).

tff(f15376,plain,
    ( spl250_792
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_792])]) ).

tff(f5666,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1))) ),
    inference(cnf_transformation,[],[f4175]) ).

tff(f15374,plain,
    spl250_791,
    inference(avatar_split_clause,[],[f5664,f15372]) ).

tff(f15372,plain,
    ( spl250_791
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_791])]) ).

tff(f5664,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ),
    inference(cnf_transformation,[],[f4174]) ).

tff(f15370,plain,
    spl250_790,
    inference(avatar_split_clause,[],[f5663,f15368]) ).

tff(f15368,plain,
    ( spl250_790
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_790])]) ).

tff(f5663,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1))) ),
    inference(cnf_transformation,[],[f4174]) ).

tff(f15366,plain,
    spl250_789,
    inference(avatar_split_clause,[],[f5661,f15364]) ).

tff(f15364,plain,
    ( spl250_789
  <=> ! [X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_789])]) ).

tff(f5661,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)),X1)) ),
    inference(cnf_transformation,[],[f4172]) ).

tff(f4172,plain,
    ! [X0: int,X1: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)),X1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)),X1)) ) ),
    inference(nnf_transformation,[],[f2047]) ).

tff(f2047,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)),X1))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(rectify,[],[f1055]) ).

tff(f1055,axiom,
    ! [X136: int,X53: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X136),one_one_int)),X53))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X136),X53)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1054_add1__zle__eq) ).

tff(f15361,plain,
    spl250_788,
    inference(avatar_split_clause,[],[f5658,f15359]) ).

tff(f5658,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4170]) ).

tff(f4170,plain,
    ! [X0: nat,X1: nat] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1))) ) ),
    inference(nnf_transformation,[],[f2045]) ).

tff(f2045,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(rectify,[],[f1111]) ).

tff(f1111,axiom,
    ! [X8: nat,X36: nat] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X8)),hAPP_nat_int(semiri1621563631at_int,X36)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X8),X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1110_transfer__int__nat__relations_I3_J) ).

tff(f15356,plain,
    spl250_787,
    inference(avatar_split_clause,[],[f5657,f15354]) ).

tff(f5657,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1))) ),
    inference(cnf_transformation,[],[f4170]) ).

tff(f15352,plain,
    ( spl250_786
    | ~ spl250_46
    | ~ spl250_719 ),
    inference(avatar_split_clause,[],[f14853,f14223,f7524,f15350]) ).

tff(f15350,plain,
    ( spl250_786
  <=> ! [X0: fun_a_bool] : ~ sP9(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_786])]) ).

tff(f7524,plain,
    ( spl250_46
  <=> ! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_46])]) ).

tff(f14223,plain,
    ( spl250_719
  <=> ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK170(X0,X1)),sK171(X0,X1))))
        | ~ sP9(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_719])]) ).

tff(f14853,plain,
    ( ! [X0: fun_a_bool] : ~ sP9(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),X0)
    | ~ spl250_46
    | ~ spl250_719 ),
    inference(resolution,[],[f14224,f7525]) ).

tff(f7525,plain,
    ( ! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),X0))
    | ~ spl250_46 ),
    inference(avatar_component_clause,[],[f7524]) ).

tff(f14224,plain,
    ( ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK170(X0,X1)),sK171(X0,X1))))
        | ~ sP9(X0,X1) )
    | ~ spl250_719 ),
    inference(avatar_component_clause,[],[f14223]) ).

tff(f15347,plain,
    spl250_785,
    inference(avatar_split_clause,[],[f5654,f15345]) ).

tff(f5654,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4168]) ).

tff(f4168,plain,
    ! [X0: nat,X1: nat] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1))) ) ),
    inference(nnf_transformation,[],[f2043]) ).

tff(f2043,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(rectify,[],[f1102]) ).

tff(f1102,axiom,
    ! [X22: nat,X14: nat] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X22)),hAPP_nat_int(semiri1621563631at_int,X14)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X14)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1101_zless__int) ).

tff(f15342,plain,
    spl250_784,
    inference(avatar_split_clause,[],[f5653,f15340]) ).

tff(f5653,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),hAPP_nat_int(semiri1621563631at_int,X1))) ),
    inference(cnf_transformation,[],[f4168]) ).

tff(f15338,plain,
    spl250_783,
    inference(avatar_split_clause,[],[f5652,f15336]) ).

tff(f15336,plain,
    ( spl250_783
  <=> ! [X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),one_one_int)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_783])]) ).

tff(f5652,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4167]) ).

tff(f4167,plain,
    ! [X0: int,X1: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),one_one_int)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),one_one_int))) ) ),
    inference(nnf_transformation,[],[f2042]) ).

tff(f2042,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),one_one_int)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(rectify,[],[f1049]) ).

tff(f1049,axiom,
    ! [X136: int,X53: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X136),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X53),one_one_int)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X136),X53)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1048_zle__diff1__eq) ).

tff(f15334,plain,
    spl250_782,
    inference(avatar_split_clause,[],[f5651,f15332]) ).

tff(f15332,plain,
    ( spl250_782
  <=> ! [X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),one_one_int))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_782])]) ).

tff(f5651,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),one_one_int))) ),
    inference(cnf_transformation,[],[f4167]) ).

tff(f15330,plain,
    spl250_781,
    inference(avatar_split_clause,[],[f5649,f15328]) ).

tff(f15328,plain,
    ( spl250_781
  <=> ! [X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_781])]) ).

tff(f5649,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4166]) ).

tff(f15326,plain,
    spl250_780,
    inference(avatar_split_clause,[],[f5647,f15324]) ).

tff(f15324,plain,
    ( spl250_780
  <=> ! [X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_780])]) ).

tff(f5647,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4164]) ).

tff(f4164,plain,
    ! [X0: int,X1: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int))) ) ),
    inference(nnf_transformation,[],[f2040]) ).

tff(f2040,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(rectify,[],[f1054]) ).

tff(f1054,axiom,
    ! [X136: int,X53: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X136),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X53),one_one_int)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X136),X53)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1053_zle__add1__eq__le) ).

tff(f15322,plain,
    spl250_779,
    inference(avatar_split_clause,[],[f5646,f15320]) ).

tff(f15320,plain,
    ( spl250_779
  <=> ! [X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_779])]) ).

tff(f5646,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int))) ),
    inference(cnf_transformation,[],[f4164]) ).

tff(f15306,plain,
    ( spl250_778
    | ~ spl250_369
    | ~ spl250_574
    | ~ spl250_777 ),
    inference(avatar_split_clause,[],[f15302,f15298,f11754,f9687,f15304]) ).

tff(f15304,plain,
    ( spl250_778
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool,X3: nat] :
        ( hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(ord_less_eq_bool,X0),X1),X3))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_778])]) ).

tff(f15298,plain,
    ( spl250_777
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool,X3: nat] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X3)),hAPP_nat_bool(X1,X3)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_777])]) ).

tff(f15302,plain,
    ( ! [X3: nat,X0: fun_nat_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(ord_less_eq_bool,X0),X1),X3))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) )
    | ~ spl250_369
    | ~ spl250_574
    | ~ spl250_777 ),
    inference(forward_demodulation,[],[f15301,f11755]) ).

tff(f15301,plain,
    ( ! [X3: nat,X0: fun_nat_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(ord_less_eq_bool,X0),X3),hAPP_nat_bool(X1,X3)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) )
    | ~ spl250_369
    | ~ spl250_777 ),
    inference(forward_demodulation,[],[f15299,f9688]) ).

tff(f15299,plain,
    ( ! [X3: nat,X0: fun_nat_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X3)),hAPP_nat_bool(X1,X3)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) )
    | ~ spl250_777 ),
    inference(avatar_component_clause,[],[f15298]) ).

tff(f15300,plain,
    spl250_777,
    inference(avatar_split_clause,[],[f5508,f15298]) ).

tff(f5508,plain,
    ! [X3: nat,X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X0,X3)),hAPP_nat_bool(X1,X3)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ),
    inference(cnf_transformation,[],[f4071]) ).

tff(f15296,plain,
    spl250_776,
    inference(avatar_split_clause,[],[f5507,f15294]) ).

tff(f15294,plain,
    ( spl250_776
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_776])]) ).

tff(f5507,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) ),
    inference(cnf_transformation,[],[f4067]) ).

tff(f4067,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) )
      & ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ) ),
    inference(nnf_transformation,[],[f1986]) ).

tff(f1986,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
    <=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) ),
    inference(rectify,[],[f1135]) ).

tff(f1135,axiom,
    ! [X2: fun_nat_bool,X7: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X7))
    <=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,X2)),image_nat_int(semiri1621563631at_int,X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1134_transfer__nat__int__set__relations_I5_J) ).

tff(f15292,plain,
    spl250_775,
    inference(avatar_split_clause,[],[f5505,f15290]) ).

tff(f15290,plain,
    ( spl250_775
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X0),X1))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_775])]) ).

tff(f5505,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X0),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) ),
    inference(cnf_transformation,[],[f4066]) ).

tff(f4066,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X0),X1))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) )
      & ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X0),X1)) ) ),
    inference(nnf_transformation,[],[f1985]) ).

tff(f1985,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X0),X1))
    <=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) ),
    inference(rectify,[],[f1134]) ).

tff(f1134,axiom,
    ! [X2: fun_nat_bool,X7: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X2),X7))
    <=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,X2)),image_nat_int(semiri1621563631at_int,X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1133_transfer__nat__int__set__relations_I4_J) ).

tff(f15288,plain,
    spl250_774,
    inference(avatar_split_clause,[],[f5504,f15286]) ).

tff(f15286,plain,
    ( spl250_774
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_774])]) ).

tff(f5504,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X0),X1)) ),
    inference(cnf_transformation,[],[f4066]) ).

tff(f15284,plain,
    spl250_773,
    inference(avatar_split_clause,[],[f5503,f15282]) ).

tff(f15282,plain,
    ( spl250_773
  <=> ! [X0: nat,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_773])]) ).

tff(f5503,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) ),
    inference(cnf_transformation,[],[f4065]) ).

tff(f4065,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) )
      & ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ) ),
    inference(nnf_transformation,[],[f1984]) ).

tff(f1984,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
    <=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,X0)),image_nat_int(semiri1621563631at_int,X1))) ),
    inference(rectify,[],[f1138]) ).

tff(f1138,axiom,
    ! [X8: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X2))
    <=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,X8)),image_nat_int(semiri1621563631at_int,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1137_transfer__nat__int__set__relations_I2_J) ).

tff(f15270,plain,
    ( spl250_772
    | ~ spl250_368
    | ~ spl250_573
    | ~ spl250_771 ),
    inference(avatar_split_clause,[],[f15266,f15262,f11750,f9683,f15268]) ).

tff(f15268,plain,
    ( spl250_772
  <=> ! [X0: fun_int_bool,X1: fun_int_bool,X3: int] :
        ( hBOOL(hAPP_int_bool(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(ord_less_eq_bool,X0),X1),X3))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_772])]) ).

tff(f15262,plain,
    ( spl250_771
  <=> ! [X0: fun_int_bool,X1: fun_int_bool,X3: int] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X3)),hAPP_int_bool(X1,X3)))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_771])]) ).

tff(f15266,plain,
    ( ! [X3: int,X0: fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_int_bool(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(ord_less_eq_bool,X0),X1),X3))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) )
    | ~ spl250_368
    | ~ spl250_573
    | ~ spl250_771 ),
    inference(forward_demodulation,[],[f15265,f11751]) ).

tff(f15265,plain,
    ( ! [X3: int,X0: fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_bool_bool(hAPP_i68813070l_bool(cOMBB_1652995168ol_int(ord_less_eq_bool,X0),X3),hAPP_int_bool(X1,X3)))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) )
    | ~ spl250_368
    | ~ spl250_771 ),
    inference(forward_demodulation,[],[f15263,f9684]) ).

tff(f15263,plain,
    ( ! [X3: int,X0: fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X3)),hAPP_int_bool(X1,X3)))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) )
    | ~ spl250_771 ),
    inference(avatar_component_clause,[],[f15262]) ).

tff(f15264,plain,
    spl250_771,
    inference(avatar_split_clause,[],[f5498,f15262]) ).

tff(f5498,plain,
    ! [X3: int,X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X0,X3)),hAPP_int_bool(X1,X3)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ),
    inference(cnf_transformation,[],[f4063]) ).

tff(f15257,plain,
    ( spl250_770
    | ~ spl250_367
    | ~ spl250_568
    | ~ spl250_769 ),
    inference(avatar_split_clause,[],[f15253,f15249,f11730,f9678,f15255]) ).

tff(f15255,plain,
    ( spl250_770
  <=> ! [X0: fun_a_bool,X1: fun_a_bool,X3: x_a] :
        ( hBOOL(hAPP_a_bool(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(ord_less_eq_bool,X0),X1),X3))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_770])]) ).

tff(f15249,plain,
    ( spl250_769
  <=> ! [X0: fun_a_bool,X1: fun_a_bool,X3: x_a] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X3)),hAPP_a_bool(X1,X3)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_769])]) ).

tff(f15253,plain,
    ( ! [X3: x_a,X0: fun_a_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_a_bool(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(ord_less_eq_bool,X0),X1),X3))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) )
    | ~ spl250_367
    | ~ spl250_568
    | ~ spl250_769 ),
    inference(forward_demodulation,[],[f15252,f11731]) ).

tff(f15252,plain,
    ( ! [X3: x_a,X0: fun_a_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_bool_bool(hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(ord_less_eq_bool,X0),X3),hAPP_a_bool(X1,X3)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) )
    | ~ spl250_367
    | ~ spl250_769 ),
    inference(forward_demodulation,[],[f15250,f9679]) ).

tff(f15250,plain,
    ( ! [X3: x_a,X0: fun_a_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X3)),hAPP_a_bool(X1,X3)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) )
    | ~ spl250_769 ),
    inference(avatar_component_clause,[],[f15249]) ).

tff(f15251,plain,
    spl250_769,
    inference(avatar_split_clause,[],[f5494,f15249]) ).

tff(f5494,plain,
    ! [X3: x_a,X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X0,X3)),hAPP_a_bool(X1,X3)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ),
    inference(cnf_transformation,[],[f4058]) ).

tff(f15247,plain,
    spl250_768,
    inference(avatar_split_clause,[],[f5393,f15245]) ).

tff(f15245,plain,
    ( spl250_768
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_768])]) ).

tff(f5393,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1))) ),
    inference(cnf_transformation,[],[f3042]) ).

tff(f3042,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1))) ),
    inference(ennf_transformation,[],[f1936]) ).

tff(f1936,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(rectify,[],[f876]) ).

tff(f876,axiom,
    ! [X12: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X12)),hAPP_nat_nat(suc,X11)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),X11)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_875_Suc__less__SucD) ).

tff(f15243,plain,
    spl250_767,
    inference(avatar_split_clause,[],[f5381,f15241]) ).

tff(f15241,plain,
    ( spl250_767
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),sK124(X0,X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_767])]) ).

tff(f5381,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),sK124(X0,X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1)) ),
    inference(cnf_transformation,[],[f3996]) ).

tff(f3996,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( hAPP_nat_nat(suc,sK124(X0,X1)) = X1 )
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),sK124(X0,X1))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK124])],[f3028,f3995]) ).

tff(f3995,plain,
    ! [X0: nat,X1: nat] :
      ( ? [X2: nat] :
          ( ( hAPP_nat_nat(suc,X2) = X1 )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2)) )
     => ( ( hAPP_nat_nat(suc,sK124(X0,X1)) = X1 )
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),sK124(X0,X1))) ) ),
    introduced(choice_axiom,[]) ).

tff(f3028,plain,
    ! [X0: nat,X1: nat] :
      ( ? [X2: nat] :
          ( ( hAPP_nat_nat(suc,X2) = X1 )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1)) ),
    inference(ennf_transformation,[],[f1925]) ).

tff(f1925,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1))
     => ~ ! [X2: nat] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X2))
           => ( hAPP_nat_nat(suc,X2) != X1 ) ) ),
    inference(rectify,[],[f921]) ).

tff(f921,axiom,
    ! [X20: nat,X19: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X20)),X19))
     => ~ ! [X124: nat] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X20),X124))
           => ( hAPP_nat_nat(suc,X124) != X19 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_920_Suc__lessE) ).

tff(f15239,plain,
    spl250_766,
    inference(avatar_split_clause,[],[f5347,f15237]) ).

tff(f15237,plain,
    ( spl250_766
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_766])]) ).

tff(f5347,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2985]) ).

tff(f2985,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1895]) ).

tff(f1895,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1))) ),
    inference(rectify,[],[f857]) ).

tff(f857,axiom,
    ! [X12: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),X11))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X12)),hAPP_nat_nat(suc,X11))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_856_Suc__mono) ).

tff(f15235,plain,
    spl250_765,
    inference(avatar_split_clause,[],[f5333,f15233]) ).

tff(f15233,plain,
    ( spl250_765
  <=> ! [X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)),X1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_765])]) ).

tff(f5333,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2969]) ).

tff(f2969,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(ennf_transformation,[],[f1882]) ).

tff(f1882,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)),X1)) ),
    inference(rectify,[],[f1056]) ).

tff(f1056,axiom,
    ! [X132: int,X95: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X132),X95))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X132),one_one_int)),X95)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1055_zless__imp__add1__zle) ).

tff(f15231,plain,
    spl250_764,
    inference(avatar_split_clause,[],[f5274,f15229]) ).

tff(f15229,plain,
    ( spl250_764
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_764])]) ).

tff(f5274,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f3975]) ).

tff(f3975,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1)))
          | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
        & ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
          | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1))) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(nnf_transformation,[],[f2895]) ).

tff(f2895,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1)))
      <=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(ennf_transformation,[],[f1833]) ).

tff(f1833,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
     => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1)))
      <=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    inference(rectify,[],[f571]) ).

tff(f571,axiom,
    ! [X2: fun_nat_bool,X7: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
     => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X7)))
      <=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_570_finite__Diff2) ).

tff(f15227,plain,
    spl250_763,
    inference(avatar_split_clause,[],[f5242,f15225]) ).

tff(f15225,plain,
    ( spl250_763
  <=> ! [X0: fun_nat_int,X1: fun_nat_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_nat_int(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_763])]) ).

tff(f5242,plain,
    ! [X0: fun_nat_int,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_nat_int(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f2865]) ).

tff(f2865,plain,
    ! [X0: fun_nat_int,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_nat_int(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(ennf_transformation,[],[f1814]) ).

tff(f1814,plain,
    ! [X0: fun_nat_int,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_nat_int(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1))) ),
    inference(rectify,[],[f71]) ).

tff(f71,axiom,
    ! [X6: fun_nat_int,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_nat_int(X6,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_card__image__le) ).

tff(f15223,plain,
    spl250_762,
    inference(avatar_split_clause,[],[f5241,f15221]) ).

tff(f15221,plain,
    ( spl250_762
  <=> ! [X0: fun_nat_pname,X1: fun_nat_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_762])]) ).

tff(f5241,plain,
    ! [X0: fun_nat_pname,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f2864]) ).

tff(f2864,plain,
    ! [X0: fun_nat_pname,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(ennf_transformation,[],[f1813]) ).

tff(f1813,plain,
    ! [X0: fun_nat_pname,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X0,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1))) ),
    inference(rectify,[],[f68]) ).

tff(f68,axiom,
    ! [X6: fun_nat_pname,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X6,X2))),hAPP_f22106695ol_nat(finite_card_nat,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_card__image__le) ).

tff(f15219,plain,
    spl250_761,
    inference(avatar_split_clause,[],[f5231,f15217]) ).

tff(f15217,plain,
    ( spl250_761
  <=> ! [X0: fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_761])]) ).

tff(f5231,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f3964]) ).

tff(f3964,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1)))
          | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) )
        & ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
          | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1))) ) )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(nnf_transformation,[],[f2855]) ).

tff(f2855,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1)))
      <=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(ennf_transformation,[],[f1804]) ).

tff(f1804,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
     => ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1)))
      <=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
    inference(rectify,[],[f570]) ).

tff(f570,axiom,
    ! [X2: fun_int_bool,X7: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7))
     => ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X7)))
      <=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_569_finite__Diff2) ).

tff(f15215,plain,
    spl250_760,
    inference(avatar_split_clause,[],[f5199,f15213]) ).

tff(f15213,plain,
    ( spl250_760
  <=> ! [X0: fun_int_pname,X1: fun_int_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_int_pname(X0,X1))),hAPP_f957591787ol_nat(finite_card_int,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_760])]) ).

tff(f5199,plain,
    ! [X0: fun_int_pname,X1: fun_int_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_int_pname(X0,X1))),hAPP_f957591787ol_nat(finite_card_int,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f2825]) ).

tff(f2825,plain,
    ! [X0: fun_int_pname,X1: fun_int_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_int_pname(X0,X1))),hAPP_f957591787ol_nat(finite_card_int,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(ennf_transformation,[],[f1785]) ).

tff(f1785,plain,
    ! [X0: fun_int_pname,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_int_pname(X0,X1))),hAPP_f957591787ol_nat(finite_card_int,X1))) ),
    inference(rectify,[],[f69]) ).

tff(f69,axiom,
    ! [X6: fun_int_pname,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_int_pname(X6,X2))),hAPP_f957591787ol_nat(finite_card_int,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_card__image__le) ).

tff(f15211,plain,
    spl250_759,
    inference(avatar_split_clause,[],[f5160,f15209]) ).

tff(f15209,plain,
    ( spl250_759
  <=> ! [X0: fun_a_nat,X1: fun_a_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_759])]) ).

tff(f5160,plain,
    ! [X0: fun_a_nat,X1: fun_a_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(cnf_transformation,[],[f2788]) ).

tff(f2788,plain,
    ! [X0: fun_a_nat,X1: fun_a_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(ennf_transformation,[],[f1759]) ).

tff(f1759,plain,
    ! [X0: fun_a_nat,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1))) ),
    inference(rectify,[],[f56]) ).

tff(f56,axiom,
    ! [X6: fun_a_nat,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X6,X2))),hAPP_fun_a_bool_nat(finite_card_a,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_card__image__le) ).

tff(f15207,plain,
    spl250_758,
    inference(avatar_split_clause,[],[f5159,f15205]) ).

tff(f15205,plain,
    ( spl250_758
  <=> ! [X0: fun_a_a,X1: fun_a_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_758])]) ).

tff(f5159,plain,
    ! [X0: fun_a_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(cnf_transformation,[],[f2787]) ).

tff(f2787,plain,
    ! [X0: fun_a_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(ennf_transformation,[],[f1758]) ).

tff(f1758,plain,
    ! [X0: fun_a_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1))) ),
    inference(rectify,[],[f50]) ).

tff(f50,axiom,
    ! [X6: fun_a_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X6,X2))),hAPP_fun_a_bool_nat(finite_card_a,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_card__image__le) ).

tff(f15203,plain,
    spl250_757,
    inference(avatar_split_clause,[],[f5158,f15201]) ).

tff(f15201,plain,
    ( spl250_757
  <=> ! [X0: fun_a_int,X1: fun_a_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_a_int(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_757])]) ).

tff(f5158,plain,
    ! [X0: fun_a_int,X1: fun_a_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_a_int(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(cnf_transformation,[],[f2786]) ).

tff(f2786,plain,
    ! [X0: fun_a_int,X1: fun_a_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_a_int(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(ennf_transformation,[],[f1757]) ).

tff(f1757,plain,
    ! [X0: fun_a_int,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_a_int(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1))) ),
    inference(rectify,[],[f62]) ).

tff(f62,axiom,
    ! [X6: fun_a_int,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_a_int(X6,X2))),hAPP_fun_a_bool_nat(finite_card_a,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_card__image__le) ).

tff(f15199,plain,
    spl250_756,
    inference(avatar_split_clause,[],[f5157,f15197]) ).

tff(f15197,plain,
    ( spl250_756
  <=> ! [X0: fun_a_pname,X1: fun_a_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_756])]) ).

tff(f5157,plain,
    ! [X0: fun_a_pname,X1: fun_a_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(cnf_transformation,[],[f2785]) ).

tff(f2785,plain,
    ! [X0: fun_a_pname,X1: fun_a_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(ennf_transformation,[],[f1756]) ).

tff(f1756,plain,
    ! [X0: fun_a_pname,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X0,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1))) ),
    inference(rectify,[],[f67]) ).

tff(f67,axiom,
    ! [X6: fun_a_pname,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X6,X2))),hAPP_fun_a_bool_nat(finite_card_a,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_card__image__le) ).

tff(f15195,plain,
    spl250_755,
    inference(avatar_split_clause,[],[f5151,f15193]) ).

tff(f15193,plain,
    ( spl250_755
  <=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_755])]) ).

tff(f5151,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f3943]) ).

tff(f3943,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X1)))
          | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) )
        & ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
          | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X1))) ) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(nnf_transformation,[],[f2780]) ).

tff(f2780,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X1)))
      <=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(ennf_transformation,[],[f1751]) ).

tff(f1751,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),X1)))
      <=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
    inference(rectify,[],[f572]) ).

tff(f572,axiom,
    ! [X2: fun_pname_bool,X7: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X7)))
      <=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_571_finite__Diff2) ).

tff(f15191,plain,
    spl250_754,
    inference(avatar_split_clause,[],[f5119,f15189]) ).

tff(f15189,plain,
    ( spl250_754
  <=> ! [X0: fun_pname_nat,X1: fun_pname_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_754])]) ).

tff(f5119,plain,
    ! [X0: fun_pname_nat,X1: fun_pname_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f2750]) ).

tff(f2750,plain,
    ! [X0: fun_pname_nat,X1: fun_pname_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(ennf_transformation,[],[f1732]) ).

tff(f1732,plain,
    ! [X0: fun_pname_nat,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1))) ),
    inference(rectify,[],[f55]) ).

tff(f55,axiom,
    ! [X6: fun_pname_nat,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X6,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_card__image__le) ).

tff(f15187,plain,
    spl250_753,
    inference(avatar_split_clause,[],[f5118,f15185]) ).

tff(f15185,plain,
    ( spl250_753
  <=> ! [X0: fun_pname_a,X1: fun_pname_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_753])]) ).

tff(f5118,plain,
    ! [X0: fun_pname_a,X1: fun_pname_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f2749]) ).

tff(f2749,plain,
    ! [X0: fun_pname_a,X1: fun_pname_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(ennf_transformation,[],[f1731]) ).

tff(f1731,plain,
    ! [X0: fun_pname_a,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1))) ),
    inference(rectify,[],[f70]) ).

tff(f70,axiom,
    ! [X6: fun_pname_a,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X6,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_card__image__le) ).

tff(f15183,plain,
    spl250_752,
    inference(avatar_split_clause,[],[f5117,f15181]) ).

tff(f15181,plain,
    ( spl250_752
  <=> ! [X0: fun_pname_int,X1: fun_pname_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_pname_int(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_752])]) ).

tff(f5117,plain,
    ! [X0: fun_pname_int,X1: fun_pname_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_pname_int(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f2748]) ).

tff(f2748,plain,
    ! [X0: fun_pname_int,X1: fun_pname_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_pname_int(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(ennf_transformation,[],[f1730]) ).

tff(f1730,plain,
    ! [X0: fun_pname_int,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_pname_int(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1))) ),
    inference(rectify,[],[f61]) ).

tff(f61,axiom,
    ! [X6: fun_pname_int,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_pname_int(X6,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_card__image__le) ).

tff(f15179,plain,
    spl250_751,
    inference(avatar_split_clause,[],[f5116,f15177]) ).

tff(f15177,plain,
    ( spl250_751
  <=> ! [X0: fun_pname_pname,X1: fun_pname_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_751])]) ).

tff(f5116,plain,
    ! [X0: fun_pname_pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f2747]) ).

tff(f2747,plain,
    ! [X0: fun_pname_pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(ennf_transformation,[],[f1729]) ).

tff(f1729,plain,
    ! [X0: fun_pname_pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X0,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1))) ),
    inference(rectify,[],[f49]) ).

tff(f49,axiom,
    ! [X6: fun_pname_pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X6,X2))),hAPP_f921600141ol_nat(finite_card_pname,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_card__image__le) ).

tff(f15175,plain,
    spl250_750,
    inference(avatar_split_clause,[],[f5080,f15173]) ).

tff(f15173,plain,
    ( spl250_750
  <=> ! [X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_750])]) ).

tff(f5080,plain,
    ! [X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(cnf_transformation,[],[f2699]) ).

tff(f2699,plain,
    ! [X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(ennf_transformation,[],[f1697]) ).

tff(f1697,plain,
    ! [X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1))) ),
    inference(rectify,[],[f59]) ).

tff(f59,axiom,
    ! [X6: fun_fu1668467777ol_nat,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X6,X2))),hAPP_f55526627ol_nat(finite1340463720e_bool,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_card__image__le) ).

tff(f15171,plain,
    spl250_749,
    inference(avatar_split_clause,[],[f5079,f15169]) ).

tff(f15169,plain,
    ( spl250_749
  <=> ! [X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_749])]) ).

tff(f5079,plain,
    ! [X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(cnf_transformation,[],[f2698]) ).

tff(f2698,plain,
    ! [X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(ennf_transformation,[],[f1696]) ).

tff(f1696,plain,
    ! [X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1))) ),
    inference(rectify,[],[f58]) ).

tff(f58,axiom,
    ! [X6: fun_fun_nat_bool_nat,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X6,X2))),hAPP_f696928925ol_nat(finite346522414t_bool,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_card__image__le) ).

tff(f15167,plain,
    spl250_748,
    inference(avatar_split_clause,[],[f5078,f15165]) ).

tff(f15165,plain,
    ( spl250_748
  <=> ! [X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_748])]) ).

tff(f5078,plain,
    ! [X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(cnf_transformation,[],[f2697]) ).

tff(f2697,plain,
    ! [X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(ennf_transformation,[],[f1695]) ).

tff(f1695,plain,
    ! [X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1))) ),
    inference(rectify,[],[f60]) ).

tff(f60,axiom,
    ! [X6: fun_fun_a_bool_nat,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X6,X2))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_card__image__le) ).

tff(f15163,plain,
    spl250_747,
    inference(avatar_split_clause,[],[f5077,f15161]) ).

tff(f15161,plain,
    ( spl250_747
  <=> ! [X0: fun_fun_int_bool_nat,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1431733819ol_nat(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_747])]) ).

tff(f5077,plain,
    ! [X0: fun_fun_int_bool_nat,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1431733819ol_nat(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(cnf_transformation,[],[f2696]) ).

tff(f2696,plain,
    ! [X0: fun_fun_int_bool_nat,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1431733819ol_nat(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(ennf_transformation,[],[f1694]) ).

tff(f1694,plain,
    ! [X0: fun_fun_int_bool_nat,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1431733819ol_nat(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1))) ),
    inference(rectify,[],[f57]) ).

tff(f57,axiom,
    ! [X6: fun_fun_int_bool_nat,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1431733819ol_nat(X6,X2))),hAPP_f521865025ol_nat(finite1876863882t_bool,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_card__image__le) ).

tff(f15159,plain,
    spl250_746,
    inference(avatar_split_clause,[],[f5076,f15157]) ).

tff(f15157,plain,
    ( spl250_746
  <=> ! [X0: fun_fun_pname_bool_a,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_746])]) ).

tff(f5076,plain,
    ! [X0: fun_fun_pname_bool_a,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(cnf_transformation,[],[f2695]) ).

tff(f2695,plain,
    ! [X0: fun_fun_pname_bool_a,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(ennf_transformation,[],[f1693]) ).

tff(f1693,plain,
    ! [X0: fun_fun_pname_bool_a,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1))) ),
    inference(rectify,[],[f53]) ).

tff(f53,axiom,
    ! [X6: fun_fun_pname_bool_a,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X6,X2))),hAPP_f55526627ol_nat(finite1340463720e_bool,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_card__image__le) ).

tff(f15155,plain,
    spl250_745,
    inference(avatar_split_clause,[],[f5075,f15153]) ).

tff(f15153,plain,
    ( spl250_745
  <=> ! [X0: fun_fun_int_bool_a,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_int_bool_a(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_745])]) ).

tff(f5075,plain,
    ! [X0: fun_fun_int_bool_a,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_int_bool_a(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(cnf_transformation,[],[f2694]) ).

tff(f2694,plain,
    ! [X0: fun_fun_int_bool_a,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_int_bool_a(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(ennf_transformation,[],[f1692]) ).

tff(f1692,plain,
    ! [X0: fun_fun_int_bool_a,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_int_bool_a(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1))) ),
    inference(rectify,[],[f51]) ).

tff(f51,axiom,
    ! [X6: fun_fun_int_bool_a,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_int_bool_a(X6,X2))),hAPP_f521865025ol_nat(finite1876863882t_bool,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_card__image__le) ).

tff(f15151,plain,
    spl250_744,
    inference(avatar_split_clause,[],[f5074,f15149]) ).

tff(f15149,plain,
    ( spl250_744
  <=> ! [X0: fun_fun_a_bool_a,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_744])]) ).

tff(f5074,plain,
    ! [X0: fun_fun_a_bool_a,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(cnf_transformation,[],[f2693]) ).

tff(f2693,plain,
    ! [X0: fun_fun_a_bool_a,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(ennf_transformation,[],[f1691]) ).

tff(f1691,plain,
    ! [X0: fun_fun_a_bool_a,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1))) ),
    inference(rectify,[],[f54]) ).

tff(f54,axiom,
    ! [X6: fun_fun_a_bool_a,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X6,X2))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_card__image__le) ).

tff(f15147,plain,
    spl250_743,
    inference(avatar_split_clause,[],[f5073,f15145]) ).

tff(f15145,plain,
    ( spl250_743
  <=> ! [X0: fun_fun_nat_bool_a,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_743])]) ).

tff(f5073,plain,
    ! [X0: fun_fun_nat_bool_a,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(cnf_transformation,[],[f2692]) ).

tff(f2692,plain,
    ! [X0: fun_fun_nat_bool_a,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(ennf_transformation,[],[f1690]) ).

tff(f1690,plain,
    ! [X0: fun_fun_nat_bool_a,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1))) ),
    inference(rectify,[],[f52]) ).

tff(f52,axiom,
    ! [X6: fun_fun_nat_bool_a,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X6,X2))),hAPP_f696928925ol_nat(finite346522414t_bool,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_card__image__le) ).

tff(f15143,plain,
    spl250_742,
    inference(avatar_split_clause,[],[f5072,f15141]) ).

tff(f15141,plain,
    ( spl250_742
  <=> ! [X0: fun_fun_int_bool_int,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_2069007511ol_int(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_742])]) ).

tff(f5072,plain,
    ! [X0: fun_fun_int_bool_int,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_2069007511ol_int(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(cnf_transformation,[],[f2691]) ).

tff(f2691,plain,
    ! [X0: fun_fun_int_bool_int,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_2069007511ol_int(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(ennf_transformation,[],[f1689]) ).

tff(f1689,plain,
    ! [X0: fun_fun_int_bool_int,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_2069007511ol_int(X0,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1))) ),
    inference(rectify,[],[f63]) ).

tff(f63,axiom,
    ! [X6: fun_fun_int_bool_int,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_2069007511ol_int(X6,X2))),hAPP_f521865025ol_nat(finite1876863882t_bool,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_card__image__le) ).

tff(f15139,plain,
    spl250_741,
    inference(avatar_split_clause,[],[f5071,f15137]) ).

tff(f15137,plain,
    ( spl250_741
  <=> ! [X0: fun_fun_a_bool_int,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_fun_a_bool_int(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_741])]) ).

tff(f5071,plain,
    ! [X0: fun_fun_a_bool_int,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_fun_a_bool_int(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(cnf_transformation,[],[f2690]) ).

tff(f2690,plain,
    ! [X0: fun_fun_a_bool_int,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_fun_a_bool_int(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(ennf_transformation,[],[f1688]) ).

tff(f1688,plain,
    ! [X0: fun_fun_a_bool_int,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_fun_a_bool_int(X0,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1))) ),
    inference(rectify,[],[f66]) ).

tff(f66,axiom,
    ! [X6: fun_fun_a_bool_int,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_fun_a_bool_int(X6,X2))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_card__image__le) ).

tff(f15135,plain,
    spl250_740,
    inference(avatar_split_clause,[],[f5070,f15133]) ).

tff(f15133,plain,
    ( spl250_740
  <=> ! [X0: fun_fun_nat_bool_int,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_1133522419ol_int(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_740])]) ).

tff(f5070,plain,
    ! [X0: fun_fun_nat_bool_int,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_1133522419ol_int(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(cnf_transformation,[],[f2689]) ).

tff(f2689,plain,
    ! [X0: fun_fun_nat_bool_int,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_1133522419ol_int(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(ennf_transformation,[],[f1687]) ).

tff(f1687,plain,
    ! [X0: fun_fun_nat_bool_int,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_1133522419ol_int(X0,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1))) ),
    inference(rectify,[],[f64]) ).

tff(f64,axiom,
    ! [X6: fun_fun_nat_bool_int,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_1133522419ol_int(X6,X2))),hAPP_f696928925ol_nat(finite346522414t_bool,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_card__image__le) ).

tff(f15131,plain,
    spl250_739,
    inference(avatar_split_clause,[],[f5069,f15129]) ).

tff(f15129,plain,
    ( spl250_739
  <=> ! [X0: fun_fu1830380701ol_int,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_41399353ol_int(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_739])]) ).

tff(f5069,plain,
    ! [X0: fun_fu1830380701ol_int,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_41399353ol_int(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(cnf_transformation,[],[f2688]) ).

tff(f2688,plain,
    ! [X0: fun_fu1830380701ol_int,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_41399353ol_int(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(ennf_transformation,[],[f1686]) ).

tff(f1686,plain,
    ! [X0: fun_fu1830380701ol_int,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_41399353ol_int(X0,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1))) ),
    inference(rectify,[],[f65]) ).

tff(f65,axiom,
    ! [X6: fun_fu1830380701ol_int,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_41399353ol_int(X6,X2))),hAPP_f55526627ol_nat(finite1340463720e_bool,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_card__image__le) ).

tff(f15127,plain,
    spl250_738,
    inference(avatar_split_clause,[],[f5050,f15125]) ).

tff(f15125,plain,
    ( spl250_738
  <=> ! [X0: nat,X1: fun_nat_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK90(X0,X1)),X0))
        | ~ hBOOL(hAPP_nat_bool(X1,X0))
        | hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_738])]) ).

tff(f5050,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK90(X0,X1)),X0))
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
    inference(cnf_transformation,[],[f3932]) ).

tff(f15123,plain,
    spl250_737,
    inference(avatar_split_clause,[],[f5047,f15121]) ).

tff(f15121,plain,
    ( spl250_737
  <=> ! [X0: nat,X1: fun_nat_bool] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK89(X0,X1)),X0))
        | ~ hBOOL(hAPP_nat_bool(X1,X0))
        | hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_737])]) ).

tff(f5047,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK89(X0,X1)),X0))
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
    inference(cnf_transformation,[],[f3930]) ).

tff(f15119,plain,
    spl250_736,
    inference(avatar_split_clause,[],[f4785,f15117]) ).

tff(f15117,plain,
    ( spl250_736
  <=> ! [X0: fun_nat_bool] :
        ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK57(X0)),sK56(X0)) = X0 )
        | ( bot_bot_fun_nat_bool = X0 )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_736])]) ).

tff(f4785,plain,
    ! [X0: fun_nat_bool] :
      ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK57(X0)),sK56(X0)) = X0 )
      | ( bot_bot_fun_nat_bool = X0 )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ),
    inference(cnf_transformation,[],[f3821]) ).

tff(f3821,plain,
    ! [X0: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | ( ! [X1: fun_nat_bool,X2: nat] :
              ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
              | ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1) != X0 ) )
          & ( bot_bot_fun_nat_bool != X0 ) ) )
      & ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK56(X0)))
          & ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK57(X0)),sK56(X0)) = X0 ) )
        | ( bot_bot_fun_nat_bool = X0 )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK56,sK57])],[f3819,f3820]) ).

tff(f3820,plain,
    ! [X0: fun_nat_bool] :
      ( ? [X3: fun_nat_bool,X4: nat] :
          ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
          & ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4),X3) = X0 ) )
     => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK56(X0)))
        & ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK57(X0)),sK56(X0)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f3819,plain,
    ! [X0: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | ( ! [X1: fun_nat_bool,X2: nat] :
              ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
              | ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1) != X0 ) )
          & ( bot_bot_fun_nat_bool != X0 ) ) )
      & ( ? [X3: fun_nat_bool,X4: nat] :
            ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
            & ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4),X3) = X0 ) )
        | ( bot_bot_fun_nat_bool = X0 )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    inference(rectify,[],[f3818]) ).

tff(f3818,plain,
    ! [X0: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | ( ! [X1: fun_nat_bool,X2: nat] :
              ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
              | ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1) != X0 ) )
          & ( bot_bot_fun_nat_bool != X0 ) ) )
      & ( ? [X1: fun_nat_bool,X2: nat] :
            ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
            & ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1) = X0 ) )
        | ( bot_bot_fun_nat_bool = X0 )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    inference(flattening,[],[f3817]) ).

tff(f3817,plain,
    ! [X0: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | ( ! [X1: fun_nat_bool,X2: nat] :
              ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
              | ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1) != X0 ) )
          & ( bot_bot_fun_nat_bool != X0 ) ) )
      & ( ? [X1: fun_nat_bool,X2: nat] :
            ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
            & ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1) = X0 ) )
        | ( bot_bot_fun_nat_bool = X0 )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    inference(nnf_transformation,[],[f1478]) ).

tff(f1478,plain,
    ! [X0: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
    <=> ( ? [X1: fun_nat_bool,X2: nat] :
            ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
            & ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1) = X0 ) )
        | ( bot_bot_fun_nat_bool = X0 ) ) ),
    inference(rectify,[],[f694]) ).

tff(f694,axiom,
    ! [X5: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
    <=> ( ? [X78: fun_nat_bool,X75: nat] :
            ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X78))
            & ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X75),X78) = X5 ) )
        | ( bot_bot_fun_nat_bool = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_693_finite_Osimps) ).

tff(f15115,plain,
    spl250_735,
    inference(avatar_split_clause,[],[f4779,f15113]) ).

tff(f15113,plain,
    ( spl250_735
  <=> ! [X0: fun_int_bool] :
        ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK55(X0)),sK54(X0)) = X0 )
        | ( bot_bot_fun_int_bool = X0 )
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_735])]) ).

tff(f4779,plain,
    ! [X0: fun_int_bool] :
      ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK55(X0)),sK54(X0)) = X0 )
      | ( bot_bot_fun_int_bool = X0 )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ),
    inference(cnf_transformation,[],[f3815]) ).

tff(f3815,plain,
    ! [X0: fun_int_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
        | ( ! [X1: fun_int_bool,X2: int] :
              ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
              | ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1) != X0 ) )
          & ( bot_bot_fun_int_bool != X0 ) ) )
      & ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK54(X0)))
          & ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK55(X0)),sK54(X0)) = X0 ) )
        | ( bot_bot_fun_int_bool = X0 )
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK54,sK55])],[f3813,f3814]) ).

tff(f3814,plain,
    ! [X0: fun_int_bool] :
      ( ? [X3: fun_int_bool,X4: int] :
          ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
          & ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4),X3) = X0 ) )
     => ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK54(X0)))
        & ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK55(X0)),sK54(X0)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f3813,plain,
    ! [X0: fun_int_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
        | ( ! [X1: fun_int_bool,X2: int] :
              ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
              | ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1) != X0 ) )
          & ( bot_bot_fun_int_bool != X0 ) ) )
      & ( ? [X3: fun_int_bool,X4: int] :
            ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
            & ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4),X3) = X0 ) )
        | ( bot_bot_fun_int_bool = X0 )
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
    inference(rectify,[],[f3812]) ).

tff(f3812,plain,
    ! [X0: fun_int_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
        | ( ! [X1: fun_int_bool,X2: int] :
              ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
              | ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1) != X0 ) )
          & ( bot_bot_fun_int_bool != X0 ) ) )
      & ( ? [X1: fun_int_bool,X2: int] :
            ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
            & ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1) = X0 ) )
        | ( bot_bot_fun_int_bool = X0 )
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
    inference(flattening,[],[f3811]) ).

tff(f3811,plain,
    ! [X0: fun_int_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
        | ( ! [X1: fun_int_bool,X2: int] :
              ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
              | ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1) != X0 ) )
          & ( bot_bot_fun_int_bool != X0 ) ) )
      & ( ? [X1: fun_int_bool,X2: int] :
            ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
            & ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1) = X0 ) )
        | ( bot_bot_fun_int_bool = X0 )
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
    inference(nnf_transformation,[],[f1476]) ).

tff(f1476,plain,
    ! [X0: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
    <=> ( ? [X1: fun_int_bool,X2: int] :
            ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
            & ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1) = X0 ) )
        | ( bot_bot_fun_int_bool = X0 ) ) ),
    inference(rectify,[],[f693]) ).

tff(f693,axiom,
    ! [X5: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
    <=> ( ? [X78: fun_int_bool,X75: int] :
            ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X78))
            & ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X75),X78) = X5 ) )
        | ( bot_bot_fun_int_bool = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_692_finite_Osimps) ).

tff(f15111,plain,
    spl250_734,
    inference(avatar_split_clause,[],[f4775,f15109]) ).

tff(f15109,plain,
    ( spl250_734
  <=> ! [X0: fun_a_bool] :
        ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK53(X0)),sK52(X0)) = X0 )
        | ( bot_bot_fun_a_bool = X0 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_734])]) ).

tff(f4775,plain,
    ! [X0: fun_a_bool] :
      ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK53(X0)),sK52(X0)) = X0 )
      | ( bot_bot_fun_a_bool = X0 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ),
    inference(cnf_transformation,[],[f3810]) ).

tff(f3810,plain,
    ! [X0: fun_a_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
        | ( ! [X1: fun_a_bool,X2: x_a] :
              ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
              | ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1) != X0 ) )
          & ( bot_bot_fun_a_bool != X0 ) ) )
      & ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK52(X0)))
          & ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK53(X0)),sK52(X0)) = X0 ) )
        | ( bot_bot_fun_a_bool = X0 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK52,sK53])],[f3808,f3809]) ).

tff(f3809,plain,
    ! [X0: fun_a_bool] :
      ( ? [X3: fun_a_bool,X4: x_a] :
          ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
          & ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4),X3) = X0 ) )
     => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK52(X0)))
        & ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK53(X0)),sK52(X0)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f3808,plain,
    ! [X0: fun_a_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
        | ( ! [X1: fun_a_bool,X2: x_a] :
              ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
              | ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1) != X0 ) )
          & ( bot_bot_fun_a_bool != X0 ) ) )
      & ( ? [X3: fun_a_bool,X4: x_a] :
            ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
            & ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4),X3) = X0 ) )
        | ( bot_bot_fun_a_bool = X0 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
    inference(rectify,[],[f3807]) ).

tff(f3807,plain,
    ! [X0: fun_a_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
        | ( ! [X1: fun_a_bool,X2: x_a] :
              ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
              | ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1) != X0 ) )
          & ( bot_bot_fun_a_bool != X0 ) ) )
      & ( ? [X1: fun_a_bool,X2: x_a] :
            ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
            & ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1) = X0 ) )
        | ( bot_bot_fun_a_bool = X0 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
    inference(flattening,[],[f3806]) ).

tff(f3806,plain,
    ! [X0: fun_a_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
        | ( ! [X1: fun_a_bool,X2: x_a] :
              ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
              | ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1) != X0 ) )
          & ( bot_bot_fun_a_bool != X0 ) ) )
      & ( ? [X1: fun_a_bool,X2: x_a] :
            ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
            & ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1) = X0 ) )
        | ( bot_bot_fun_a_bool = X0 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
    inference(nnf_transformation,[],[f1475]) ).

tff(f1475,plain,
    ! [X0: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
    <=> ( ? [X1: fun_a_bool,X2: x_a] :
            ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
            & ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1) = X0 ) )
        | ( bot_bot_fun_a_bool = X0 ) ) ),
    inference(rectify,[],[f692]) ).

tff(f692,axiom,
    ! [X5: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
    <=> ( ? [X78: fun_a_bool,X75: x_a] :
            ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X78))
            & ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X75),X78) = X5 ) )
        | ( bot_bot_fun_a_bool = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_finite_Osimps) ).

tff(f15107,plain,
    spl250_733,
    inference(avatar_split_clause,[],[f4771,f15105]) ).

tff(f15105,plain,
    ( spl250_733
  <=> ! [X0: fun_pname_bool] :
        ( ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK51(X0)),sK50(X0)) = X0 )
        | ( bot_bo844097828e_bool = X0 )
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_733])]) ).

tff(f4771,plain,
    ! [X0: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK51(X0)),sK50(X0)) = X0 )
      | ( bot_bo844097828e_bool = X0 )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ),
    inference(cnf_transformation,[],[f3805]) ).

tff(f3805,plain,
    ! [X0: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
        | ( ! [X1: fun_pname_bool,X2: pname] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
              | ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1) != X0 ) )
          & ( bot_bo844097828e_bool != X0 ) ) )
      & ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK50(X0)))
          & ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK51(X0)),sK50(X0)) = X0 ) )
        | ( bot_bo844097828e_bool = X0 )
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK50,sK51])],[f3803,f3804]) ).

tff(f3804,plain,
    ! [X0: fun_pname_bool] :
      ( ? [X3: fun_pname_bool,X4: pname] :
          ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
          & ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4),X3) = X0 ) )
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK50(X0)))
        & ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK51(X0)),sK50(X0)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f3803,plain,
    ! [X0: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
        | ( ! [X1: fun_pname_bool,X2: pname] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
              | ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1) != X0 ) )
          & ( bot_bo844097828e_bool != X0 ) ) )
      & ( ? [X3: fun_pname_bool,X4: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
            & ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4),X3) = X0 ) )
        | ( bot_bo844097828e_bool = X0 )
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
    inference(rectify,[],[f3802]) ).

tff(f3802,plain,
    ! [X0: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
        | ( ! [X1: fun_pname_bool,X2: pname] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
              | ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1) != X0 ) )
          & ( bot_bo844097828e_bool != X0 ) ) )
      & ( ? [X1: fun_pname_bool,X2: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
            & ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1) = X0 ) )
        | ( bot_bo844097828e_bool = X0 )
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
    inference(flattening,[],[f3801]) ).

tff(f3801,plain,
    ! [X0: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
        | ( ! [X1: fun_pname_bool,X2: pname] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
              | ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1) != X0 ) )
          & ( bot_bo844097828e_bool != X0 ) ) )
      & ( ? [X1: fun_pname_bool,X2: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
            & ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1) = X0 ) )
        | ( bot_bo844097828e_bool = X0 )
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
    inference(nnf_transformation,[],[f1474]) ).

tff(f1474,plain,
    ! [X0: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
    <=> ( ? [X1: fun_pname_bool,X2: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
            & ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1) = X0 ) )
        | ( bot_bo844097828e_bool = X0 ) ) ),
    inference(rectify,[],[f695]) ).

tff(f695,axiom,
    ! [X5: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
    <=> ( ? [X78: fun_pname_bool,X75: pname] :
            ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X78))
            & ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X75),X78) = X5 ) )
        | ( bot_bo844097828e_bool = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_694_finite_Osimps) ).

tff(f14772,plain,
    ( spl250_732
    | ~ spl250_43
    | ~ spl250_673 ),
    inference(avatar_split_clause,[],[f13853,f12741,f7512,f14770]) ).

tff(f14770,plain,
    ( spl250_732
  <=> ! [X0: nat,X1: nat] : ~ sP24(nat_neg,X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_732])]) ).

tff(f7512,plain,
    ( spl250_43
  <=> ! [X0: nat] : ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_nat_int(semiri1621563631at_int,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_43])]) ).

tff(f13853,plain,
    ( ! [X0: nat,X1: nat] : ~ sP24(nat_neg,X0,X1)
    | ~ spl250_43
    | ~ spl250_673 ),
    inference(resolution,[],[f12742,f7513]) ).

tff(f7513,plain,
    ( ! [X0: nat] : ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_nat_int(semiri1621563631at_int,X0)))
    | ~ spl250_43 ),
    inference(avatar_component_clause,[],[f7512]) ).

tff(f14457,plain,
    ( spl250_731
    | ~ spl250_48
    | ~ spl250_670 ),
    inference(avatar_split_clause,[],[f13786,f12729,f7532,f14455]) ).

tff(f14455,plain,
    ( spl250_731
  <=> ! [X0: fun_nat_bool,X1: nat] : sP23(X0,bot_bot_fun_nat_bool,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_731])]) ).

tff(f12729,plain,
    ( spl250_670
  <=> ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
        ( sP23(X2,X0,X1)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_670])]) ).

tff(f13786,plain,
    ( ! [X0: fun_nat_bool,X1: nat] : sP23(X0,bot_bot_fun_nat_bool,X1)
    | ~ spl250_48
    | ~ spl250_670 ),
    inference(resolution,[],[f12730,f7533]) ).

tff(f12730,plain,
    ( ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))
        | sP23(X2,X0,X1) )
    | ~ spl250_670 ),
    inference(avatar_component_clause,[],[f12729]) ).

tff(f14271,plain,
    spl250_730,
    inference(avatar_split_clause,[],[f7230,f14269]) ).

tff(f14269,plain,
    ( spl250_730
  <=> ! [X2: fun_pname_bool,X0: x_a,X1: pname] :
        ( ( collect_a(hAPP_a_fun_a_bool(fequal_a,X0)) = image_pname_a(cOMBK_a_pname(X0),X2) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_730])]) ).

tff(f7230,plain,
    ! [X2: fun_pname_bool,X0: x_a,X1: pname] :
      ( ( collect_a(hAPP_a_fun_a_bool(fequal_a,X0)) = image_pname_a(cOMBK_a_pname(X0),X2) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
    inference(forward_demodulation,[],[f6061,f4680]) ).

tff(f6061,plain,
    ! [X2: fun_pname_bool,X0: x_a,X1: pname] :
      ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = image_pname_a(cOMBK_a_pname(X0),X2) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
    inference(cnf_transformation,[],[f3328]) ).

tff(f3328,plain,
    ! [X0: x_a,X1: pname,X2: fun_pname_bool] :
      ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = image_pname_a(cOMBK_a_pname(X0),X2) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
    inference(ennf_transformation,[],[f2293]) ).

tff(f2293,plain,
    ! [X0: x_a,X1: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
     => ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = image_pname_a(cOMBK_a_pname(X0),X2) ) ),
    inference(rectify,[],[f667]) ).

tff(f667,axiom,
    ! [X29: x_a,X8: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X2))
     => ( image_pname_a(cOMBK_a_pname(X29),X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X29),bot_bot_fun_a_bool) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_666_image__constant) ).

tff(f14267,plain,
    spl250_729,
    inference(avatar_split_clause,[],[f6997,f14265]) ).

tff(f14265,plain,
    ( spl250_729
  <=> ! [X0: fun_nat_bool,X1: nat] :
        ( ( hAPP_n1699378549t_bool(fequal_nat,X1) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X1)),X0) )
        | ~ hBOOL(hAPP_nat_bool(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_729])]) ).

tff(f6997,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( ( hAPP_n1699378549t_bool(fequal_nat,X1) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X1)),X0) )
      | ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
    inference(forward_demodulation,[],[f6996,f4588]) ).

tff(f6996,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( ( hAPP_n1699378549t_bool(fequal_nat,X1) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X1)),X0)) )
      | ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
    inference(forward_demodulation,[],[f4962,f6931]) ).

tff(f4962,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X1)),X0)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool) )
      | ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f2619]) ).

tff(f2619,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( ( ( bot_bot_fun_nat_bool = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X1)),X0)) )
        | hBOOL(hAPP_nat_bool(X0,X1)) )
      & ( ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X1)),X0)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool) )
        | ~ hBOOL(hAPP_nat_bool(X0,X1)) ) ),
    inference(ennf_transformation,[],[f1602]) ).

tff(f1602,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( ( ~ hBOOL(hAPP_nat_bool(X0,X1))
       => ( bot_bot_fun_nat_bool = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X1)),X0)) ) )
      & ( hBOOL(hAPP_nat_bool(X0,X1))
       => ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X1)),X0)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool) ) ) ),
    inference(rectify,[],[f636]) ).

tff(f636,axiom,
    ! [X10: fun_nat_bool,X5: nat] :
      ( ( ~ hBOOL(hAPP_nat_bool(X10,X5))
       => ( bot_bot_fun_nat_bool = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X5)),X10)) ) )
      & ( hBOOL(hAPP_nat_bool(X10,X5))
       => ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5),bot_bot_fun_nat_bool) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X5)),X10)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_635_Collect__conv__if2) ).

tff(f14263,plain,
    spl250_728,
    inference(avatar_split_clause,[],[f6989,f14261]) ).

tff(f14261,plain,
    ( spl250_728
  <=> ! [X0: fun_int_bool,X1: int] :
        ( ( hAPP_i1948725293t_bool(fequal_int,X1) = cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X1)),X0) )
        | ~ hBOOL(hAPP_int_bool(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_728])]) ).

tff(f6989,plain,
    ! [X0: fun_int_bool,X1: int] :
      ( ( hAPP_i1948725293t_bool(fequal_int,X1) = cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X1)),X0) )
      | ~ hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(forward_demodulation,[],[f6988,f4586]) ).

tff(f6988,plain,
    ! [X0: fun_int_bool,X1: int] :
      ( ( hAPP_i1948725293t_bool(fequal_int,X1) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X1)),X0)) )
      | ~ hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(forward_demodulation,[],[f4958,f6930]) ).

tff(f4958,plain,
    ! [X0: fun_int_bool,X1: int] :
      ( ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X1)),X0)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool) )
      | ~ hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f2617]) ).

tff(f2617,plain,
    ! [X0: fun_int_bool,X1: int] :
      ( ( ( bot_bot_fun_int_bool = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X1)),X0)) )
        | hBOOL(hAPP_int_bool(X0,X1)) )
      & ( ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X1)),X0)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool) )
        | ~ hBOOL(hAPP_int_bool(X0,X1)) ) ),
    inference(ennf_transformation,[],[f1600]) ).

tff(f1600,plain,
    ! [X0: fun_int_bool,X1: int] :
      ( ( ~ hBOOL(hAPP_int_bool(X0,X1))
       => ( bot_bot_fun_int_bool = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X1)),X0)) ) )
      & ( hBOOL(hAPP_int_bool(X0,X1))
       => ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X1)),X0)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool) ) ) ),
    inference(rectify,[],[f635]) ).

tff(f635,axiom,
    ! [X10: fun_int_bool,X5: int] :
      ( ( ~ hBOOL(hAPP_int_bool(X10,X5))
       => ( bot_bot_fun_int_bool = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X5)),X10)) ) )
      & ( hBOOL(hAPP_int_bool(X10,X5))
       => ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5),bot_bot_fun_int_bool) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X5)),X10)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_634_Collect__conv__if2) ).

tff(f14259,plain,
    ( spl250_727
    | ~ spl250_244
    | ~ spl250_670 ),
    inference(avatar_split_clause,[],[f13785,f12729,f8801,f14257]) ).

tff(f14257,plain,
    ( spl250_727
  <=> ! [X0: fun_nat_bool,X1: nat] : sP23(X0,X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_727])]) ).

tff(f8801,plain,
    ( spl250_244
  <=> ! [X0: fun_nat_bool,X1: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_244])]) ).

tff(f13785,plain,
    ( ! [X0: fun_nat_bool,X1: nat] : sP23(X0,X0,X1)
    | ~ spl250_244
    | ~ spl250_670 ),
    inference(resolution,[],[f12730,f8802]) ).

tff(f8802,plain,
    ( ! [X0: fun_nat_bool,X1: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0)))
    | ~ spl250_244 ),
    inference(avatar_component_clause,[],[f8801]) ).

tff(f14255,plain,
    spl250_726,
    inference(avatar_split_clause,[],[f6943,f14253]) ).

tff(f14253,plain,
    ( spl250_726
  <=> ! [X0: int] :
        ( hBOOL(hAPP_int_bool(nat_neg,X0))
        | ( hAPP_nat_nat(suc,number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_726])]) ).

tff(f6943,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(nat_neg,X0))
      | ( hAPP_nat_nat(suc,number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)) ) ),
    inference(forward_demodulation,[],[f6587,f4587]) ).

tff(f6587,plain,
    ! [X0: int] :
      ( ( hAPP_nat_nat(suc,number_number_of_nat(X0)) = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int)) )
      | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
    inference(definition_unfolding,[],[f4698,f4661]) ).

tff(f4698,plain,
    ! [X0: int] :
      ( ( number_number_of_nat(succ(X0)) = hAPP_nat_nat(suc,number_number_of_nat(X0)) )
      | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
    inference(cnf_transformation,[],[f2577]) ).

tff(f2577,plain,
    ! [X0: int] :
      ( ( ( number_number_of_nat(succ(X0)) = hAPP_nat_nat(suc,number_number_of_nat(X0)) )
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
      & ( ( one_one_nat = hAPP_nat_nat(suc,number_number_of_nat(X0)) )
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) ),
    inference(ennf_transformation,[],[f1424]) ).

tff(f1424,plain,
    ! [X0: int] :
      ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
       => ( number_number_of_nat(succ(X0)) = hAPP_nat_nat(suc,number_number_of_nat(X0)) ) )
      & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
       => ( one_one_nat = hAPP_nat_nat(suc,number_number_of_nat(X0)) ) ) ),
    inference(rectify,[],[f1164]) ).

tff(f1164,axiom,
    ! [X130: int] :
      ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X130)))
       => ( number_number_of_nat(succ(X130)) = hAPP_nat_nat(suc,number_number_of_nat(X130)) ) )
      & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X130)))
       => ( one_one_nat = hAPP_nat_nat(suc,number_number_of_nat(X130)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1163_Suc__nat__number__of) ).

tff(f14250,plain,
    spl250_725,
    inference(avatar_split_clause,[],[f6566,f14247]) ).

tff(f14247,plain,
    ( spl250_725
  <=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),one_one_int) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_725])]) ).

tff(f14245,plain,
    spl250_724,
    inference(avatar_split_clause,[],[f6319,f14243]) ).

tff(f14243,plain,
    ( spl250_724
  <=> ! [X2: nat,X0: fun_nat_bool,X1: nat] :
        ( sP19(X0,X1,X2)
        | ~ hBOOL(hAPP_nat_bool(X0,sK247(X0,X1,X2)))
        | ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_724])]) ).

tff(f6319,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: nat] :
      ( sP19(X0,X1,X2)
      | ~ hBOOL(hAPP_nat_bool(X0,sK247(X0,X1,X2)))
      | ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ),
    inference(cnf_transformation,[],[f4431]) ).

tff(f14241,plain,
    spl250_723,
    inference(avatar_split_clause,[],[f6311,f14239]) ).

tff(f14239,plain,
    ( spl250_723
  <=> ! [X2: nat,X0: fun_nat_bool,X1: nat] :
        ( sP18(X0,X1,X2)
        | ~ hBOOL(hAPP_nat_bool(X0,sK246(X0,X1,X2)))
        | ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_723])]) ).

tff(f6311,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: nat] :
      ( sP18(X0,X1,X2)
      | ~ hBOOL(hAPP_nat_bool(X0,sK246(X0,X1,X2)))
      | ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ),
    inference(cnf_transformation,[],[f4425]) ).

tff(f14237,plain,
    spl250_722,
    inference(avatar_split_clause,[],[f6291,f14235]) ).

tff(f14235,plain,
    ( spl250_722
  <=> ! [X2: x_a,X0: x_a,X1: fun_a_bool] :
        ( hBOOL(hAPP_a_bool(X1,X2))
        | ( X0 = X2 )
        | ~ hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_722])]) ).

tff(f6291,plain,
    ! [X2: x_a,X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_a_bool(X1,X2))
      | ( X0 = X2 )
      | ~ hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),X2)) ),
    inference(cnf_transformation,[],[f4404]) ).

tff(f4404,plain,
    ! [X0: x_a,X1: fun_a_bool,X2: x_a] :
      ( ( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),X2))
        | ( ~ hBOOL(hAPP_a_bool(X1,X2))
          & ( X0 != X2 ) ) )
      & ( hBOOL(hAPP_a_bool(X1,X2))
        | ( X0 = X2 )
        | ~ hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),X2)) ) ),
    inference(flattening,[],[f4403]) ).

tff(f4403,plain,
    ! [X0: x_a,X1: fun_a_bool,X2: x_a] :
      ( ( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),X2))
        | ( ~ hBOOL(hAPP_a_bool(X1,X2))
          & ( X0 != X2 ) ) )
      & ( hBOOL(hAPP_a_bool(X1,X2))
        | ( X0 = X2 )
        | ~ hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),X2)) ) ),
    inference(nnf_transformation,[],[f2470]) ).

tff(f2470,plain,
    ! [X0: x_a,X1: fun_a_bool,X2: x_a] :
      ( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),X2))
    <=> ( hBOOL(hAPP_a_bool(X1,X2))
        | ( X0 = X2 ) ) ),
    inference(rectify,[],[f389]) ).

tff(f389,axiom,
    ! [X36: x_a,X2: fun_a_bool,X8: x_a] :
      ( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X36),X2),X8))
    <=> ( hBOOL(hAPP_a_bool(X2,X8))
        | ( X8 = X36 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_insert__code) ).

tff(f14233,plain,
    spl250_721,
    inference(avatar_split_clause,[],[f5975,f14231]) ).

tff(f5975,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK189(X0,X1)),sK190(X0,X1))))
      | ~ sP11(X0,X1) ),
    inference(cnf_transformation,[],[f4275]) ).

tff(f4275,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK189(X0,X1)),sK190(X0,X1))))
        & hBOOL(hAPP_f54304608l_bool(X0,sK190(X0,X1)))
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK189(X0,X1)),sK190(X0,X1)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK189(X0,X1)),X1))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK190(X0,X1))) )
      | ~ sP11(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK189,sK190])],[f4273,f4274]) ).

tff(f4274,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( ? [X2: nat,X3: fun_nat_bool] :
          ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3)))
          & hBOOL(hAPP_f54304608l_bool(X0,X3))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) )
     => ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK189(X0,X1)),sK190(X0,X1))))
        & hBOOL(hAPP_f54304608l_bool(X0,sK190(X0,X1)))
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK189(X0,X1)),sK190(X0,X1)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK189(X0,X1)),X1))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK190(X0,X1))) ) ),
    introduced(choice_axiom,[]) ).

tff(f4273,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( ? [X2: nat,X3: fun_nat_bool] :
          ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3)))
          & hBOOL(hAPP_f54304608l_bool(X0,X3))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) )
      | ~ sP11(X0,X1) ),
    inference(rectify,[],[f4272]) ).

tff(f4272,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( ? [X3: nat,X4: fun_nat_bool] :
          ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4)))
          & hBOOL(hAPP_f54304608l_bool(X0,X4))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X1))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4)) )
      | ~ sP11(X0,X1) ),
    inference(nnf_transformation,[],[f3705]) ).

tff(f14229,plain,
    spl250_720,
    inference(avatar_split_clause,[],[f5941,f14227]) ).

tff(f5941,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK180(X0,X1)),sK181(X0,X1))))
      | ~ sP10(X0,X1) ),
    inference(cnf_transformation,[],[f4257]) ).

tff(f4257,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK180(X0,X1)),sK181(X0,X1))))
        & hBOOL(hAPP_f448129468l_bool(X0,sK181(X0,X1)))
        & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK180(X0,X1)),sK181(X0,X1)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK180(X0,X1)),X1))
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK181(X0,X1))) )
      | ~ sP10(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK180,sK181])],[f4255,f4256]) ).

tff(f4256,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( ? [X2: int,X3: fun_int_bool] :
          ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3)))
          & hBOOL(hAPP_f448129468l_bool(X0,X3))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X3))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) )
     => ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK180(X0,X1)),sK181(X0,X1))))
        & hBOOL(hAPP_f448129468l_bool(X0,sK181(X0,X1)))
        & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK180(X0,X1)),sK181(X0,X1)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK180(X0,X1)),X1))
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK181(X0,X1))) ) ),
    introduced(choice_axiom,[]) ).

tff(f4255,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( ? [X2: int,X3: fun_int_bool] :
          ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3)))
          & hBOOL(hAPP_f448129468l_bool(X0,X3))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X3))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) )
      | ~ sP10(X0,X1) ),
    inference(rectify,[],[f4254]) ).

tff(f4254,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( ? [X3: int,X4: fun_int_bool] :
          ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4)))
          & hBOOL(hAPP_f448129468l_bool(X0,X4))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X1))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4)) )
      | ~ sP10(X0,X1) ),
    inference(nnf_transformation,[],[f3703]) ).

tff(f14225,plain,
    spl250_719,
    inference(avatar_split_clause,[],[f5906,f14223]) ).

tff(f5906,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK170(X0,X1)),sK171(X0,X1))))
      | ~ sP9(X0,X1) ),
    inference(cnf_transformation,[],[f4237]) ).

tff(f4237,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK170(X0,X1)),sK171(X0,X1))))
        & hBOOL(hAPP_fun_a_bool_bool(X0,sK171(X0,X1)))
        & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK170(X0,X1)),sK171(X0,X1)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK170(X0,X1)),X1))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK171(X0,X1))) )
      | ~ sP9(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK170,sK171])],[f4235,f4236]) ).

tff(f4236,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( ? [X2: x_a,X3: fun_a_bool] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3)))
          & hBOOL(hAPP_fun_a_bool_bool(X0,X3))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3)) )
     => ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK170(X0,X1)),sK171(X0,X1))))
        & hBOOL(hAPP_fun_a_bool_bool(X0,sK171(X0,X1)))
        & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK170(X0,X1)),sK171(X0,X1)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK170(X0,X1)),X1))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK171(X0,X1))) ) ),
    introduced(choice_axiom,[]) ).

tff(f4235,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( ? [X2: x_a,X3: fun_a_bool] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3)))
          & hBOOL(hAPP_fun_a_bool_bool(X0,X3))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3)) )
      | ~ sP9(X0,X1) ),
    inference(rectify,[],[f4234]) ).

tff(f4234,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( ? [X3: x_a,X4: fun_a_bool] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4)))
          & hBOOL(hAPP_fun_a_bool_bool(X0,X4))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4)) )
      | ~ sP9(X0,X1) ),
    inference(nnf_transformation,[],[f3701]) ).

tff(f14221,plain,
    spl250_718,
    inference(avatar_split_clause,[],[f5868,f14219]) ).

tff(f5868,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK160(X0,X1)),sK161(X0,X1))))
      | ~ sP8(X0,X1) ),
    inference(cnf_transformation,[],[f4217]) ).

tff(f4217,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK160(X0,X1)),sK161(X0,X1))))
        & hBOOL(hAPP_f1664156314l_bool(X0,sK161(X0,X1)))
        & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK160(X0,X1)),sK161(X0,X1)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK160(X0,X1)),X1))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK161(X0,X1))) )
      | ~ sP8(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK160,sK161])],[f4215,f4216]) ).

tff(f4216,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( ? [X2: pname,X3: fun_pname_bool] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X3)))
          & hBOOL(hAPP_f1664156314l_bool(X0,X3))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3)) )
     => ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK160(X0,X1)),sK161(X0,X1))))
        & hBOOL(hAPP_f1664156314l_bool(X0,sK161(X0,X1)))
        & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK160(X0,X1)),sK161(X0,X1)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK160(X0,X1)),X1))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK161(X0,X1))) ) ),
    introduced(choice_axiom,[]) ).

tff(f4215,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( ? [X2: pname,X3: fun_pname_bool] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X3)))
          & hBOOL(hAPP_f1664156314l_bool(X0,X3))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3)) )
      | ~ sP8(X0,X1) ),
    inference(rectify,[],[f4214]) ).

tff(f4214,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( ? [X3: pname,X4: fun_pname_bool] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4)))
          & hBOOL(hAPP_f1664156314l_bool(X0,X4))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4)) )
      | ~ sP8(X0,X1) ),
    inference(nnf_transformation,[],[f3699]) ).

tff(f14217,plain,
    spl250_717,
    inference(avatar_split_clause,[],[f5529,f14215]) ).

tff(f14215,plain,
    ( spl250_717
  <=> ! [X0: nat,X1: nat] :
        ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK142(X0,X1)) = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_717])]) ).

tff(f5529,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK142(X0,X1)) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4095]) ).

tff(f4095,plain,
    ! [X0: nat,X1: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
        | ! [X2: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2) != X1 ) )
      & ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK142(X0,X1)) = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK142])],[f4093,f4094]) ).

tff(f4094,plain,
    ! [X0: nat,X1: nat] :
      ( ? [X3: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X3) = X1 )
     => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK142(X0,X1)) = X1 ) ),
    introduced(choice_axiom,[]) ).

tff(f4093,plain,
    ! [X0: nat,X1: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
        | ! [X2: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2) != X1 ) )
      & ( ? [X3: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X3) = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    inference(rectify,[],[f4092]) ).

tff(f4092,plain,
    ! [X0: nat,X1: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
        | ! [X2: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2) != X1 ) )
      & ( ? [X2: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2) = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    inference(nnf_transformation,[],[f1996]) ).

tff(f1996,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
    <=> ? [X2: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2) = X1 ) ),
    inference(rectify,[],[f825]) ).

tff(f825,axiom,
    ! [X22: nat,X14: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X14))
    <=> ? [X116: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X22),X116) = X14 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_824_le__iff__add) ).

tff(f14213,plain,
    ( spl250_716
    | ~ spl250_47
    | ~ spl250_667 ),
    inference(avatar_split_clause,[],[f13765,f12716,f7528,f14211]) ).

tff(f14211,plain,
    ( spl250_716
  <=> ! [X0: fun_int_bool,X1: int] : sP22(X0,bot_bot_fun_int_bool,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_716])]) ).

tff(f12716,plain,
    ( spl250_667
  <=> ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] :
        ( sP22(X2,X0,X1)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_667])]) ).

tff(f13765,plain,
    ( ! [X0: fun_int_bool,X1: int] : sP22(X0,bot_bot_fun_int_bool,X1)
    | ~ spl250_47
    | ~ spl250_667 ),
    inference(resolution,[],[f12717,f7529]) ).

tff(f12717,plain,
    ( ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] :
        ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))
        | sP22(X2,X0,X1) )
    | ~ spl250_667 ),
    inference(avatar_component_clause,[],[f12716]) ).

tff(f14209,plain,
    spl250_715,
    inference(avatar_split_clause,[],[f5514,f14207]) ).

tff(f14207,plain,
    ( spl250_715
  <=> ! [X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | ( X0 = X1 )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_715])]) ).

tff(f5514,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4074]) ).

tff(f4074,plain,
    ! [X0: int,X1: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | ( X0 = X1 )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
      & ( ( ( X0 != X1 )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
    inference(flattening,[],[f4073]) ).

tff(f4073,plain,
    ! [X0: int,X1: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
        | ( X0 = X1 )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
      & ( ( ( X0 != X1 )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
    inference(nnf_transformation,[],[f1989]) ).

tff(f1989,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
    <=> ( ( X0 != X1 )
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
    inference(rectify,[],[f1051]) ).

tff(f1051,axiom,
    ! [X53: int,X136: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X53),X136))
    <=> ( ( X53 != X136 )
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X53),X136)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1050_zless__le) ).

tff(f14205,plain,
    spl250_714,
    inference(avatar_split_clause,[],[f5382,f14203]) ).

tff(f14203,plain,
    ( spl250_714
  <=> ! [X0: nat,X1: nat] :
        ( ( hAPP_nat_nat(suc,sK124(X0,X1)) = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_714])]) ).

tff(f5382,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(suc,sK124(X0,X1)) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1)) ),
    inference(cnf_transformation,[],[f3996]) ).

tff(f14201,plain,
    spl250_713,
    inference(avatar_split_clause,[],[f5363,f14199]) ).

tff(f14199,plain,
    ( spl250_713
  <=> ! [X0: nat,X1: nat] :
        ( ( X0 = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_713])]) ).

tff(f5363,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3003]) ).

tff(f3003,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(flattening,[],[f3002]) ).

tff(f3002,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1909]) ).

tff(f1909,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
       => ( X0 = X1 ) ) ),
    inference(rectify,[],[f127]) ).

tff(f127,axiom,
    ! [X12: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X11))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X11),X12))
       => ( X11 = X12 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_le__antisym) ).

tff(f14197,plain,
    spl250_712,
    inference(avatar_split_clause,[],[f5362,f14195]) ).

tff(f14195,plain,
    ( spl250_712
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
        | ( X0 = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_712])]) ).

tff(f5362,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3001]) ).

tff(f3001,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(flattening,[],[f3000]) ).

tff(f3000,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1908]) ).

tff(f1908,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
     => ( ( X0 != X1 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    inference(rectify,[],[f891]) ).

tff(f891,axiom,
    ! [X12: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X11))
     => ( ( X11 != X12 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),X11)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_890_le__neq__implies__less) ).

tff(f14193,plain,
    spl250_711,
    inference(avatar_split_clause,[],[f5353,f14191]) ).

tff(f14191,plain,
    ( spl250_711
  <=> ! [X0: nat,X1: nat] :
        ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK123(X0,X1)) = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_711])]) ).

tff(f5353,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK123(X0,X1)) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3992]) ).

tff(f3992,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK123(X0,X1)) = X1 )
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK123(X0,X1))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK123])],[f2991,f3991]) ).

tff(f3991,plain,
    ! [X0: nat,X1: nat] :
      ( ? [X2: nat] :
          ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2) = X1 )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) )
     => ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),sK123(X0,X1)) = X1 )
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK123(X0,X1))) ) ),
    introduced(choice_axiom,[]) ).

tff(f2991,plain,
    ! [X0: nat,X1: nat] :
      ( ? [X2: nat] :
          ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2) = X1 )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1899]) ).

tff(f1899,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
     => ? [X2: nat] :
          ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2) = X1 )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ) ),
    inference(rectify,[],[f972]) ).

tff(f972,axiom,
    ! [X20: nat,X21: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X20),X21))
     => ? [X116: nat] :
          ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X20),X116) = X21 )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X116)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_971_less__imp__add__positive) ).

tff(f14189,plain,
    spl250_710,
    inference(avatar_split_clause,[],[f5335,f14187]) ).

tff(f14187,plain,
    ( spl250_710
  <=> ! [X0: int,X1: int] :
        ( ( X0 = X1 )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_710])]) ).

tff(f5335,plain,
    ! [X0: int,X1: int] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2972]) ).

tff(f2972,plain,
    ! [X0: int,X1: int] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(flattening,[],[f2971]) ).

tff(f2971,plain,
    ! [X0: int,X1: int] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(ennf_transformation,[],[f1884]) ).

tff(f1884,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
       => ( X0 = X1 ) ) ),
    inference(rectify,[],[f1048]) ).

tff(f1048,axiom,
    ! [X95: int,X132: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X95),X132))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X132),X95))
       => ( X95 = X132 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1047_zle__antisym) ).

tff(f14185,plain,
    spl250_709,
    inference(avatar_split_clause,[],[f5328,f14183]) ).

tff(f14183,plain,
    ( spl250_709
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( ( X0 = X1 )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_709])]) ).

tff(f5328,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ),
    inference(cnf_transformation,[],[f2963]) ).

tff(f2963,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ),
    inference(flattening,[],[f2962]) ).

tff(f2962,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1)) ),
    inference(ennf_transformation,[],[f1878]) ).

tff(f1878,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
       => ( X0 = X1 ) ) ),
    inference(rectify,[],[f355]) ).

tff(f355,axiom,
    ! [X36: fun_nat_bool,X8: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X36),X8))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X8),X36))
       => ( X8 = X36 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_xt1_I5_J) ).

tff(f14181,plain,
    spl250_708,
    inference(avatar_split_clause,[],[f5320,f14179]) ).

tff(f14179,plain,
    ( spl250_708
  <=> ! [X0: fun_int_bool,X1: fun_int_bool] :
        ( ( X0 = X1 )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_708])]) ).

tff(f5320,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ),
    inference(cnf_transformation,[],[f2952]) ).

tff(f2952,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ),
    inference(flattening,[],[f2951]) ).

tff(f2951,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1)) ),
    inference(ennf_transformation,[],[f1871]) ).

tff(f1871,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
       => ( X0 = X1 ) ) ),
    inference(rectify,[],[f344]) ).

tff(f344,axiom,
    ! [X8: fun_int_bool,X36: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X8),X36))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X36),X8))
       => ( X8 = X36 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_order__antisym) ).

tff(f14177,plain,
    spl250_707,
    inference(avatar_split_clause,[],[f5312,f14175]) ).

tff(f14175,plain,
    ( spl250_707
  <=> ! [X0: fun_a_bool,X1: fun_a_bool] :
        ( ( X0 = X1 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_707])]) ).

tff(f5312,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ),
    inference(cnf_transformation,[],[f2941]) ).

tff(f2941,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ),
    inference(flattening,[],[f2940]) ).

tff(f2940,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ),
    inference(ennf_transformation,[],[f1864]) ).

tff(f1864,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
       => ( X0 = X1 ) ) ),
    inference(rectify,[],[f287]) ).

tff(f287,axiom,
    ! [X2: fun_a_bool,X7: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),X2))
       => ( X2 = X7 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_equalityI) ).

tff(f14173,plain,
    spl250_706,
    inference(avatar_split_clause,[],[f5278,f14171]) ).

tff(f14171,plain,
    ( spl250_706
  <=> ! [X0: fun_nat_bool,X1: nat] :
        ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
        | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,sK120(X0))))
        | ~ hBOOL(hAPP_nat_bool(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_706])]) ).

tff(f5278,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
      | hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,sK120(X0))))
      | ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f3979]) ).

tff(f3979,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
      | ( ~ hBOOL(hAPP_nat_bool(X0,sK120(X0)))
        & hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,sK120(X0)))) )
      | ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK120])],[f2899,f3978]) ).

tff(f3978,plain,
    ! [X0: fun_nat_bool] :
      ( ? [X2: nat] :
          ( ~ hBOOL(hAPP_nat_bool(X0,X2))
          & hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,X2))) )
     => ( ~ hBOOL(hAPP_nat_bool(X0,sK120(X0)))
        & hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,sK120(X0)))) ) ),
    introduced(choice_axiom,[]) ).

tff(f2899,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
      | ? [X2: nat] :
          ( ~ hBOOL(hAPP_nat_bool(X0,X2))
          & hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,X2))) )
      | ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
    inference(flattening,[],[f2898]) ).

tff(f2898,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
      | ? [X2: nat] :
          ( ~ hBOOL(hAPP_nat_bool(X0,X2))
          & hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,X2))) )
      | ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
    inference(ennf_transformation,[],[f1835]) ).

tff(f1835,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_nat_bool(X0,X1))
     => ( ! [X2: nat] :
            ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(suc,X2)))
           => hBOOL(hAPP_nat_bool(X0,X2)) )
       => hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ) ),
    inference(rectify,[],[f975]) ).

tff(f975,axiom,
    ! [X10: fun_nat_bool,X13: nat] :
      ( hBOOL(hAPP_nat_bool(X10,X13))
     => ( ! [X26: nat] :
            ( hBOOL(hAPP_nat_bool(X10,hAPP_nat_nat(suc,X26)))
           => hBOOL(hAPP_nat_bool(X10,X26)) )
       => hBOOL(hAPP_nat_bool(X10,zero_zero_nat)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_974_zero__induct) ).

tff(f14169,plain,
    ( spl250_705
    | ~ spl250_241
    | ~ spl250_667 ),
    inference(avatar_split_clause,[],[f13764,f12716,f8789,f14167]) ).

tff(f14167,plain,
    ( spl250_705
  <=> ! [X0: fun_int_bool,X1: int] : sP22(X0,X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_705])]) ).

tff(f8789,plain,
    ( spl250_241
  <=> ! [X0: fun_int_bool,X1: int] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_241])]) ).

tff(f13764,plain,
    ( ! [X0: fun_int_bool,X1: int] : sP22(X0,X0,X1)
    | ~ spl250_241
    | ~ spl250_667 ),
    inference(resolution,[],[f12717,f8790]) ).

tff(f8790,plain,
    ( ! [X0: fun_int_bool,X1: int] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0)))
    | ~ spl250_241 ),
    inference(avatar_component_clause,[],[f8789]) ).

tff(f14165,plain,
    spl250_704,
    inference(avatar_split_clause,[],[f5277,f14163]) ).

tff(f14163,plain,
    ( spl250_704
  <=> ! [X0: nat,X1: fun_nat_bool] :
        ( hBOOL(hAPP_nat_bool(X1,X0))
        | ~ hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK119(X1))))
        | ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_704])]) ).

tff(f5277,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(X1,X0))
      | ~ hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK119(X1))))
      | ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
    inference(cnf_transformation,[],[f3977]) ).

tff(f3977,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(X1,X0))
      | ( ~ hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK119(X1))))
        & hBOOL(hAPP_nat_bool(X1,sK119(X1))) )
      | ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK119])],[f2897,f3976]) ).

tff(f3976,plain,
    ! [X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( ~ hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,X2)))
          & hBOOL(hAPP_nat_bool(X1,X2)) )
     => ( ~ hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,sK119(X1))))
        & hBOOL(hAPP_nat_bool(X1,sK119(X1))) ) ),
    introduced(choice_axiom,[]) ).

tff(f2897,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(X1,X0))
      | ? [X2: nat] :
          ( ~ hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,X2)))
          & hBOOL(hAPP_nat_bool(X1,X2)) )
      | ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
    inference(flattening,[],[f2896]) ).

tff(f2896,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(X1,X0))
      | ? [X2: nat] :
          ( ~ hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,X2)))
          & hBOOL(hAPP_nat_bool(X1,X2)) )
      | ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
    inference(ennf_transformation,[],[f1834]) ).

tff(f1834,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
     => ( ! [X2: nat] :
            ( hBOOL(hAPP_nat_bool(X1,X2))
           => hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,X2))) )
       => hBOOL(hAPP_nat_bool(X1,X0)) ) ),
    inference(rectify,[],[f977]) ).

tff(f977,axiom,
    ! [X14: nat,X10: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(X10,zero_zero_nat))
     => ( ! [X26: nat] :
            ( hBOOL(hAPP_nat_bool(X10,X26))
           => hBOOL(hAPP_nat_bool(X10,hAPP_nat_nat(suc,X26))) )
       => hBOOL(hAPP_nat_bool(X10,X14)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_976_nat__induct) ).

tff(f14161,plain,
    spl250_703,
    inference(avatar_split_clause,[],[f5000,f14159]) ).

tff(f14159,plain,
    ( spl250_703
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_703])]) ).

tff(f5000,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f2624]) ).

tff(f2624,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | ( X0 = X1 ) ),
    inference(flattening,[],[f2623]) ).

tff(f2623,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | ( X0 = X1 ) ),
    inference(ennf_transformation,[],[f1636]) ).

tff(f1636,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 != X1 )
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0)) ) ),
    inference(rectify,[],[f861]) ).

tff(f861,axiom,
    ! [X15: nat,X16: nat] :
      ( ( X15 != X16 )
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X16))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X16),X15)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_860_linorder__neqE__nat) ).

tff(f14157,plain,
    spl250_702,
    inference(avatar_split_clause,[],[f4995,f14155]) ).

tff(f14155,plain,
    ( spl250_702
  <=> ! [X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
        | ( X0 = X1 )
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_702])]) ).

tff(f4995,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ( X0 = X1 )
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f1631]) ).

tff(f1631,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X0))
      | ( X0 = X1 )
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(rectify,[],[f1050]) ).

tff(f1050,axiom,
    ! [X15: int,X16: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X16),X15))
      | ( X15 = X16 )
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X15),X16)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1049_zless__linear) ).

tff(f14153,plain,
    spl250_701,
    inference(avatar_split_clause,[],[f4957,f14151]) ).

tff(f14151,plain,
    ( spl250_701
  <=> ! [X0: fun_a_bool,X1: x_a] :
        ( ( bot_bot_fun_a_bool = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),X0)) )
        | hBOOL(hAPP_a_bool(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_701])]) ).

tff(f4957,plain,
    ! [X0: fun_a_bool,X1: x_a] :
      ( ( bot_bot_fun_a_bool = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),X0)) )
      | hBOOL(hAPP_a_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f2616]) ).

tff(f14149,plain,
    spl250_700,
    inference(avatar_split_clause,[],[f4916,f14147]) ).

tff(f14147,plain,
    ( spl250_700
  <=> ! [X0: nat,X1: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(suc,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_700])]) ).

tff(f4916,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(suc,X1)) ),
    inference(cnf_transformation,[],[f1564]) ).

tff(f1564,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),hAPP_nat_nat(suc,X1)) ),
    inference(rectify,[],[f820]) ).

tff(f820,axiom,
    ! [X12: nat,X11: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X12),hAPP_nat_nat(suc,X11)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X12),X11)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_819_add__Suc__right) ).

tff(f14145,plain,
    spl250_699,
    inference(avatar_split_clause,[],[f4915,f14143]) ).

tff(f14143,plain,
    ( spl250_699
  <=> ! [X0: nat,X1: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_699])]) ).

tff(f4915,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X0)),X1) ),
    inference(cnf_transformation,[],[f1563]) ).

tff(f1563,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X0)),X1) ),
    inference(rectify,[],[f821]) ).

tff(f821,axiom,
    ! [X12: nat,X11: nat] : ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X12),X11)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X12)),X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_820_add__Suc) ).

tff(f14141,plain,
    spl250_698,
    inference(avatar_split_clause,[],[f4914,f14139]) ).

tff(f14139,plain,
    ( spl250_698
  <=> ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_698])]) ).

tff(f4914,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)) ),
    inference(cnf_transformation,[],[f1562]) ).

tff(f1562,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X0)),hAPP_nat_nat(suc,X1)) ),
    inference(rectify,[],[f173]) ).

tff(f173,axiom,
    ! [X12: nat,X11: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X12),X11) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X12)),hAPP_nat_nat(suc,X11)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_diff__Suc__Suc) ).

tff(f14137,plain,
    spl250_697,
    inference(avatar_split_clause,[],[f4913,f14135]) ).

tff(f14135,plain,
    ( spl250_697
  <=> ! [X0: x_a,X1: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_697])]) ).

tff(f4913,plain,
    ! [X0: x_a,X1: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)) ),
    inference(cnf_transformation,[],[f1561]) ).

tff(f1561,plain,
    ! [X0: x_a,X1: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)) ),
    inference(rectify,[],[f383]) ).

tff(f383,axiom,
    ! [X8: x_a,X2: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_insert__absorb2) ).

tff(f14133,plain,
    spl250_696,
    inference(avatar_split_clause,[],[f4729,f14131]) ).

tff(f14131,plain,
    ( spl250_696
  <=> ! [X0: nat] :
        ( ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),one_one_nat)) = X0 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_696])]) ).

tff(f4729,plain,
    ! [X0: nat] :
      ( ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),one_one_nat)) = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f2601]) ).

tff(f2601,plain,
    ! [X0: nat] :
      ( ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),one_one_nat)) = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(ennf_transformation,[],[f1452]) ).

tff(f1452,plain,
    ! [X0: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
     => ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),one_one_nat)) = X0 ) ),
    inference(rectify,[],[f968]) ).

tff(f968,axiom,
    ! [X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X11))
     => ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X11),one_one_nat)) = X11 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_967_Suc__pred_H) ).

tff(f14120,plain,
    spl250_695,
    inference(avatar_split_clause,[],[f4546,f14117]) ).

tff(f14117,plain,
    ( spl250_695
  <=> ( hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_695])]) ).

tff(f4546,plain,
    hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)),
    inference(cnf_transformation,[],[f1306]) ).

tff(f1306,axiom,
    hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).

tff(f13963,plain,
    ( spl250_694
    | ~ spl250_46
    | ~ spl250_665 ),
    inference(avatar_split_clause,[],[f13739,f12708,f7524,f13961]) ).

tff(f13961,plain,
    ( spl250_694
  <=> ! [X0: fun_a_bool,X1: x_a] : sP21(X0,bot_bot_fun_a_bool,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_694])]) ).

tff(f12708,plain,
    ( spl250_665
  <=> ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
        ( sP21(X2,X0,X1)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_665])]) ).

tff(f13739,plain,
    ( ! [X0: fun_a_bool,X1: x_a] : sP21(X0,bot_bot_fun_a_bool,X1)
    | ~ spl250_46
    | ~ spl250_665 ),
    inference(resolution,[],[f12709,f7525]) ).

tff(f12709,plain,
    ( ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))
        | sP21(X2,X0,X1) )
    | ~ spl250_665 ),
    inference(avatar_component_clause,[],[f12708]) ).

tff(f13763,plain,
    ( spl250_693
    | ~ spl250_238
    | ~ spl250_665 ),
    inference(avatar_split_clause,[],[f13738,f12708,f8712,f13761]) ).

tff(f13761,plain,
    ( spl250_693
  <=> ! [X0: fun_a_bool,X1: x_a] : sP21(X0,X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_693])]) ).

tff(f8712,plain,
    ( spl250_238
  <=> ! [X0: fun_a_bool,X1: x_a] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_238])]) ).

tff(f13738,plain,
    ( ! [X0: fun_a_bool,X1: x_a] : sP21(X0,X0,X1)
    | ~ spl250_238
    | ~ spl250_665 ),
    inference(resolution,[],[f12709,f8713]) ).

tff(f8713,plain,
    ( ! [X0: fun_a_bool,X1: x_a] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0)))
    | ~ spl250_238 ),
    inference(avatar_component_clause,[],[f8712]) ).

tff(f13622,plain,
    ( spl250_692
    | ~ spl250_570
    | ~ spl250_668 ),
    inference(avatar_split_clause,[],[f12767,f12720,f11738,f13620]) ).

tff(f11738,plain,
    ( spl250_570
  <=> ! [X2: fun_a_bool,X0: fun_fu554186387l_bool,X1: fun_fun_a_bool_bool] : ( hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f198738859l_bool(X0,X2),hAPP_fun_a_bool_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_570])]) ).

tff(f12720,plain,
    ( spl250_668
  <=> ( fFalse = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_668])]) ).

tff(f12767,plain,
    ( ! [X0: fun_fu554186387l_bool] : ( hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X0,hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g))),image_pname_a(mgt_call,u)) = hAPP_bool_bool(hAPP_f198738859l_bool(X0,image_pname_a(mgt_call,u)),fFalse) )
    | ~ spl250_570
    | ~ spl250_668 ),
    inference(superposition,[],[f11739,f12722]) ).

tff(f12722,plain,
    ( ( fFalse = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u)) )
    | ~ spl250_668 ),
    inference(avatar_component_clause,[],[f12720]) ).

tff(f11739,plain,
    ( ! [X2: fun_a_bool,X0: fun_fu554186387l_bool,X1: fun_fun_a_bool_bool] : ( hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f198738859l_bool(X0,X2),hAPP_fun_a_bool_bool(X1,X2)) )
    | ~ spl250_570 ),
    inference(avatar_component_clause,[],[f11738]) ).

tff(f13089,plain,
    ( spl250_691
    | ~ spl250_363
    | ~ spl250_668 ),
    inference(avatar_split_clause,[],[f12768,f12720,f9662,f13087]) ).

tff(f13087,plain,
    ( spl250_691
  <=> ! [X0: fun_bo1549164019l_bool] : ( hAPP_b589554111l_bool(X0,fFalse) = hAPP_f198738859l_bool(cOMBB_338059395a_bool(X0,hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g))),image_pname_a(mgt_call,u)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_691])]) ).

tff(f9662,plain,
    ( spl250_363
  <=> ! [X2: fun_a_bool,X0: fun_bo1549164019l_bool,X1: fun_fun_a_bool_bool] : ( hAPP_f198738859l_bool(cOMBB_338059395a_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_fun_a_bool_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_363])]) ).

tff(f12768,plain,
    ( ! [X0: fun_bo1549164019l_bool] : ( hAPP_b589554111l_bool(X0,fFalse) = hAPP_f198738859l_bool(cOMBB_338059395a_bool(X0,hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g))),image_pname_a(mgt_call,u)) )
    | ~ spl250_363
    | ~ spl250_668 ),
    inference(superposition,[],[f9663,f12722]) ).

tff(f9663,plain,
    ( ! [X2: fun_a_bool,X0: fun_bo1549164019l_bool,X1: fun_fun_a_bool_bool] : ( hAPP_f198738859l_bool(cOMBB_338059395a_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_fun_a_bool_bool(X1,X2)) )
    | ~ spl250_363 ),
    inference(avatar_component_clause,[],[f9662]) ).

tff(f13016,plain,
    ( spl250_690
    | ~ spl250_66
    | ~ spl250_152
    | ~ spl250_688 ),
    inference(avatar_split_clause,[],[f12895,f12810,f8093,f7608,f13013]) ).

tff(f13013,plain,
    ( spl250_690
  <=> ( fFalse = bot_bot_bool ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_690])]) ).

tff(f12810,plain,
    ( spl250_688
  <=> ( bot_bot_fun_int_bool = cOMBK_bool_int(bot_bot_bool) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_688])]) ).

tff(f12895,plain,
    ( ( fFalse = bot_bot_bool )
    | ~ spl250_66
    | ~ spl250_152
    | ~ spl250_688 ),
    inference(forward_demodulation,[],[f12894,f8094]) ).

tff(f12894,plain,
    ( ! [X0: int] : ( bot_bot_bool = hAPP_int_bool(bot_bot_fun_int_bool,X0) )
    | ~ spl250_66
    | ~ spl250_688 ),
    inference(superposition,[],[f7609,f12812]) ).

tff(f12812,plain,
    ( ( bot_bot_fun_int_bool = cOMBK_bool_int(bot_bot_bool) )
    | ~ spl250_688 ),
    inference(avatar_component_clause,[],[f12810]) ).

tff(f12817,plain,
    spl250_689,
    inference(avatar_split_clause,[],[f7232,f12815]) ).

tff(f12815,plain,
    ( spl250_689
  <=> ! [X2: fun_nat_bool,X0: int,X1: nat] :
        ( ( hAPP_i1948725293t_bool(fequal_int,X0) = image_nat_int(cOMBK_int_nat(X0),X2) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_689])]) ).

tff(f7232,plain,
    ! [X2: fun_nat_bool,X0: int,X1: nat] :
      ( ( hAPP_i1948725293t_bool(fequal_int,X0) = image_nat_int(cOMBK_int_nat(X0),X2) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
    inference(forward_demodulation,[],[f6102,f6930]) ).

tff(f6102,plain,
    ! [X2: fun_nat_bool,X0: int,X1: nat] :
      ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = image_nat_int(cOMBK_int_nat(X0),X2) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f3393]) ).

tff(f3393,plain,
    ! [X0: int,X1: nat,X2: fun_nat_bool] :
      ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = image_nat_int(cOMBK_int_nat(X0),X2) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
    inference(ennf_transformation,[],[f2334]) ).

tff(f2334,plain,
    ! [X0: int,X1: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
     => ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = image_nat_int(cOMBK_int_nat(X0),X2) ) ),
    inference(rectify,[],[f666]) ).

tff(f666,axiom,
    ! [X29: int,X8: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X2))
     => ( image_nat_int(cOMBK_int_nat(X29),X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X29),bot_bot_fun_int_bool) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_665_image__constant) ).

tff(f12813,plain,
    ( spl250_688
    | spl250_58
    | ~ spl250_544 ),
    inference(avatar_split_clause,[],[f12472,f10924,f7572,f12810]) ).

tff(f7572,plain,
    ( spl250_58
  <=> hBOOL(bot_bot_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_58])]) ).

tff(f12472,plain,
    ( ( bot_bot_fun_int_bool = cOMBK_bool_int(bot_bot_bool) )
    | spl250_58
    | ~ spl250_544 ),
    inference(resolution,[],[f10925,f7573]) ).

tff(f7573,plain,
    ( ~ hBOOL(bot_bot_bool)
    | spl250_58 ),
    inference(avatar_component_clause,[],[f7572]) ).

tff(f12808,plain,
    spl250_687,
    inference(avatar_split_clause,[],[f7155,f12806]) ).

tff(f12806,plain,
    ( spl250_687
  <=> ! [X0: nat,X1: nat] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
        | hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X0)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_687])]) ).

tff(f7155,plain,
    ! [X0: nat,X1: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X0)),X1)) ),
    inference(forward_demodulation,[],[f5593,f4670]) ).

tff(f4670,plain,
    ! [X0: nat] : ( hAPP_n1699378549t_bool(ord_less_nat,X0) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)) ),
    inference(cnf_transformation,[],[f1398]) ).

tff(f1398,plain,
    ! [X0: nat] : ( hAPP_n1699378549t_bool(ord_less_nat,X0) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)) ),
    inference(rectify,[],[f914]) ).

tff(f914,axiom,
    ! [X27: nat] : ( hAPP_n1699378549t_bool(ord_less_nat,X27) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_913_less__eq__Suc__le__raw) ).

tff(f5593,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X0)),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1)) ),
    inference(cnf_transformation,[],[f4133]) ).

tff(f4133,plain,
    ! [X0: nat,X1: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
        | ~ hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X0)),X1)) )
      & ( hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X0)),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1)) ) ),
    inference(nnf_transformation,[],[f2024]) ).

tff(f2024,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
    <=> hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X0)),X1)) ),
    inference(rectify,[],[f490]) ).

tff(f490,axiom,
    ! [X22: nat,X14: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X22)),X14))
    <=> hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X22)),X14)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_489_less__eq__nat_Osimps_I2_J) ).

tff(f12804,plain,
    spl250_686,
    inference(avatar_split_clause,[],[f7154,f12802]) ).

tff(f12802,plain,
    ( spl250_686
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
        | ~ hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X0)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_686])]) ).

tff(f7154,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X0)),X1)) ),
    inference(forward_demodulation,[],[f5594,f4670]) ).

tff(f5594,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
      | ~ hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X0)),X1)) ),
    inference(cnf_transformation,[],[f4133]) ).

tff(f12800,plain,
    spl250_685,
    inference(avatar_split_clause,[],[f6938,f12798]) ).

tff(f12798,plain,
    ( spl250_685
  <=> ! [X0: fun_int_bool] : ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,pls)),X0)) = image_nat_int(semiri1621563631at_int,cOMBB_int_bool_nat(X0,semiri1621563631at_int)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_685])]) ).

tff(f6938,plain,
    ! [X0: fun_int_bool] : ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,pls)),X0)) = image_nat_int(semiri1621563631at_int,cOMBB_int_bool_nat(X0,semiri1621563631at_int)) ),
    inference(forward_demodulation,[],[f6583,f4588]) ).

tff(f6583,plain,
    ! [X0: fun_int_bool] : ( image_nat_int(semiri1621563631at_int,collect_nat(cOMBB_int_bool_nat(X0,semiri1621563631at_int))) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,pls)),X0)) ),
    inference(definition_unfolding,[],[f4693,f4550]) ).

tff(f4693,plain,
    ! [X0: fun_int_bool] : ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X0)) = image_nat_int(semiri1621563631at_int,collect_nat(cOMBB_int_bool_nat(X0,semiri1621563631at_int))) ),
    inference(cnf_transformation,[],[f1421]) ).

tff(f1421,plain,
    ! [X0: fun_int_bool] : ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X0)) = image_nat_int(semiri1621563631at_int,collect_nat(cOMBB_int_bool_nat(X0,semiri1621563631at_int))) ),
    inference(rectify,[],[f1118]) ).

tff(f1118,axiom,
    ! [X10: fun_int_bool] : ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X10)) = image_nat_int(semiri1621563631at_int,collect_nat(cOMBB_int_bool_nat(X10,semiri1621563631at_int))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1117_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J) ).

tff(f12793,plain,
    ( spl250_684
    | ~ spl250_103
    | ~ spl250_349
    | ~ spl250_683 ),
    inference(avatar_split_clause,[],[f12789,f12786,f9606,f7825,f12791]) ).

tff(f12791,plain,
    ( spl250_684
  <=> ! [X0: int,X1: int] :
        ( ( pls != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1) )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_684])]) ).

tff(f7825,plain,
    ( spl250_103
  <=> ! [X0: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_103])]) ).

tff(f9606,plain,
    ( spl250_349
  <=> ! [X0: int,X1: int] : ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_349])]) ).

tff(f12786,plain,
    ( spl250_683
  <=> ! [X0: int,X1: int,X3: int] :
        ( ( X0 = X1 )
        | ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_683])]) ).

tff(f12789,plain,
    ( ! [X0: int,X1: int] :
        ( ( pls != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1) )
        | ( X0 = X1 ) )
    | ~ spl250_103
    | ~ spl250_349
    | ~ spl250_683 ),
    inference(forward_demodulation,[],[f12787,f9982]) ).

tff(f9982,plain,
    ( ! [X0: int] : ( pls = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X0) )
    | ~ spl250_103
    | ~ spl250_349 ),
    inference(superposition,[],[f9607,f7826]) ).

tff(f7826,plain,
    ( ! [X0: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),X0) = X0 )
    | ~ spl250_103 ),
    inference(avatar_component_clause,[],[f7825]) ).

tff(f9607,plain,
    ( ! [X0: int,X1: int] : ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),X1) = X0 )
    | ~ spl250_349 ),
    inference(avatar_component_clause,[],[f9606]) ).

tff(f12787,plain,
    ( ! [X3: int,X0: int,X1: int] :
        ( ( X0 = X1 )
        | ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),X3) ) )
    | ~ spl250_683 ),
    inference(avatar_component_clause,[],[f12786]) ).

tff(f12788,plain,
    spl250_683,
    inference(avatar_split_clause,[],[f6898,f12786]) ).

tff(f6898,plain,
    ! [X3: int,X0: int,X1: int] :
      ( ( X0 = X1 )
      | ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),X3) ) ),
    inference(equality_resolution,[],[f6507]) ).

tff(f6507,plain,
    ! [X2: int,X3: int,X0: int,X1: int] :
      ( ( X0 = X1 )
      | ( X2 != X3 )
      | ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X2),X3) ) ),
    inference(cnf_transformation,[],[f4513]) ).

tff(f4513,plain,
    ! [X0: int,X1: int,X2: int,X3: int] :
      ( ( ( ( X0 = X1 )
          | ( X2 != X3 ) )
        & ( ( X2 = X3 )
          | ( X0 != X1 ) ) )
      | ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X2),X3) ) ),
    inference(nnf_transformation,[],[f3664]) ).

tff(f3664,plain,
    ! [X0: int,X1: int,X2: int,X3: int] :
      ( ( ( X0 = X1 )
      <=> ( X2 = X3 ) )
      | ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X2),X3) ) ),
    inference(ennf_transformation,[],[f2558]) ).

tff(f2558,plain,
    ! [X0: int,X1: int,X2: int,X3: int] :
      ( ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X2),X3) )
     => ( ( X0 = X1 )
      <=> ( X2 = X3 ) ) ),
    inference(rectify,[],[f670]) ).

tff(f670,axiom,
    ! [X5: int,X28: int,X29: int,X70: int] :
      ( ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X5),X28) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X29),X70) )
     => ( ( X5 = X28 )
      <=> ( X29 = X70 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_669_diff__eq__diff__eq) ).

tff(f12784,plain,
    spl250_682,
    inference(avatar_split_clause,[],[f6802,f12782]) ).

tff(f12782,plain,
    ( spl250_682
  <=> ! [X2: nat,X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X2))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_682])]) ).

tff(f6802,plain,
    ! [X2: nat,X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X2))))),
    inference(equality_resolution,[],[f5516]) ).

tff(f5516,plain,
    ! [X2: nat,X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
      | ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X2))) != X1 ) ),
    inference(cnf_transformation,[],[f4078]) ).

tff(f12780,plain,
    spl250_681,
    inference(avatar_split_clause,[],[f6685,f12778]) ).

tff(f12778,plain,
    ( spl250_681
  <=> ! [X2: nat,X0: fun_int_bool,X1: nat] :
        ( hBOOL(hAPP_int_bool(X0,pls))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
        | ~ sP24(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_681])]) ).

tff(f6685,plain,
    ! [X2: nat,X0: fun_int_bool,X1: nat] :
      ( hBOOL(hAPP_int_bool(X0,pls))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
      | ~ sP24(X0,X1,X2) ),
    inference(definition_unfolding,[],[f6393,f4550]) ).

tff(f6393,plain,
    ! [X2: nat,X0: fun_int_bool,X1: nat] :
      ( hBOOL(hAPP_int_bool(X0,zero_zero_int))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
      | ~ sP24(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4476]) ).

tff(f12776,plain,
    spl250_680,
    inference(avatar_split_clause,[],[f6684,f12774]) ).

tff(f12774,plain,
    ( spl250_680
  <=> ! [X2: nat,X0: fun_int_bool,X1: nat] :
        ( sP24(X0,X1,X2)
        | ~ hBOOL(hAPP_int_bool(X0,pls))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_680])]) ).

tff(f6684,plain,
    ! [X2: nat,X0: fun_int_bool,X1: nat] :
      ( sP24(X0,X1,X2)
      | ~ hBOOL(hAPP_int_bool(X0,pls))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(definition_unfolding,[],[f6396,f4550]) ).

tff(f6396,plain,
    ! [X2: nat,X0: fun_int_bool,X1: nat] :
      ( sP24(X0,X1,X2)
      | ~ hBOOL(hAPP_int_bool(X0,zero_zero_int))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f4476]) ).

tff(f12772,plain,
    spl250_679,
    inference(avatar_split_clause,[],[f6680,f12770]) ).

tff(f12770,plain,
    ( spl250_679
  <=> ! [X2: bool,X0: bool,X1: int] :
        ( hBOOL(X0)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
        | ~ hBOOL(X2)
        | ~ sP16(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_679])]) ).

tff(f6680,plain,
    ! [X2: bool,X0: bool,X1: int] :
      ( hBOOL(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(X2)
      | ~ sP16(X0,X1,X2) ),
    inference(definition_unfolding,[],[f6256,f4550]) ).

tff(f6256,plain,
    ! [X2: bool,X0: bool,X1: int] :
      ( hBOOL(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(X2)
      | ~ sP16(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4368]) ).

tff(f4368,plain,
    ! [X0: bool,X1: int,X2: bool] :
      ( ( ( hBOOL(X2)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
          | ( ~ hBOOL(X0)
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) )
        & ( hBOOL(X0)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
          | ( ~ hBOOL(X2)
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) ) )
      | ~ sP16(X0,X1,X2) ),
    inference(rectify,[],[f4367]) ).

tff(f4367,plain,
    ! [X0: bool,X2: int,X1: bool] :
      ( ( ( hBOOL(X1)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
          | ( ~ hBOOL(X0)
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
        & ( hBOOL(X0)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
          | ( ~ hBOOL(X1)
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ) )
      | ~ sP16(X0,X2,X1) ),
    inference(flattening,[],[f4366]) ).

tff(f4366,plain,
    ! [X0: bool,X2: int,X1: bool] :
      ( ( ( hBOOL(X1)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
          | ( ~ hBOOL(X0)
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
        & ( hBOOL(X0)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
          | ( ~ hBOOL(X1)
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ) )
      | ~ sP16(X0,X2,X1) ),
    inference(nnf_transformation,[],[f3715]) ).

tff(f3715,plain,
    ! [X0: bool,X2: int,X1: bool] :
      ( ( ( hBOOL(X1)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
      <=> ( hBOOL(X0)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
      | ~ sP16(X0,X2,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).

tff(f12763,plain,
    spl250_678,
    inference(avatar_split_clause,[],[f6678,f12761]) ).

tff(f12761,plain,
    ( spl250_678
  <=> ! [X2: bool,X0: bool,X1: int] :
        ( hBOOL(X2)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
        | ~ hBOOL(X0)
        | ~ sP16(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_678])]) ).

tff(f6678,plain,
    ! [X2: bool,X0: bool,X1: int] :
      ( hBOOL(X2)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ hBOOL(X0)
      | ~ sP16(X0,X1,X2) ),
    inference(definition_unfolding,[],[f6258,f4550]) ).

tff(f6258,plain,
    ! [X2: bool,X0: bool,X1: int] :
      ( hBOOL(X2)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ hBOOL(X0)
      | ~ sP16(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4368]) ).

tff(f12759,plain,
    spl250_677,
    inference(avatar_split_clause,[],[f6675,f12757]) ).

tff(f12757,plain,
    ( spl250_677
  <=> ! [X2: bool,X0: bool,X1: int] :
        ( hBOOL(X0)
        | ~ hBOOL(X2)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
        | ~ sP15(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_677])]) ).

tff(f6675,plain,
    ! [X2: bool,X0: bool,X1: int] :
      ( hBOOL(X0)
      | ~ hBOOL(X2)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ sP15(X0,X1,X2) ),
    inference(definition_unfolding,[],[f6249,f4550]) ).

tff(f6249,plain,
    ! [X2: bool,X0: bool,X1: int] :
      ( hBOOL(X0)
      | ~ hBOOL(X2)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ sP15(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4363]) ).

tff(f4363,plain,
    ! [X0: bool,X1: int,X2: bool] :
      ( ( ( ( hBOOL(X2)
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
          | ~ hBOOL(X0)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
        & ( ( hBOOL(X0)
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
          | ~ hBOOL(X2)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) )
      | ~ sP15(X0,X1,X2) ),
    inference(rectify,[],[f4362]) ).

tff(f4362,plain,
    ! [X0: bool,X2: int,X1: bool] :
      ( ( ( ( hBOOL(X1)
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
          | ~ hBOOL(X0)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
        & ( ( hBOOL(X0)
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
          | ~ hBOOL(X1)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
      | ~ sP15(X0,X2,X1) ),
    inference(flattening,[],[f4361]) ).

tff(f4361,plain,
    ! [X0: bool,X2: int,X1: bool] :
      ( ( ( ( hBOOL(X1)
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
          | ~ hBOOL(X0)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
        & ( ( hBOOL(X0)
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
          | ~ hBOOL(X1)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
      | ~ sP15(X0,X2,X1) ),
    inference(nnf_transformation,[],[f3713]) ).

tff(f3713,plain,
    ! [X0: bool,X2: int,X1: bool] :
      ( ( ( hBOOL(X1)
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
      <=> ( hBOOL(X0)
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
      | ~ sP15(X0,X2,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).

tff(f12755,plain,
    spl250_676,
    inference(avatar_split_clause,[],[f6673,f12753]) ).

tff(f12753,plain,
    ( spl250_676
  <=> ! [X2: bool,X0: bool,X1: int] :
        ( hBOOL(X2)
        | ~ hBOOL(X0)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
        | ~ sP15(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_676])]) ).

tff(f6673,plain,
    ! [X2: bool,X0: bool,X1: int] :
      ( hBOOL(X2)
      | ~ hBOOL(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
      | ~ sP15(X0,X1,X2) ),
    inference(definition_unfolding,[],[f6251,f4550]) ).

tff(f6251,plain,
    ! [X2: bool,X0: bool,X1: int] :
      ( hBOOL(X2)
      | ~ hBOOL(X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
      | ~ sP15(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4363]) ).

tff(f12751,plain,
    spl250_675,
    inference(avatar_split_clause,[],[f6620,f12749]) ).

tff(f12749,plain,
    ( spl250_675
  <=> ! [X0: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_675])]) ).

tff(f6620,plain,
    ! [X0: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,X0))) ),
    inference(definition_unfolding,[],[f4839,f4550]) ).

tff(f4839,plain,
    ! [X0: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X0))) ),
    inference(cnf_transformation,[],[f3857]) ).

tff(f3857,plain,
    ! [X0: nat] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X0)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X0))) ) ),
    inference(nnf_transformation,[],[f1503]) ).

tff(f1503,plain,
    ! [X0: nat] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X0)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(rectify,[],[f1127]) ).

tff(f1127,axiom,
    ! [X14: nat] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X14)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X14)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1126_zero__less__int__conv) ).

tff(f12747,plain,
    spl250_674,
    inference(avatar_split_clause,[],[f6619,f12745]) ).

tff(f12745,plain,
    ( spl250_674
  <=> ! [X0: nat] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,X0)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_674])]) ).

tff(f6619,plain,
    ! [X0: nat] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(definition_unfolding,[],[f4840,f4550]) ).

tff(f4840,plain,
    ! [X0: nat] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X0)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f3857]) ).

tff(f12743,plain,
    spl250_673,
    inference(avatar_split_clause,[],[f6399,f12741]) ).

tff(f6399,plain,
    ! [X2: nat,X0: fun_int_bool,X1: nat] :
      ( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))))
      | ~ sP24(X0,X2,X1) ),
    inference(cnf_transformation,[],[f4477]) ).

tff(f4477,plain,
    ! [X0: fun_int_bool,X1: nat,X2: nat] :
      ( ( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))))
        | ~ sP24(X0,X2,X1) )
      & ( sP24(X0,X2,X1)
        | ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))) ) ),
    inference(nnf_transformation,[],[f3732]) ).

tff(f3732,plain,
    ! [X0: fun_int_bool,X1: nat,X2: nat] :
      ( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))))
    <=> sP24(X0,X2,X1) ),
    inference(definition_folding,[],[f3593,f3731]) ).

tff(f3593,plain,
    ! [X0: fun_int_bool,X1: nat,X2: nat] :
      ( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))))
    <=> ( ( hBOOL(hAPP_int_bool(X0,zero_zero_int))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
        & ( hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ) ) ),
    inference(ennf_transformation,[],[f2494]) ).

tff(f2494,plain,
    ! [X0: fun_int_bool,X1: nat,X2: nat] :
      ( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))))
    <=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
         => hBOOL(hAPP_int_bool(X0,zero_zero_int)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
         => hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))) ) ) ),
    inference(rectify,[],[f1130]) ).

tff(f1130,axiom,
    ! [X10: fun_int_bool,X8: nat,X36: nat] :
      ( hBOOL(hAPP_int_bool(X10,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X8),X36))))
    <=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X8),X36))
         => hBOOL(hAPP_int_bool(X10,zero_zero_int)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X36),X8))
         => hBOOL(hAPP_int_bool(X10,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X8)),hAPP_nat_int(semiri1621563631at_int,X36)))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1129_zdiff__int__split) ).

tff(f12739,plain,
    spl250_672,
    inference(avatar_split_clause,[],[f6398,f12737]) ).

tff(f6398,plain,
    ! [X2: nat,X0: fun_int_bool,X1: nat] :
      ( sP24(X0,X2,X1)
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))) ),
    inference(cnf_transformation,[],[f4477]) ).

tff(f12735,plain,
    spl250_671,
    inference(avatar_split_clause,[],[f6388,f12733]) ).

tff(f12733,plain,
    ( spl250_671
  <=> ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))
        | ~ sP23(X2,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_671])]) ).

tff(f6388,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))
      | ~ sP23(X2,X0,X1) ),
    inference(cnf_transformation,[],[f4471]) ).

tff(f4471,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))
        | ~ sP23(X2,X0,X1) )
      & ( sP23(X2,X0,X1)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))) ) ),
    inference(nnf_transformation,[],[f3730]) ).

tff(f3730,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))
    <=> sP23(X2,X0,X1) ),
    inference(definition_folding,[],[f3592,f3729]) ).

tff(f3592,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))
    <=> ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X2))
          | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) )
        & ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))),X2))
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) ) ) ),
    inference(ennf_transformation,[],[f2492]) ).

tff(f2492,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))
    <=> ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X2)) )
        & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))),X2)) ) ) ),
    inference(rectify,[],[f568]) ).

tff(f568,axiom,
    ! [X2: fun_nat_bool,X8: nat,X7: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X7)))
    <=> ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X2))
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X7)) )
        & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X2))
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),bot_bot_fun_nat_bool))),X7)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_567_subset__insert__iff) ).

tff(f12731,plain,
    spl250_670,
    inference(avatar_split_clause,[],[f6387,f12729]) ).

tff(f6387,plain,
    ! [X2: fun_nat_bool,X0: fun_nat_bool,X1: nat] :
      ( sP23(X2,X0,X1)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))) ),
    inference(cnf_transformation,[],[f4471]) ).

tff(f12727,plain,
    spl250_669,
    inference(avatar_split_clause,[],[f6371,f12725]) ).

tff(f12725,plain,
    ( spl250_669
  <=> ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))
        | ~ sP22(X2,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_669])]) ).

tff(f6371,plain,
    ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))
      | ~ sP22(X2,X0,X1) ),
    inference(cnf_transformation,[],[f4461]) ).

tff(f4461,plain,
    ! [X0: fun_int_bool,X1: int,X2: fun_int_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))
        | ~ sP22(X2,X0,X1) )
      & ( sP22(X2,X0,X1)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))) ) ),
    inference(nnf_transformation,[],[f3728]) ).

tff(f3728,plain,
    ! [X0: fun_int_bool,X1: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))
    <=> sP22(X2,X0,X1) ),
    inference(definition_folding,[],[f3591,f3727]) ).

tff(f3591,plain,
    ! [X0: fun_int_bool,X1: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))
    <=> ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X2))
          | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) )
        & ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))),X2))
          | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) ) ) ),
    inference(ennf_transformation,[],[f2488]) ).

tff(f2488,plain,
    ! [X0: fun_int_bool,X1: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))
    <=> ( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
         => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X2)) )
        & ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
         => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))),X2)) ) ) ),
    inference(rectify,[],[f567]) ).

tff(f567,axiom,
    ! [X2: fun_int_bool,X8: int,X7: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X7)))
    <=> ( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X2))
         => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X7)) )
        & ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X2))
         => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),bot_bot_fun_int_bool))),X7)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_566_subset__insert__iff) ).

tff(f12723,plain,
    ( spl250_668
    | ~ spl250_66
    | ~ spl250_152
    | ~ spl250_647 ),
    inference(avatar_split_clause,[],[f12678,f12632,f8093,f7608,f12720]) ).

tff(f12632,plain,
    ( spl250_647
  <=> ( bot_bot_fun_int_bool = cOMBK_bool_int(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_647])]) ).

tff(f12678,plain,
    ( ( fFalse = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u)) )
    | ~ spl250_66
    | ~ spl250_152
    | ~ spl250_647 ),
    inference(forward_demodulation,[],[f12677,f8094]) ).

tff(f12677,plain,
    ( ! [X0: int] : ( hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u)) = hAPP_int_bool(bot_bot_fun_int_bool,X0) )
    | ~ spl250_66
    | ~ spl250_647 ),
    inference(superposition,[],[f7609,f12634]) ).

tff(f12634,plain,
    ( ( bot_bot_fun_int_bool = cOMBK_bool_int(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))) )
    | ~ spl250_647 ),
    inference(avatar_component_clause,[],[f12632]) ).

tff(f12718,plain,
    spl250_667,
    inference(avatar_split_clause,[],[f6370,f12716]) ).

tff(f6370,plain,
    ! [X2: fun_int_bool,X0: fun_int_bool,X1: int] :
      ( sP22(X2,X0,X1)
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))) ),
    inference(cnf_transformation,[],[f4461]) ).

tff(f12714,plain,
    spl250_666,
    inference(avatar_split_clause,[],[f6354,f12712]) ).

tff(f12712,plain,
    ( spl250_666
  <=> ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))
        | ~ sP21(X2,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_666])]) ).

tff(f6354,plain,
    ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))
      | ~ sP21(X2,X0,X1) ),
    inference(cnf_transformation,[],[f4451]) ).

tff(f4451,plain,
    ! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))
        | ~ sP21(X2,X0,X1) )
      & ( sP21(X2,X0,X1)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))) ) ),
    inference(nnf_transformation,[],[f3726]) ).

tff(f3726,plain,
    ! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))
    <=> sP21(X2,X0,X1) ),
    inference(definition_folding,[],[f3590,f3725]) ).

tff(f3590,plain,
    ! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))
    <=> ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X2))
          | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) )
        & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))),X2))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) ) ) ),
    inference(ennf_transformation,[],[f2484]) ).

tff(f2484,plain,
    ! [X0: fun_a_bool,X1: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))
    <=> ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
         => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X2)) )
        & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
         => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))),X2)) ) ) ),
    inference(rectify,[],[f566]) ).

tff(f566,axiom,
    ! [X2: fun_a_bool,X8: x_a,X7: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X7)))
    <=> ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X2))
         => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7)) )
        & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X2))
         => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),bot_bot_fun_a_bool))),X7)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_565_subset__insert__iff) ).

tff(f12710,plain,
    spl250_665,
    inference(avatar_split_clause,[],[f6353,f12708]) ).

tff(f6353,plain,
    ! [X2: fun_a_bool,X0: fun_a_bool,X1: x_a] :
      ( sP21(X2,X0,X1)
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))) ),
    inference(cnf_transformation,[],[f4451]) ).

tff(f12706,plain,
    spl250_664,
    inference(avatar_split_clause,[],[f6331,f12704]) ).

tff(f12704,plain,
    ( spl250_664
  <=> ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))
        | ~ sP20(X2,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_664])]) ).

tff(f6331,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))
      | ~ sP20(X2,X0,X1) ),
    inference(cnf_transformation,[],[f4437]) ).

tff(f4437,plain,
    ! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))
        | ~ sP20(X2,X0,X1) )
      & ( sP20(X2,X0,X1)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))) ) ),
    inference(nnf_transformation,[],[f3724]) ).

tff(f3724,plain,
    ! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))
    <=> sP20(X2,X0,X1) ),
    inference(definition_folding,[],[f3589,f3723]) ).

tff(f3589,plain,
    ! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))
    <=> ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X2))
          | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool))),X2))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) ) ) ),
    inference(ennf_transformation,[],[f2478]) ).

tff(f2478,plain,
    ! [X0: fun_pname_bool,X1: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))
    <=> ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
         => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X2)) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
         => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool))),X2)) ) ) ),
    inference(rectify,[],[f569]) ).

tff(f569,axiom,
    ! [X2: fun_pname_bool,X8: pname,X7: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),X7)))
    <=> ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X2))
         => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X7)) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X2))
         => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),bot_bo844097828e_bool))),X7)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_568_subset__insert__iff) ).

tff(f12702,plain,
    spl250_663,
    inference(avatar_split_clause,[],[f6330,f12700]) ).

tff(f6330,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
      ( sP20(X2,X0,X1)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))) ),
    inference(cnf_transformation,[],[f4437]) ).

tff(f12698,plain,
    spl250_662,
    inference(avatar_split_clause,[],[f6314,f12696]) ).

tff(f12696,plain,
    ( spl250_662
  <=> ! [X2: nat,X0: fun_nat_bool,X1: nat] :
        ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
        | ~ sP19(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_662])]) ).

tff(f6314,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ sP19(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4431]) ).

tff(f12694,plain,
    spl250_661,
    inference(avatar_split_clause,[],[f6306,f12692]) ).

tff(f12692,plain,
    ( spl250_661
  <=> ! [X2: nat,X0: fun_nat_bool,X1: nat] :
        ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
        | ~ sP18(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_661])]) ).

tff(f6306,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
      | ~ sP18(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4425]) ).

tff(f12690,plain,
    spl250_660,
    inference(avatar_split_clause,[],[f6229,f12688]) ).

tff(f12688,plain,
    ( spl250_660
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( X0 = X2 )
        | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_660])]) ).

tff(f6229,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( X0 = X2 )
      | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1) ) ),
    inference(cnf_transformation,[],[f3539]) ).

tff(f3539,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( X0 = X2 )
      | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1) ) ),
    inference(ennf_transformation,[],[f2439]) ).

tff(f2439,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1) )
     => ( X0 = X2 ) ),
    inference(rectify,[],[f798]) ).

tff(f798,axiom,
    ! [X92: nat,X93: nat,X94: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X92),X93) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X94),X93) )
     => ( X92 = X94 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_797_add__right__imp__eq) ).

tff(f12686,plain,
    spl250_659,
    inference(avatar_split_clause,[],[f6227,f12684]) ).

tff(f12684,plain,
    ( spl250_659
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( X1 = X2 )
        | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_659])]) ).

tff(f6227,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( X1 = X2 )
      | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2) ) ),
    inference(cnf_transformation,[],[f3537]) ).

tff(f3537,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( X1 = X2 )
      | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2) ) ),
    inference(ennf_transformation,[],[f2437]) ).

tff(f2437,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X2) )
     => ( X1 = X2 ) ),
    inference(rectify,[],[f796]) ).

tff(f796,axiom,
    ! [X89: nat,X90: nat,X91: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X89),X90) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X89),X91) )
     => ( X90 = X91 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_795_add__imp__eq) ).

tff(f12682,plain,
    spl250_658,
    inference(avatar_split_clause,[],[f6225,f12680]) ).

tff(f12680,plain,
    ( spl250_658
  <=> ! [X2: int,X0: int,X1: int] :
        ( ( X1 = X2 )
        | ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_658])]) ).

tff(f6225,plain,
    ! [X2: int,X0: int,X1: int] :
      ( ( X1 = X2 )
      | ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2) ) ),
    inference(cnf_transformation,[],[f3535]) ).

tff(f3535,plain,
    ! [X0: int,X1: int,X2: int] :
      ( ( X1 = X2 )
      | ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2) ) ),
    inference(ennf_transformation,[],[f2435]) ).

tff(f2435,plain,
    ! [X0: int,X1: int,X2: int] :
      ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X2) )
     => ( X1 = X2 ) ),
    inference(rectify,[],[f795]) ).

tff(f795,axiom,
    ! [X89: int,X90: int,X91: int] :
      ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X89),X90) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X89),X91) )
     => ( X90 = X91 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_794_add__imp__eq) ).

tff(f12675,plain,
    spl250_657,
    inference(avatar_split_clause,[],[f6224,f12673]) ).

tff(f12673,plain,
    ( spl250_657
  <=> ! [X2: int,X0: int,X1: int] :
        ( ( X0 = X2 )
        | ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_657])]) ).

tff(f6224,plain,
    ! [X2: int,X0: int,X1: int] :
      ( ( X0 = X2 )
      | ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X1) ) ),
    inference(cnf_transformation,[],[f3534]) ).

tff(f3534,plain,
    ! [X0: int,X1: int,X2: int] :
      ( ( X0 = X2 )
      | ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X1) ) ),
    inference(ennf_transformation,[],[f2434]) ).

tff(f2434,plain,
    ! [X0: int,X1: int,X2: int] :
      ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X1) )
     => ( X0 = X2 ) ),
    inference(rectify,[],[f797]) ).

tff(f797,axiom,
    ! [X92: int,X93: int,X94: int] :
      ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X92),X93) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X94),X93) )
     => ( X92 = X94 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_796_add__right__imp__eq) ).

tff(f12671,plain,
    spl250_656,
    inference(avatar_split_clause,[],[f5778,f12669]) ).

tff(f12669,plain,
    ( spl250_656
  <=> ! [X2: bool,X0: nat,X1: nat] :
        ( ( hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X2),X0),X1)) )
        | hBOOL(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_656])]) ).

tff(f5778,plain,
    ! [X2: bool,X0: nat,X1: nat] :
      ( ( hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X2),X0),X1)) )
      | hBOOL(X2) ),
    inference(cnf_transformation,[],[f3067]) ).

tff(f3067,plain,
    ! [X0: nat,X1: nat,X2: bool] :
      ( ( ( hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X2),X0),X1)) )
        | hBOOL(X2) )
      & ( ( hAPP_nat_int(semiri1621563631at_int,X0) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X2),X0),X1)) )
        | ~ hBOOL(X2) ) ),
    inference(ennf_transformation,[],[f2153]) ).

tff(f2153,plain,
    ! [X0: nat,X1: nat,X2: bool] :
      ( ( ~ hBOOL(X2)
       => ( hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X2),X0),X1)) ) )
      & ( hBOOL(X2)
       => ( hAPP_nat_int(semiri1621563631at_int,X0) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X2),X0),X1)) ) ) ),
    inference(rectify,[],[f1139]) ).

tff(f1139,axiom,
    ! [X8: nat,X36: nat,X10: bool] :
      ( ( ~ hBOOL(X10)
       => ( hAPP_nat_int(semiri1621563631at_int,X36) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X10),X8),X36)) ) )
      & ( hBOOL(X10)
       => ( hAPP_nat_int(semiri1621563631at_int,X8) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X10),X8),X36)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1138_int__if__cong) ).

tff(f12667,plain,
    spl250_655,
    inference(avatar_split_clause,[],[f5777,f12665]) ).

tff(f12665,plain,
    ( spl250_655
  <=> ! [X2: bool,X0: nat,X1: nat] :
        ( ( hAPP_nat_int(semiri1621563631at_int,X0) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X2),X0),X1)) )
        | ~ hBOOL(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_655])]) ).

tff(f5777,plain,
    ! [X2: bool,X0: nat,X1: nat] :
      ( ( hAPP_nat_int(semiri1621563631at_int,X0) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X2),X0),X1)) )
      | ~ hBOOL(X2) ),
    inference(cnf_transformation,[],[f3067]) ).

tff(f12663,plain,
    spl250_654,
    inference(avatar_split_clause,[],[f5630,f12661]) ).

tff(f12661,plain,
    ( spl250_654
  <=> ! [X0: fun_a_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_654])]) ).

tff(f5630,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1)))) ),
    inference(cnf_transformation,[],[f4155]) ).

tff(f12659,plain,
    spl250_653,
    inference(avatar_split_clause,[],[f5629,f12657]) ).

tff(f12657,plain,
    ( spl250_653
  <=> ! [X0: fun_a_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_653])]) ).

tff(f5629,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X0),X1)))) ),
    inference(cnf_transformation,[],[f4155]) ).

tff(f12655,plain,
    spl250_652,
    inference(avatar_split_clause,[],[f5627,f12653]) ).

tff(f12653,plain,
    ( spl250_652
  <=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_652])]) ).

tff(f5627,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))) ),
    inference(cnf_transformation,[],[f4153]) ).

tff(f12651,plain,
    spl250_651,
    inference(avatar_split_clause,[],[f5626,f12649]) ).

tff(f12649,plain,
    ( spl250_651
  <=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_651])]) ).

tff(f5626,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X0),X1)))) ),
    inference(cnf_transformation,[],[f4153]) ).

tff(f12647,plain,
    spl250_650,
    inference(avatar_split_clause,[],[f5624,f12645]) ).

tff(f12645,plain,
    ( spl250_650
  <=> ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_650])]) ).

tff(f5624,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))) ),
    inference(cnf_transformation,[],[f4151]) ).

tff(f12643,plain,
    spl250_649,
    inference(avatar_split_clause,[],[f5623,f12641]) ).

tff(f12641,plain,
    ( spl250_649
  <=> ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_649])]) ).

tff(f5623,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X0),X1)))) ),
    inference(cnf_transformation,[],[f4151]) ).

tff(f12639,plain,
    spl250_648,
    inference(avatar_split_clause,[],[f5621,f12637]) ).

tff(f12637,plain,
    ( spl250_648
  <=> ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_648])]) ).

tff(f5621,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))) ),
    inference(cnf_transformation,[],[f4149]) ).

tff(f12635,plain,
    ( spl250_647
    | spl250_7
    | ~ spl250_544 ),
    inference(avatar_split_clause,[],[f12545,f10924,f7344,f12632]) ).

tff(f12545,plain,
    ( ( bot_bot_fun_int_bool = cOMBK_bool_int(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))) )
    | spl250_7
    | ~ spl250_544 ),
    inference(resolution,[],[f10925,f7346]) ).

tff(f12630,plain,
    spl250_646,
    inference(avatar_split_clause,[],[f5620,f12628]) ).

tff(f12628,plain,
    ( spl250_646
  <=> ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_646])]) ).

tff(f5620,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X0),X1)))) ),
    inference(cnf_transformation,[],[f4149]) ).

tff(f12626,plain,
    spl250_645,
    inference(avatar_split_clause,[],[f5618,f12624]) ).

tff(f12624,plain,
    ( spl250_645
  <=> ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_645])]) ).

tff(f5618,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))) ),
    inference(cnf_transformation,[],[f4147]) ).

tff(f12622,plain,
    spl250_644,
    inference(avatar_split_clause,[],[f5617,f12620]) ).

tff(f12620,plain,
    ( spl250_644
  <=> ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_644])]) ).

tff(f5617,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X0),X1)))) ),
    inference(cnf_transformation,[],[f4147]) ).

tff(f12618,plain,
    spl250_643,
    inference(avatar_split_clause,[],[f5615,f12616]) ).

tff(f12616,plain,
    ( spl250_643
  <=> ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X0),X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_643])]) ).

tff(f5615,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X0),X1)))) ),
    inference(cnf_transformation,[],[f4145]) ).

tff(f12614,plain,
    spl250_642,
    inference(avatar_split_clause,[],[f5614,f12612]) ).

tff(f12612,plain,
    ( spl250_642
  <=> ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X0),X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_642])]) ).

tff(f5614,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X0),X1)))) ),
    inference(cnf_transformation,[],[f4145]) ).

tff(f12610,plain,
    spl250_641,
    inference(avatar_split_clause,[],[f5579,f12608]) ).

tff(f12608,plain,
    ( spl250_641
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_641])]) ).

tff(f5579,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ),
    inference(cnf_transformation,[],[f4122]) ).

tff(f4122,plain,
    ! [X0: nat,X1: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ) ),
    inference(nnf_transformation,[],[f2019]) ).

tff(f2019,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(rectify,[],[f903]) ).

tff(f903,axiom,
    ! [X22: nat,X14: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),hAPP_nat_nat(suc,X14)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X14)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_902_less__Suc__eq__le) ).

tff(f12606,plain,
    spl250_640,
    inference(avatar_split_clause,[],[f5487,f12604]) ).

tff(f12604,plain,
    ( spl250_640
  <=> ! [X0: nat,X1: nat] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_640])]) ).

tff(f5487,plain,
    ! [X0: nat,X1: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0))) ),
    inference(cnf_transformation,[],[f4051]) ).

tff(f4051,plain,
    ! [X0: nat,X1: nat] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    inference(nnf_transformation,[],[f1976]) ).

tff(f1976,plain,
    ! [X0: nat,X1: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0))) ),
    inference(rectify,[],[f866]) ).

tff(f866,axiom,
    ! [X22: nat,X14: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X14))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),hAPP_nat_nat(suc,X22))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_865_not__less__eq) ).

tff(f12602,plain,
    spl250_639,
    inference(avatar_split_clause,[],[f5486,f12600]) ).

tff(f12600,plain,
    ( spl250_639
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_639])]) ).

tff(f5486,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X0)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4051]) ).

tff(f12598,plain,
    spl250_638,
    inference(avatar_split_clause,[],[f5430,f12596]) ).

tff(f12596,plain,
    ( spl250_638
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK134(X0,X1)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_638])]) ).

tff(f5430,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK134(X0,X1)),X0)) ),
    inference(cnf_transformation,[],[f4018]) ).

tff(f4018,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK134(X0,X1)),X0))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK134(X0,X1)),X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK134])],[f3064,f4017]) ).

tff(f4017,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK134(X0,X1)),X0))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK134(X0,X1)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3064,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
      | ? [X2: nat] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ) ),
    inference(ennf_transformation,[],[f1958]) ).

tff(f1958,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ! [X2: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) )
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0)) ),
    inference(rectify,[],[f479]) ).

tff(f479,axiom,
    ! [X7: fun_nat_bool,X2: fun_nat_bool] :
      ( ! [X27: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X27),X2))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X27),X7)) )
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_478_subsetI) ).

tff(f12594,plain,
    spl250_637,
    inference(avatar_split_clause,[],[f5429,f12592]) ).

tff(f12592,plain,
    ( spl250_637
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK134(X0,X1)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_637])]) ).

tff(f5429,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X0))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK134(X0,X1)),X1)) ),
    inference(cnf_transformation,[],[f4018]) ).

tff(f12467,plain,
    spl250_636,
    inference(avatar_split_clause,[],[f5428,f12465]) ).

tff(f12465,plain,
    ( spl250_636
  <=> ! [X0: fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK133(X0,X1)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_636])]) ).

tff(f5428,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK133(X0,X1)),X0)) ),
    inference(cnf_transformation,[],[f4016]) ).

tff(f4016,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
      | ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK133(X0,X1)),X0))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK133(X0,X1)),X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK133])],[f3063,f4015]) ).

tff(f4015,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ? [X2: int] :
          ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X0))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) )
     => ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK133(X0,X1)),X0))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK133(X0,X1)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3063,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
      | ? [X2: int] :
          ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X0))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ) ),
    inference(ennf_transformation,[],[f1957]) ).

tff(f1957,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ! [X2: int] :
          ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
         => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X0)) )
     => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0)) ),
    inference(rectify,[],[f478]) ).

tff(f478,axiom,
    ! [X7: fun_int_bool,X2: fun_int_bool] :
      ( ! [X27: int] :
          ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X27),X2))
         => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X27),X7)) )
     => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_477_subsetI) ).

tff(f12463,plain,
    spl250_635,
    inference(avatar_split_clause,[],[f5427,f12461]) ).

tff(f12461,plain,
    ( spl250_635
  <=> ! [X0: fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK133(X0,X1)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_635])]) ).

tff(f5427,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X0))
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK133(X0,X1)),X1)) ),
    inference(cnf_transformation,[],[f4016]) ).

tff(f12459,plain,
    spl250_634,
    inference(avatar_split_clause,[],[f5426,f12457]) ).

tff(f12457,plain,
    ( spl250_634
  <=> ! [X0: fun_a_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK132(X0,X1)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_634])]) ).

tff(f5426,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK132(X0,X1)),X0)) ),
    inference(cnf_transformation,[],[f4014]) ).

tff(f4014,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK132(X0,X1)),X0))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK132(X0,X1)),X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK132])],[f3062,f4013]) ).

tff(f4013,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( ? [X2: x_a] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) )
     => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK132(X0,X1)),X0))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK132(X0,X1)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3062,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
      | ? [X2: x_a] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ) ),
    inference(ennf_transformation,[],[f1956]) ).

tff(f1956,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( ! [X2: x_a] :
          ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
         => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0)) )
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0)) ),
    inference(rectify,[],[f480]) ).

tff(f480,axiom,
    ! [X7: fun_a_bool,X2: fun_a_bool] :
      ( ! [X27: x_a] :
          ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X27),X2))
         => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X27),X7)) )
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_479_subsetI) ).

tff(f12455,plain,
    spl250_633,
    inference(avatar_split_clause,[],[f5425,f12453]) ).

tff(f12453,plain,
    ( spl250_633
  <=> ! [X0: fun_a_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK132(X0,X1)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_633])]) ).

tff(f5425,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X0))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK132(X0,X1)),X1)) ),
    inference(cnf_transformation,[],[f4014]) ).

tff(f12451,plain,
    spl250_632,
    inference(avatar_split_clause,[],[f5424,f12449]) ).

tff(f5424,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK131(X0,X1)),X0)) ),
    inference(cnf_transformation,[],[f4012]) ).

tff(f4012,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK131(X0,X1)),X0))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK131(X0,X1)),X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK131])],[f3061,f4011]) ).

tff(f4011,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( ? [X2: pname] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X0))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) )
     => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK131(X0,X1)),X0))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK131(X0,X1)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3061,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
      | ? [X2: pname] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X0))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ) ),
    inference(ennf_transformation,[],[f1955]) ).

tff(f1955,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( ! [X2: pname] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
         => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X0)) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0)) ),
    inference(rectify,[],[f481]) ).

tff(f481,axiom,
    ! [X7: fun_pname_bool,X2: fun_pname_bool] :
      ( ! [X27: pname] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X27),X2))
         => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X27),X7)) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_480_subsetI) ).

tff(f12447,plain,
    spl250_631,
    inference(avatar_split_clause,[],[f5423,f12445]) ).

tff(f5423,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X0))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK131(X0,X1)),X1)) ),
    inference(cnf_transformation,[],[f4012]) ).

tff(f12443,plain,
    spl250_630,
    inference(avatar_split_clause,[],[f5409,f12441]) ).

tff(f12441,plain,
    ( spl250_630
  <=> ! [X0: fun_a_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X0))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_630])]) ).

tff(f5409,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X0))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0))) ),
    inference(cnf_transformation,[],[f3052]) ).

tff(f3052,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X0))))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0)))
        & ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) ) ),
    inference(ennf_transformation,[],[f1946]) ).

tff(f1946,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X0)))
        | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) )
     => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X0)))) ),
    inference(rectify,[],[f112]) ).

tff(f112,axiom,
    ! [X9: fun_a_bool,X10: fun_a_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X9)))
        | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X10))) )
     => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X10),X9)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_finite__Collect__conjI) ).

tff(f12439,plain,
    spl250_629,
    inference(avatar_split_clause,[],[f5408,f12437]) ).

tff(f12437,plain,
    ( spl250_629
  <=> ! [X0: fun_a_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X0))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_629])]) ).

tff(f5408,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X0))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) ),
    inference(cnf_transformation,[],[f3052]) ).

tff(f12435,plain,
    spl250_628,
    inference(avatar_split_clause,[],[f5407,f12433]) ).

tff(f12433,plain,
    ( spl250_628
  <=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X0))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_628])]) ).

tff(f5407,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X0))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0))) ),
    inference(cnf_transformation,[],[f3051]) ).

tff(f3051,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X0))))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0)))
        & ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) ) ),
    inference(ennf_transformation,[],[f1945]) ).

tff(f1945,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X0)))
        | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) )
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X0)))) ),
    inference(rectify,[],[f117]) ).

tff(f117,axiom,
    ! [X9: fun_pname_bool,X10: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X9)))
        | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X10))) )
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X10),X9)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_finite__Collect__conjI) ).

tff(f12431,plain,
    spl250_627,
    inference(avatar_split_clause,[],[f5406,f12429]) ).

tff(f12429,plain,
    ( spl250_627
  <=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X0))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_627])]) ).

tff(f5406,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X0))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) ),
    inference(cnf_transformation,[],[f3051]) ).

tff(f12427,plain,
    spl250_626,
    inference(avatar_split_clause,[],[f5405,f12425]) ).

tff(f12425,plain,
    ( spl250_626
  <=> ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0))))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_626])]) ).

tff(f5405,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0))))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0))) ),
    inference(cnf_transformation,[],[f3050]) ).

tff(f3050,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0))))
      | ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0)))
        & ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1))) ) ),
    inference(ennf_transformation,[],[f1944]) ).

tff(f1944,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
      ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X0)))
        | hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1))) )
     => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0)))) ),
    inference(rectify,[],[f114]) ).

tff(f114,axiom,
    ! [X9: fun_fu425979586l_bool,X10: fun_fu425979586l_bool] :
      ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X9)))
        | hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X10))) )
     => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X10),X9)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_finite__Collect__conjI) ).

tff(f12423,plain,
    spl250_625,
    inference(avatar_split_clause,[],[f5404,f12421]) ).

tff(f12421,plain,
    ( spl250_625
  <=> ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0))))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_625])]) ).

tff(f5404,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X0))))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1))) ),
    inference(cnf_transformation,[],[f3050]) ).

tff(f12419,plain,
    spl250_624,
    inference(avatar_split_clause,[],[f5403,f12417]) ).

tff(f12417,plain,
    ( spl250_624
  <=> ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X0))))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_624])]) ).

tff(f5403,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X0))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0))) ),
    inference(cnf_transformation,[],[f3049]) ).

tff(f3049,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X0))))
      | ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0)))
        & ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) ) ),
    inference(ennf_transformation,[],[f1943]) ).

tff(f1943,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X0)))
        | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) )
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X0)))) ),
    inference(rectify,[],[f115]) ).

tff(f115,axiom,
    ! [X9: fun_fu1430349052l_bool,X10: fun_fu1430349052l_bool] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X9)))
        | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X10))) )
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X10),X9)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_finite__Collect__conjI) ).

tff(f12415,plain,
    spl250_623,
    inference(avatar_split_clause,[],[f5402,f12413]) ).

tff(f12413,plain,
    ( spl250_623
  <=> ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X0))))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_623])]) ).

tff(f5402,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X0))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) ),
    inference(cnf_transformation,[],[f3049]) ).

tff(f12411,plain,
    spl250_622,
    inference(avatar_split_clause,[],[f5401,f12409]) ).

tff(f12409,plain,
    ( spl250_622
  <=> ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,X1),X0))))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_622])]) ).

tff(f5401,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,X1),X0))))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0))) ),
    inference(cnf_transformation,[],[f3048]) ).

tff(f3048,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,X1),X0))))
      | ( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0)))
        & ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1))) ) ),
    inference(ennf_transformation,[],[f1942]) ).

tff(f1942,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
      ( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X0)))
        | hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1))) )
     => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,X1),X0)))) ),
    inference(rectify,[],[f113]) ).

tff(f113,axiom,
    ! [X9: fun_fu819804446l_bool,X10: fun_fu819804446l_bool] :
      ( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X9)))
        | hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X10))) )
     => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,X10),X9)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_finite__Collect__conjI) ).

tff(f12407,plain,
    spl250_621,
    inference(avatar_split_clause,[],[f5400,f12405]) ).

tff(f12405,plain,
    ( spl250_621
  <=> ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,X1),X0))))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_621])]) ).

tff(f5400,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,X1),X0))))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1))) ),
    inference(cnf_transformation,[],[f3048]) ).

tff(f12403,plain,
    spl250_620,
    inference(avatar_split_clause,[],[f5399,f12401]) ).

tff(f12401,plain,
    ( spl250_620
  <=> ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X0))))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_620])]) ).

tff(f5399,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X0))))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0))) ),
    inference(cnf_transformation,[],[f3047]) ).

tff(f3047,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X0))))
      | ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0)))
        & ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) ) ),
    inference(ennf_transformation,[],[f1941]) ).

tff(f1941,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
      ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X0)))
        | hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) )
     => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X0)))) ),
    inference(rectify,[],[f116]) ).

tff(f116,axiom,
    ! [X9: fun_fun_a_bool_bool,X10: fun_fun_a_bool_bool] :
      ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X9)))
        | hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X10))) )
     => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X10),X9)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_finite__Collect__conjI) ).

tff(f12399,plain,
    spl250_619,
    inference(avatar_split_clause,[],[f5398,f12397]) ).

tff(f12397,plain,
    ( spl250_619
  <=> ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X0))))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_619])]) ).

tff(f5398,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X0))))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) ),
    inference(cnf_transformation,[],[f3047]) ).

tff(f12395,plain,
    spl250_618,
    inference(avatar_split_clause,[],[f5396,f12393]) ).

tff(f12393,plain,
    ( spl250_618
  <=> ! [X0: x_a,X1: x_a] :
        ( ( X0 = X1 )
        | ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_618])]) ).

tff(f5396,plain,
    ! [X0: x_a,X1: x_a] :
      ( ( X0 = X1 )
      | ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool) ) ),
    inference(cnf_transformation,[],[f3045]) ).

tff(f3045,plain,
    ! [X0: x_a,X1: x_a] :
      ( ( X0 = X1 )
      | ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool) ) ),
    inference(ennf_transformation,[],[f1939]) ).

tff(f1939,plain,
    ! [X0: x_a,X1: x_a] :
      ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool) )
     => ( X0 = X1 ) ),
    inference(rectify,[],[f590]) ).

tff(f590,axiom,
    ! [X5: x_a,X28: x_a] :
      ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),bot_bot_fun_a_bool) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X28),bot_bot_fun_a_bool) )
     => ( X5 = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_589_singleton__inject) ).

tff(f12391,plain,
    spl250_617,
    inference(avatar_split_clause,[],[f5395,f12389]) ).

tff(f12389,plain,
    ( spl250_617
  <=> ! [X0: nat,X1: nat] :
        ( ( X0 = X1 )
        | ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_617])]) ).

tff(f5395,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool) ) ),
    inference(cnf_transformation,[],[f3044]) ).

tff(f3044,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool) ) ),
    inference(ennf_transformation,[],[f1938]) ).

tff(f1938,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool) )
     => ( X0 = X1 ) ),
    inference(rectify,[],[f591]) ).

tff(f591,axiom,
    ! [X5: nat,X28: nat] :
      ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5),bot_bot_fun_nat_bool) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X28),bot_bot_fun_nat_bool) )
     => ( X5 = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_590_singleton__inject) ).

tff(f12387,plain,
    ( ~ spl250_616
    | ~ spl250_307
    | ~ spl250_543 ),
    inference(avatar_split_clause,[],[f12340,f10887,f9056,f12384]) ).

tff(f12384,plain,
    ( spl250_616
  <=> sP17(one_one_nat,zero_zero_nat,ord_less_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_616])]) ).

tff(f9056,plain,
    ( spl250_307
  <=> ! [X2: fun_nat_fun_nat_bool,X0: nat,X1: nat] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X2,X1),X0))
        | ~ sP17(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_307])]) ).

tff(f12340,plain,
    ( ~ sP17(one_one_nat,zero_zero_nat,ord_less_nat)
    | ~ spl250_307
    | ~ spl250_543 ),
    inference(resolution,[],[f10889,f9057]) ).

tff(f9057,plain,
    ( ! [X2: fun_nat_fun_nat_bool,X0: nat,X1: nat] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X2,X1),X0))
        | ~ sP17(X0,X1,X2) )
    | ~ spl250_307 ),
    inference(avatar_component_clause,[],[f9056]) ).

tff(f12382,plain,
    spl250_615,
    inference(avatar_split_clause,[],[f5394,f12380]) ).

tff(f12380,plain,
    ( spl250_615
  <=> ! [X0: int,X1: int] :
        ( ( X0 = X1 )
        | ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_615])]) ).

tff(f5394,plain,
    ! [X0: int,X1: int] :
      ( ( X0 = X1 )
      | ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool) ) ),
    inference(cnf_transformation,[],[f3043]) ).

tff(f3043,plain,
    ! [X0: int,X1: int] :
      ( ( X0 = X1 )
      | ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool) ) ),
    inference(ennf_transformation,[],[f1937]) ).

tff(f1937,plain,
    ! [X0: int,X1: int] :
      ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool) )
     => ( X0 = X1 ) ),
    inference(rectify,[],[f592]) ).

tff(f592,axiom,
    ! [X5: int,X28: int] :
      ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5),bot_bot_fun_int_bool) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X28),bot_bot_fun_int_bool) )
     => ( X5 = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_591_singleton__inject) ).

tff(f12378,plain,
    spl250_614,
    inference(avatar_split_clause,[],[f5380,f12376]) ).

tff(f12376,plain,
    ( spl250_614
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_614])]) ).

tff(f5380,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1)) ),
    inference(cnf_transformation,[],[f3027]) ).

tff(f3027,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1)) ),
    inference(ennf_transformation,[],[f1924]) ).

tff(f1924,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X0)),X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(rectify,[],[f875]) ).

tff(f875,axiom,
    ! [X12: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X12)),X11))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),X11)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_874_Suc__lessD) ).

tff(f12374,plain,
    spl250_613,
    inference(avatar_split_clause,[],[f5356,f12372]) ).

tff(f12372,plain,
    ( spl250_613
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_613])]) ).

tff(f5356,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2994]) ).

tff(f2994,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1902]) ).

tff(f1902,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(suc,X1))) ),
    inference(rectify,[],[f167]) ).

tff(f167,axiom,
    ! [X12: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X11))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),hAPP_nat_nat(suc,X11))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_le__SucI) ).

tff(f12370,plain,
    spl250_612,
    inference(avatar_split_clause,[],[f5355,f12368]) ).

tff(f12368,plain,
    ( spl250_612
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_612])]) ).

tff(f5355,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2993]) ).

tff(f2993,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1901]) ).

tff(f1901,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ),
    inference(rectify,[],[f905]) ).

tff(f905,axiom,
    ! [X12: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X11))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),hAPP_nat_nat(suc,X11))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_904_le__imp__less__Suc) ).

tff(f12366,plain,
    spl250_611,
    inference(avatar_split_clause,[],[f5352,f12364]) ).

tff(f12364,plain,
    ( spl250_611
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK123(X0,X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_611])]) ).

tff(f5352,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK123(X0,X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f3992]) ).

tff(f12362,plain,
    spl250_610,
    inference(avatar_split_clause,[],[f5345,f12360]) ).

tff(f12360,plain,
    ( spl250_610
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_610])]) ).

tff(f5345,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2983]) ).

tff(f2983,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1893]) ).

tff(f1893,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X1))) ),
    inference(rectify,[],[f871]) ).

tff(f871,axiom,
    ! [X12: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),X11))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),hAPP_nat_nat(suc,X11))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_870_less__SucI) ).

tff(f12358,plain,
    spl250_609,
    inference(avatar_split_clause,[],[f5270,f12356]) ).

tff(f12356,plain,
    ( spl250_609
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_609])]) ).

tff(f5270,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f2888]) ).

tff(f2888,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(flattening,[],[f2887]) ).

tff(f2887,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(ennf_transformation,[],[f1829]) ).

tff(f1829,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X1))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    inference(rectify,[],[f163]) ).

tff(f163,axiom,
    ! [X2: fun_nat_bool,X7: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X7))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_rev__finite__subset) ).

tff(f12354,plain,
    spl250_608,
    inference(avatar_split_clause,[],[f5227,f12352]) ).

tff(f12352,plain,
    ( spl250_608
  <=> ! [X0: fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_608])]) ).

tff(f5227,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f2848]) ).

tff(f2848,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(flattening,[],[f2847]) ).

tff(f2847,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(ennf_transformation,[],[f1800]) ).

tff(f1800,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X1))
       => hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
    inference(rectify,[],[f164]) ).

tff(f164,axiom,
    ! [X2: fun_int_bool,X7: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X7))
       => hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_rev__finite__subset) ).

tff(f12350,plain,
    spl250_607,
    inference(avatar_split_clause,[],[f5188,f12348]) ).

tff(f12348,plain,
    ( spl250_607
  <=> ! [X0: fun_a_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_607])]) ).

tff(f5188,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(cnf_transformation,[],[f2811]) ).

tff(f2811,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(flattening,[],[f2810]) ).

tff(f2810,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(ennf_transformation,[],[f1774]) ).

tff(f1774,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
    inference(rectify,[],[f161]) ).

tff(f161,axiom,
    ! [X2: fun_a_bool,X7: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X7))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_rev__finite__subset) ).

tff(f12346,plain,
    spl250_606,
    inference(avatar_split_clause,[],[f5144,f12344]) ).

tff(f12344,plain,
    ( spl250_606
  <=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_606])]) ).

tff(f5144,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f2767]) ).

tff(f2767,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(flattening,[],[f2766]) ).

tff(f2766,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(ennf_transformation,[],[f1744]) ).

tff(f1744,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X0),X1))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
    inference(rectify,[],[f162]) ).

tff(f162,axiom,
    ! [X2: fun_pname_bool,X7: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X7))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_rev__finite__subset) ).

tff(f12334,plain,
    spl250_605,
    inference(avatar_split_clause,[],[f5100,f12332]) ).

tff(f12332,plain,
    ( spl250_605
  <=> ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_605])]) ).

tff(f5100,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(cnf_transformation,[],[f2723]) ).

tff(f2723,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(flattening,[],[f2722]) ).

tff(f2722,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(ennf_transformation,[],[f1713]) ).

tff(f1713,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X0),X1))
       => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0)) ) ),
    inference(rectify,[],[f157]) ).

tff(f157,axiom,
    ! [X2: fun_fu819804446l_bool,X7: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X7))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),X7))
       => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_rev__finite__subset) ).

tff(f12330,plain,
    spl250_604,
    inference(avatar_split_clause,[],[f5099,f12328]) ).

tff(f12328,plain,
    ( spl250_604
  <=> ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_604])]) ).

tff(f5099,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(cnf_transformation,[],[f2721]) ).

tff(f2721,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(flattening,[],[f2720]) ).

tff(f2720,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(ennf_transformation,[],[f1712]) ).

tff(f1712,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X0),X1))
       => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ) ),
    inference(rectify,[],[f158]) ).

tff(f158,axiom,
    ! [X2: fun_fu425979586l_bool,X7: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),X7))
       => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_rev__finite__subset) ).

tff(f12326,plain,
    spl250_603,
    inference(avatar_split_clause,[],[f5098,f12324]) ).

tff(f12324,plain,
    ( spl250_603
  <=> ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_603])]) ).

tff(f5098,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(cnf_transformation,[],[f2719]) ).

tff(f2719,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(flattening,[],[f2718]) ).

tff(f2718,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(ennf_transformation,[],[f1711]) ).

tff(f1711,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X0),X1))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ) ),
    inference(rectify,[],[f159]) ).

tff(f159,axiom,
    ! [X2: fun_fu1430349052l_bool,X7: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),X7))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_rev__finite__subset) ).

tff(f12322,plain,
    spl250_602,
    inference(avatar_split_clause,[],[f5097,f12320]) ).

tff(f12320,plain,
    ( spl250_602
  <=> ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_602])]) ).

tff(f5097,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(cnf_transformation,[],[f2717]) ).

tff(f2717,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(flattening,[],[f2716]) ).

tff(f2716,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(ennf_transformation,[],[f1710]) ).

tff(f1710,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X0),X1))
       => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ) ),
    inference(rectify,[],[f160]) ).

tff(f160,axiom,
    ! [X2: fun_fun_a_bool_bool,X7: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),X7))
       => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_rev__finite__subset) ).

tff(f12318,plain,
    spl250_601,
    inference(avatar_split_clause,[],[f5052,f12316]) ).

tff(f12316,plain,
    ( spl250_601
  <=> ! [X0: nat,X1: fun_nat_bool] :
        ( hBOOL(hAPP_nat_bool(X1,sK90(X0,X1)))
        | ~ hBOOL(hAPP_nat_bool(X1,X0))
        | hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_601])]) ).

tff(f5052,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(X1,sK90(X0,X1)))
      | ~ hBOOL(hAPP_nat_bool(X1,X0))
      | hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
    inference(cnf_transformation,[],[f3932]) ).

tff(f12314,plain,
    spl250_600,
    inference(avatar_split_clause,[],[f4955,f12312]) ).

tff(f12312,plain,
    ( spl250_600
  <=> ! [X0: fun_a_bool,X1: x_a] :
        ( ( bot_bot_fun_a_bool = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X1)),X0)) )
        | hBOOL(hAPP_a_bool(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_600])]) ).

tff(f4955,plain,
    ! [X0: fun_a_bool,X1: x_a] :
      ( ( bot_bot_fun_a_bool = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X1)),X0)) )
      | hBOOL(hAPP_a_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f2615]) ).

tff(f12310,plain,
    spl250_599,
    inference(avatar_split_clause,[],[f4692,f12308]) ).

tff(f12308,plain,
    ( spl250_599
  <=> ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_599])]) ).

tff(f4692,plain,
    ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X0)))),
    inference(cnf_transformation,[],[f1420]) ).

tff(f1420,plain,
    ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X0)))),
    inference(rectify,[],[f990]) ).

tff(f990,axiom,
    ! [X12: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X12),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X12),X12)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_989_le__cube) ).

tff(f12306,plain,
    spl250_598,
    inference(avatar_split_clause,[],[f4691,f12304]) ).

tff(f12304,plain,
    ( spl250_598
  <=> ! [X0: fun_nat_bool] : ( hAPP_f22106695ol_nat(the_elem_nat,X0) = hAPP_f22106695ol_nat(the_nat,cOMBB_955900739ol_nat(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),hAPP_f1570313510t_bool(cOMBC_178881787t_bool(insert_nat),bot_bot_fun_nat_bool))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_598])]) ).

tff(f4691,plain,
    ! [X0: fun_nat_bool] : ( hAPP_f22106695ol_nat(the_elem_nat,X0) = hAPP_f22106695ol_nat(the_nat,cOMBB_955900739ol_nat(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),hAPP_f1570313510t_bool(cOMBC_178881787t_bool(insert_nat),bot_bot_fun_nat_bool))) ),
    inference(cnf_transformation,[],[f1419]) ).

tff(f1419,plain,
    ! [X0: fun_nat_bool] : ( hAPP_f22106695ol_nat(the_elem_nat,X0) = hAPP_f22106695ol_nat(the_nat,cOMBB_955900739ol_nat(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),hAPP_f1570313510t_bool(cOMBC_178881787t_bool(insert_nat),bot_bot_fun_nat_bool))) ),
    inference(rectify,[],[f785]) ).

tff(f785,axiom,
    ! [X82: fun_nat_bool] : ( hAPP_f22106695ol_nat(the_elem_nat,X82) = hAPP_f22106695ol_nat(the_nat,cOMBB_955900739ol_nat(hAPP_f103356543l_bool(fequal_fun_nat_bool,X82),hAPP_f1570313510t_bool(cOMBC_178881787t_bool(insert_nat),bot_bot_fun_nat_bool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_784_the__elem__def) ).

tff(f12302,plain,
    spl250_597,
    inference(avatar_split_clause,[],[f4690,f12300]) ).

tff(f12300,plain,
    ( spl250_597
  <=> ! [X0: fun_a_bool] : ( hAPP_fun_a_bool_a(the_elem_a,X0) = hAPP_fun_a_bool_a(the_a,cOMBB_1273333599bool_a(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),hAPP_f1038053735a_bool(cOMBC_394484100a_bool(insert_a),bot_bot_fun_a_bool))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_597])]) ).

tff(f4690,plain,
    ! [X0: fun_a_bool] : ( hAPP_fun_a_bool_a(the_elem_a,X0) = hAPP_fun_a_bool_a(the_a,cOMBB_1273333599bool_a(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),hAPP_f1038053735a_bool(cOMBC_394484100a_bool(insert_a),bot_bot_fun_a_bool))) ),
    inference(cnf_transformation,[],[f1418]) ).

tff(f1418,plain,
    ! [X0: fun_a_bool] : ( hAPP_fun_a_bool_a(the_elem_a,X0) = hAPP_fun_a_bool_a(the_a,cOMBB_1273333599bool_a(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),hAPP_f1038053735a_bool(cOMBC_394484100a_bool(insert_a),bot_bot_fun_a_bool))) ),
    inference(rectify,[],[f784]) ).

tff(f784,axiom,
    ! [X82: fun_a_bool] : ( hAPP_fun_a_bool_a(the_elem_a,X82) = hAPP_fun_a_bool_a(the_a,cOMBB_1273333599bool_a(hAPP_f1631501043l_bool(fequal_fun_a_bool,X82),hAPP_f1038053735a_bool(cOMBC_394484100a_bool(insert_a),bot_bot_fun_a_bool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_783_the__elem__def) ).

tff(f12298,plain,
    spl250_596,
    inference(avatar_split_clause,[],[f4689,f12296]) ).

tff(f12296,plain,
    ( spl250_596
  <=> ! [X0: fun_int_bool] : ( hAPP_f1594865479ol_int(the_elem_int,X0) = hAPP_f1594865479ol_int(the_int,cOMBB_1418110531ol_int(hAPP_f284875647l_bool(fequal_fun_int_bool,X0),hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(insert_int),bot_bot_fun_int_bool))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_596])]) ).

tff(f4689,plain,
    ! [X0: fun_int_bool] : ( hAPP_f1594865479ol_int(the_elem_int,X0) = hAPP_f1594865479ol_int(the_int,cOMBB_1418110531ol_int(hAPP_f284875647l_bool(fequal_fun_int_bool,X0),hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(insert_int),bot_bot_fun_int_bool))) ),
    inference(cnf_transformation,[],[f1417]) ).

tff(f1417,plain,
    ! [X0: fun_int_bool] : ( hAPP_f1594865479ol_int(the_elem_int,X0) = hAPP_f1594865479ol_int(the_int,cOMBB_1418110531ol_int(hAPP_f284875647l_bool(fequal_fun_int_bool,X0),hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(insert_int),bot_bot_fun_int_bool))) ),
    inference(rectify,[],[f786]) ).

tff(f786,axiom,
    ! [X82: fun_int_bool] : ( hAPP_f1594865479ol_int(the_elem_int,X82) = hAPP_f1594865479ol_int(the_int,cOMBB_1418110531ol_int(hAPP_f284875647l_bool(fequal_fun_int_bool,X82),hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(insert_int),bot_bot_fun_int_bool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_785_the__elem__def) ).

tff(f12089,plain,
    ( spl250_595
    | ~ spl250_44
    | ~ spl250_581 ),
    inference(avatar_split_clause,[],[f12079,f11782,f7516,f12087]) ).

tff(f12087,plain,
    ( spl250_595
  <=> ! [X0: fun_nat_int,X1: nat] : ~ sP25(X0,zero_zero_nat,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_595])]) ).

tff(f7516,plain,
    ( spl250_44
  <=> ! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_44])]) ).

tff(f11782,plain,
    ( spl250_581
  <=> ! [X2: nat,X0: fun_nat_int,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK248(X0,X1,X2)),X1))
        | ~ sP25(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_581])]) ).

tff(f12079,plain,
    ( ! [X0: fun_nat_int,X1: nat] : ~ sP25(X0,zero_zero_nat,X1)
    | ~ spl250_44
    | ~ spl250_581 ),
    inference(resolution,[],[f11783,f7517]) ).

tff(f7517,plain,
    ( ! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat))
    | ~ spl250_44 ),
    inference(avatar_component_clause,[],[f7516]) ).

tff(f11783,plain,
    ( ! [X2: nat,X0: fun_nat_int,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK248(X0,X1,X2)),X1))
        | ~ sP25(X0,X1,X2) )
    | ~ spl250_581 ),
    inference(avatar_component_clause,[],[f11782]) ).

tff(f12028,plain,
    ( spl250_594
    | ~ spl250_111
    | ~ spl250_331 ),
    inference(avatar_split_clause,[],[f9548,f9154,f7857,f12026]) ).

tff(f12026,plain,
    ( spl250_594
  <=> ! [X0: nat] :
        ( ( one_one_nat != X0 )
        | sP7(zero_zero_nat,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_594])]) ).

tff(f7857,plain,
    ( spl250_111
  <=> ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),zero_zero_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_111])]) ).

tff(f9154,plain,
    ( spl250_331
  <=> ! [X0: nat,X1: nat] :
        ( ( one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) )
        | sP7(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_331])]) ).

tff(f9548,plain,
    ( ! [X0: nat] :
        ( ( one_one_nat != X0 )
        | sP7(zero_zero_nat,X0) )
    | ~ spl250_111
    | ~ spl250_331 ),
    inference(superposition,[],[f9155,f7858]) ).

tff(f7858,plain,
    ( ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),zero_zero_nat) = X0 )
    | ~ spl250_111 ),
    inference(avatar_component_clause,[],[f7857]) ).

tff(f9155,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) )
        | sP7(X1,X0) )
    | ~ spl250_331 ),
    inference(avatar_component_clause,[],[f9154]) ).

tff(f11944,plain,
    ( spl250_593
    | ~ spl250_108
    | ~ spl250_331 ),
    inference(avatar_split_clause,[],[f9545,f9154,f7845,f11942]) ).

tff(f11942,plain,
    ( spl250_593
  <=> ! [X0: nat] :
        ( ( one_one_nat != X0 )
        | sP7(X0,zero_zero_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_593])]) ).

tff(f7845,plain,
    ( spl250_108
  <=> ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_108])]) ).

tff(f9545,plain,
    ( ! [X0: nat] :
        ( ( one_one_nat != X0 )
        | sP7(X0,zero_zero_nat) )
    | ~ spl250_108
    | ~ spl250_331 ),
    inference(superposition,[],[f9155,f7846]) ).

tff(f7846,plain,
    ( ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),X0) = X0 )
    | ~ spl250_108 ),
    inference(avatar_component_clause,[],[f7845]) ).

tff(f11828,plain,
    spl250_592,
    inference(avatar_split_clause,[],[f7222,f11826]) ).

tff(f7222,plain,
    ! [X0: fun_int_bool,X1: int] :
      ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),sK205(X0,X1))))
      | ~ sP12(X0,X1) ),
    inference(forward_demodulation,[],[f6011,f4900]) ).

tff(f4900,plain,
    ! [X0: int,X1: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0) ),
    inference(cnf_transformation,[],[f1548]) ).

tff(f1548,plain,
    ! [X0: int,X1: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0) ),
    inference(rectify,[],[f1044]) ).

tff(f1044,axiom,
    ! [X95: int,X132: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X95),X132) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X132),X95) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1043_zadd__commute) ).

tff(f6011,plain,
    ! [X0: fun_int_bool,X1: int] :
      ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,sK205(X0,X1)),one_one_int)))
      | ~ sP12(X0,X1) ),
    inference(cnf_transformation,[],[f4299]) ).

tff(f4299,plain,
    ! [X0: fun_int_bool,X1: int] :
      ( ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,sK205(X0,X1)),one_one_int)))
        & hBOOL(hAPP_int_bool(X0,sK205(X0,X1)))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),sK205(X0,X1))) )
      | ~ sP12(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK205])],[f4297,f4298]) ).

tff(f4298,plain,
    ! [X0: fun_int_bool,X1: int] :
      ( ? [X2: int] :
          ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),one_one_int)))
          & hBOOL(hAPP_int_bool(X0,X2))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) )
     => ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,sK205(X0,X1)),one_one_int)))
        & hBOOL(hAPP_int_bool(X0,sK205(X0,X1)))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),sK205(X0,X1))) ) ),
    introduced(choice_axiom,[]) ).

tff(f4297,plain,
    ! [X0: fun_int_bool,X1: int] :
      ( ? [X2: int] :
          ( ~ hBOOL(hAPP_int_bool(X0,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),one_one_int)))
          & hBOOL(hAPP_int_bool(X0,X2))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) )
      | ~ sP12(X0,X1) ),
    inference(rectify,[],[f4296]) ).

tff(f4296,plain,
    ! [X1: fun_int_bool,X2: int] :
      ( ? [X3: int] :
          ( ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),one_one_int)))
          & hBOOL(hAPP_int_bool(X1,X3))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) )
      | ~ sP12(X1,X2) ),
    inference(nnf_transformation,[],[f3707]) ).

tff(f11824,plain,
    spl250_591,
    inference(avatar_split_clause,[],[f7116,f11822]) ).

tff(f11822,plain,
    ( spl250_591
  <=> ! [X0: int,X1: int] :
        ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
        | ~ sP5(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_591])]) ).

tff(f7116,plain,
    ! [X0: int,X1: int] :
      ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | ~ sP5(X0,X1) ),
    inference(forward_demodulation,[],[f7115,f4587]) ).

tff(f7115,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
      | ~ sP5(X0,X1) ),
    inference(forward_demodulation,[],[f6644,f4587]) ).

tff(f6644,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),pls))
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
      | ~ sP5(X0,X1) ),
    inference(definition_unfolding,[],[f5464,f4550]) ).

tff(f5464,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
      | ~ sP5(X0,X1) ),
    inference(cnf_transformation,[],[f4042]) ).

tff(f4042,plain,
    ! [X0: int,X1: int] :
      ( ( sP5(X0,X1)
        | ( ~ sP4(X1,X0)
          & ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
        | ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int))
          & hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) )
      & ( ( ( sP4(X1,X0)
            | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
          & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int))
            | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) )
        | ~ sP5(X0,X1) ) ),
    inference(flattening,[],[f4041]) ).

tff(f4041,plain,
    ! [X0: int,X1: int] :
      ( ( sP5(X0,X1)
        | ( ~ sP4(X1,X0)
          & ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
        | ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int))
          & hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) )
      & ( ( ( sP4(X1,X0)
            | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
          & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int))
            | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) )
        | ~ sP5(X0,X1) ) ),
    inference(nnf_transformation,[],[f3693]) ).

tff(f3693,plain,
    ! [X0: int,X1: int] :
      ( sP5(X0,X1)
    <=> ( ( sP4(X1,X0)
          | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
        & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int))
          | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).

tff(f11820,plain,
    spl250_590,
    inference(avatar_split_clause,[],[f7113,f11818]) ).

tff(f11818,plain,
    ( spl250_590
  <=> ! [X0: int,X1: int] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
        | ~ hBOOL(hAPP_int_bool(nat_neg,X0))
        | sP5(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_590])]) ).

tff(f7113,plain,
    ! [X0: int,X1: int] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | ~ hBOOL(hAPP_int_bool(nat_neg,X0))
      | sP5(X0,X1) ),
    inference(forward_demodulation,[],[f7112,f4587]) ).

tff(f7112,plain,
    ! [X0: int,X1: int] :
      ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
      | sP5(X0,X1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),pls)) ),
    inference(forward_demodulation,[],[f6643,f4587]) ).

tff(f6643,plain,
    ! [X0: int,X1: int] :
      ( sP5(X0,X1)
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),pls)) ),
    inference(definition_unfolding,[],[f5467,f4550]) ).

tff(f5467,plain,
    ! [X0: int,X1: int] :
      ( sP5(X0,X1)
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int)) ),
    inference(cnf_transformation,[],[f4042]) ).

tff(f11816,plain,
    ( spl250_589
    | ~ spl250_111
    | ~ spl250_329 ),
    inference(avatar_split_clause,[],[f9542,f9146,f7857,f11814]) ).

tff(f11814,plain,
    ( spl250_589
  <=> ! [X0: nat] :
        ( ( one_one_nat != X0 )
        | sP6(zero_zero_nat,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_589])]) ).

tff(f9146,plain,
    ( spl250_329
  <=> ! [X0: nat,X1: nat] :
        ( ( one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) )
        | sP6(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_329])]) ).

tff(f9542,plain,
    ( ! [X0: nat] :
        ( ( one_one_nat != X0 )
        | sP6(zero_zero_nat,X0) )
    | ~ spl250_111
    | ~ spl250_329 ),
    inference(superposition,[],[f9147,f7858]) ).

tff(f9147,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) )
        | sP6(X1,X0) )
    | ~ spl250_329 ),
    inference(avatar_component_clause,[],[f9146]) ).

tff(f11812,plain,
    spl250_588,
    inference(avatar_split_clause,[],[f6995,f11810]) ).

tff(f11810,plain,
    ( spl250_588
  <=> ! [X0: fun_nat_bool,X1: nat] :
        ( ( bot_bot_fun_nat_bool = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X1)),X0) )
        | hBOOL(hAPP_nat_bool(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_588])]) ).

tff(f6995,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( ( bot_bot_fun_nat_bool = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X1)),X0) )
      | hBOOL(hAPP_nat_bool(X0,X1)) ),
    inference(forward_demodulation,[],[f4963,f4588]) ).

tff(f4963,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( ( bot_bot_fun_nat_bool = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X1)),X0)) )
      | hBOOL(hAPP_nat_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f2619]) ).

tff(f11808,plain,
    spl250_587,
    inference(avatar_split_clause,[],[f6987,f11806]) ).

tff(f11806,plain,
    ( spl250_587
  <=> ! [X0: fun_int_bool,X1: int] :
        ( ( bot_bot_fun_int_bool = cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X1)),X0) )
        | hBOOL(hAPP_int_bool(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_587])]) ).

tff(f6987,plain,
    ! [X0: fun_int_bool,X1: int] :
      ( ( bot_bot_fun_int_bool = cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X1)),X0) )
      | hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(forward_demodulation,[],[f4959,f4586]) ).

tff(f4959,plain,
    ! [X0: fun_int_bool,X1: int] :
      ( ( bot_bot_fun_int_bool = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X1)),X0)) )
      | hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f2617]) ).

tff(f11804,plain,
    spl250_586,
    inference(avatar_split_clause,[],[f6690,f11802]) ).

tff(f11802,plain,
    ( spl250_586
  <=> ! [X2: fun_pname_bool,X1: pname] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
        | ( bot_bo844097828e_bool != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_586])]) ).

tff(f6690,plain,
    ! [X2: fun_pname_bool,X1: pname] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
      | ( bot_bo844097828e_bool != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2) ) ),
    inference(equality_resolution,[],[f4737]) ).

tff(f4737,plain,
    ! [X2: fun_pname_bool,X0: fun_pname_bool,X1: pname] :
      ( ( bot_bo844097828e_bool != X0 )
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
      | ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2) != X0 ) ),
    inference(cnf_transformation,[],[f3758]) ).

tff(f3758,plain,
    ! [X0: fun_pname_bool] :
      ( ( ( bot_bo844097828e_bool != X0 )
        | ! [X1: pname,X2: fun_pname_bool] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
            | ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2) != X0 ) ) )
      & ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK36(X0)),sK37(X0)))
          & ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK36(X0)),sK37(X0)) = X0 ) )
        | ( bot_bo844097828e_bool = X0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK36,sK37])],[f3756,f3757]) ).

tff(f3757,plain,
    ! [X0: fun_pname_bool] :
      ( ? [X3: pname,X4: fun_pname_bool] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
          & ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4) = X0 ) )
     => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK36(X0)),sK37(X0)))
        & ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK36(X0)),sK37(X0)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f3756,plain,
    ! [X0: fun_pname_bool] :
      ( ( ( bot_bo844097828e_bool != X0 )
        | ! [X1: pname,X2: fun_pname_bool] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
            | ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2) != X0 ) ) )
      & ( ? [X3: pname,X4: fun_pname_bool] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
            & ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4) = X0 ) )
        | ( bot_bo844097828e_bool = X0 ) ) ),
    inference(rectify,[],[f3755]) ).

tff(f3755,plain,
    ! [X0: fun_pname_bool] :
      ( ( ( bot_bo844097828e_bool != X0 )
        | ! [X1: pname,X2: fun_pname_bool] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
            | ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2) != X0 ) ) )
      & ( ? [X1: pname,X2: fun_pname_bool] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
            & ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2) = X0 ) )
        | ( bot_bo844097828e_bool = X0 ) ) ),
    inference(nnf_transformation,[],[f1458]) ).

tff(f1458,plain,
    ! [X0: fun_pname_bool] :
      ( ( bot_bo844097828e_bool != X0 )
    <=> ? [X1: pname,X2: fun_pname_bool] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
          & ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2) = X0 ) ) ),
    inference(rectify,[],[f703]) ).

tff(f703,axiom,
    ! [X2: fun_pname_bool] :
      ( ( bot_bo844097828e_bool != X2 )
    <=> ? [X27: pname,X80: fun_pname_bool] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X27),X80))
          & ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X27),X80) = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_702_nonempty__iff) ).

tff(f11800,plain,
    spl250_585,
    inference(avatar_split_clause,[],[f6630,f11798]) ).

tff(f11798,plain,
    ( spl250_585
  <=> ! [X0: int,X1: int] :
        ( ( pls = hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0) )
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_585])]) ).

tff(f6630,plain,
    ! [X0: int,X1: int] :
      ( ( pls = hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0) )
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(definition_unfolding,[],[f4969,f4550]) ).

tff(f4969,plain,
    ! [X0: int,X1: int] :
      ( ( zero_zero_int = hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X0) )
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2622]) ).

tff(f11796,plain,
    spl250_584,
    inference(avatar_split_clause,[],[f6627,f11794]) ).

tff(f11794,plain,
    ( spl250_584
  <=> ! [X2: nat,X0: fun_int_bool] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK73(X0)))
        | ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_584])]) ).

tff(f6627,plain,
    ! [X2: nat,X0: fun_int_bool] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK73(X0)))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
    inference(definition_unfolding,[],[f4867,f4550]) ).

tff(f4867,plain,
    ! [X2: nat,X0: fun_int_bool] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK73(X0)))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
    inference(cnf_transformation,[],[f3902]) ).

tff(f11792,plain,
    spl250_583,
    inference(avatar_split_clause,[],[f6626,f11790]) ).

tff(f11790,plain,
    ( spl250_583
  <=> ! [X0: fun_int_bool,X3: nat] :
        ( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK68(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_583])]) ).

tff(f6626,plain,
    ! [X3: nat,X0: fun_int_bool] :
      ( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK68(X0))) ),
    inference(definition_unfolding,[],[f4855,f4550]) ).

tff(f4855,plain,
    ! [X3: nat,X0: fun_int_bool] :
      ( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK68(X0))) ),
    inference(cnf_transformation,[],[f3881]) ).

tff(f11788,plain,
    spl250_582,
    inference(avatar_split_clause,[],[f6591,f11786]) ).

tff(f11786,plain,
    ( spl250_582
  <=> ! [X0: int] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK31(X0)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_582])]) ).

tff(f6591,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK31(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(definition_unfolding,[],[f4723,f4550]) ).

tff(f4723,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK31(X0)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
    inference(cnf_transformation,[],[f3746]) ).

tff(f3746,plain,
    ! [X0: int] :
      ( ( ( hAPP_nat_int(semiri1621563631at_int,sK31(X0)) = X0 )
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK31(X0))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f2596,f3745]) ).

tff(f3745,plain,
    ! [X0: int] :
      ( ? [X1: nat] :
          ( ( hAPP_nat_int(semiri1621563631at_int,X1) = X0 )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) )
     => ( ( hAPP_nat_int(semiri1621563631at_int,sK31(X0)) = X0 )
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK31(X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f2596,plain,
    ! [X0: int] :
      ( ? [X1: nat] :
          ( ( hAPP_nat_int(semiri1621563631at_int,X1) = X0 )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
    inference(ennf_transformation,[],[f1447]) ).

tff(f1447,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
     => ? [X1: nat] :
          ( ( hAPP_nat_int(semiri1621563631at_int,X1) = X0 )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ) ),
    inference(rectify,[],[f1132]) ).

tff(f1132,axiom,
    ! [X19: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X19))
     => ? [X26: nat] :
          ( ( hAPP_nat_int(semiri1621563631at_int,X26) = X19 )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X26)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1131_zero__less__imp__eq__int) ).

tff(f11784,plain,
    spl250_581,
    inference(avatar_split_clause,[],[f6511,f11782]) ).

tff(f6511,plain,
    ! [X2: nat,X0: fun_nat_int,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK248(X0,X1,X2)),X1))
      | ~ sP25(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4518]) ).

tff(f4518,plain,
    ! [X0: fun_nat_int,X1: nat,X2: nat] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK248(X0,X1,X2)),one_one_nat))),hAPP_nat_int(X0,sK248(X0,X1,X2))))),one_one_int))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK248(X0,X1,X2)),X1))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),sK248(X0,X1,X2))) )
      | ~ sP25(X0,X1,X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK248])],[f4516,f4517]) ).

tff(f4517,plain,
    ! [X0: fun_nat_int,X1: nat,X2: nat] :
      ( ? [X3: nat] :
          ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),one_one_nat))),hAPP_nat_int(X0,X3)))),one_one_int))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X1))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) )
     => ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK248(X0,X1,X2)),one_one_nat))),hAPP_nat_int(X0,sK248(X0,X1,X2))))),one_one_int))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK248(X0,X1,X2)),X1))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),sK248(X0,X1,X2))) ) ),
    introduced(choice_axiom,[]) ).

tff(f4516,plain,
    ! [X0: fun_nat_int,X1: nat,X2: nat] :
      ( ? [X3: nat] :
          ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),one_one_nat))),hAPP_nat_int(X0,X3)))),one_one_int))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X1))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) )
      | ~ sP25(X0,X1,X2) ),
    inference(rectify,[],[f4515]) ).

tff(f4515,plain,
    ! [X1: fun_nat_int,X2: nat,X3: nat] :
      ( ? [X4: nat] :
          ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X4),one_one_nat))),hAPP_nat_int(X1,X4)))),one_one_int))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X2))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) )
      | ~ sP25(X1,X2,X3) ),
    inference(nnf_transformation,[],[f3733]) ).

tff(f3733,plain,
    ! [X1: fun_nat_int,X2: nat,X3: nat] :
      ( ? [X4: nat] :
          ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X4),one_one_nat))),hAPP_nat_int(X1,X4)))),one_one_int))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X2))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) )
      | ~ sP25(X1,X2,X3) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP25])]) ).

tff(f11780,plain,
    spl250_580,
    inference(avatar_split_clause,[],[f6510,f11778]) ).

tff(f11778,plain,
    ( spl250_580
  <=> ! [X2: nat,X0: fun_nat_int,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),sK248(X0,X1,X2)))
        | ~ sP25(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_580])]) ).

tff(f6510,plain,
    ! [X2: nat,X0: fun_nat_int,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),sK248(X0,X1,X2)))
      | ~ sP25(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4518]) ).

tff(f11776,plain,
    spl250_579,
    inference(avatar_split_clause,[],[f5973,f11774]) ).

tff(f11774,plain,
    ( spl250_579
  <=> ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK189(X0,X1)),sK190(X0,X1)))
        | ~ sP11(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_579])]) ).

tff(f5973,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK189(X0,X1)),sK190(X0,X1)))
      | ~ sP11(X0,X1) ),
    inference(cnf_transformation,[],[f4275]) ).

tff(f11772,plain,
    ( spl250_578
    | ~ spl250_108
    | ~ spl250_329 ),
    inference(avatar_split_clause,[],[f9539,f9146,f7845,f11770]) ).

tff(f11770,plain,
    ( spl250_578
  <=> ! [X0: nat] :
        ( ( one_one_nat != X0 )
        | sP6(X0,zero_zero_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_578])]) ).

tff(f9539,plain,
    ( ! [X0: nat] :
        ( ( one_one_nat != X0 )
        | sP6(X0,zero_zero_nat) )
    | ~ spl250_108
    | ~ spl250_329 ),
    inference(superposition,[],[f9147,f7846]) ).

tff(f11768,plain,
    spl250_577,
    inference(avatar_split_clause,[],[f5939,f11766]) ).

tff(f11766,plain,
    ( spl250_577
  <=> ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
        ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK180(X0,X1)),sK181(X0,X1)))
        | ~ sP10(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_577])]) ).

tff(f5939,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK180(X0,X1)),sK181(X0,X1)))
      | ~ sP10(X0,X1) ),
    inference(cnf_transformation,[],[f4257]) ).

tff(f11764,plain,
    spl250_576,
    inference(avatar_split_clause,[],[f5904,f11762]) ).

tff(f11762,plain,
    ( spl250_576
  <=> ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK170(X0,X1)),sK171(X0,X1)))
        | ~ sP9(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_576])]) ).

tff(f5904,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK170(X0,X1)),sK171(X0,X1)))
      | ~ sP9(X0,X1) ),
    inference(cnf_transformation,[],[f4237]) ).

tff(f11760,plain,
    spl250_575,
    inference(avatar_split_clause,[],[f5866,f11758]) ).

tff(f11758,plain,
    ( spl250_575
  <=> ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK160(X0,X1)),sK161(X0,X1)))
        | ~ sP8(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_575])]) ).

tff(f5866,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK160(X0,X1)),sK161(X0,X1)))
      | ~ sP8(X0,X1) ),
    inference(cnf_transformation,[],[f4217]) ).

tff(f11756,plain,
    spl250_574,
    inference(avatar_split_clause,[],[f5743,f11754]) ).

tff(f5743,plain,
    ! [X2: nat,X0: fun_na1469252690l_bool,X1: fun_nat_bool] : ( hAPP_nat_bool(cOMBS_nat_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_n1006566506l_bool(X0,X2),hAPP_nat_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2119]) ).

tff(f2119,plain,
    ! [X0: fun_na1469252690l_bool,X1: fun_nat_bool,X2: nat] : ( hAPP_nat_bool(cOMBS_nat_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_n1006566506l_bool(X0,X2),hAPP_nat_bool(X1,X2)) ),
    inference(rectify,[],[f1250]) ).

tff(f1250,axiom,
    ! [X156: fun_na1469252690l_bool,X157: fun_nat_bool,X158: nat] : ( hAPP_nat_bool(cOMBS_nat_bool_bool(X156,X157),X158) = hAPP_bool_bool(hAPP_n1006566506l_bool(X156,X158),hAPP_nat_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

tff(f11752,plain,
    spl250_573,
    inference(avatar_split_clause,[],[f5742,f11750]) ).

tff(f5742,plain,
    ! [X2: int,X0: fun_in531499254l_bool,X1: fun_int_bool] : ( hAPP_int_bool(cOMBS_int_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_i68813070l_bool(X0,X2),hAPP_int_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2118]) ).

tff(f2118,plain,
    ! [X0: fun_in531499254l_bool,X1: fun_int_bool,X2: int] : ( hAPP_int_bool(cOMBS_int_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_i68813070l_bool(X0,X2),hAPP_int_bool(X1,X2)) ),
    inference(rectify,[],[f1249]) ).

tff(f1249,axiom,
    ! [X156: fun_in531499254l_bool,X157: fun_int_bool,X158: int] : ( hAPP_int_bool(cOMBS_int_bool_bool(X156,X157),X158) = hAPP_bool_bool(hAPP_i68813070l_bool(X156,X158),hAPP_int_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

tff(f11748,plain,
    spl250_572,
    inference(avatar_split_clause,[],[f5741,f11746]) ).

tff(f11746,plain,
    ( spl250_572
  <=> ! [X2: fun_nat_bool,X0: fun_fu1016514960l_bool,X1: fun_fu425979586l_bool] : ( hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1748468828l_bool(X0,X2),hAPP_f54304608l_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_572])]) ).

tff(f5741,plain,
    ! [X2: fun_nat_bool,X0: fun_fu1016514960l_bool,X1: fun_fu425979586l_bool] : ( hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1748468828l_bool(X0,X2),hAPP_f54304608l_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2117]) ).

tff(f2117,plain,
    ! [X0: fun_fu1016514960l_bool,X1: fun_fu425979586l_bool,X2: fun_nat_bool] : ( hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1748468828l_bool(X0,X2),hAPP_f54304608l_bool(X1,X2)) ),
    inference(rectify,[],[f1274]) ).

tff(f1274,axiom,
    ! [X156: fun_fu1016514960l_bool,X157: fun_fu425979586l_bool,X158: fun_nat_bool] : ( hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X156,X157),X158) = hAPP_bool_bool(hAPP_f1748468828l_bool(X156,X158),hAPP_f54304608l_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) ).

tff(f11744,plain,
    spl250_571,
    inference(avatar_split_clause,[],[f5740,f11742]) ).

tff(f11742,plain,
    ( spl250_571
  <=> ! [X2: fun_int_bool,X0: fun_fu989146164l_bool,X1: fun_fu819804446l_bool] : ( hAPP_f448129468l_bool(cOMBS_1912792529l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1721100032l_bool(X0,X2),hAPP_f448129468l_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_571])]) ).

tff(f5740,plain,
    ! [X2: fun_int_bool,X0: fun_fu989146164l_bool,X1: fun_fu819804446l_bool] : ( hAPP_f448129468l_bool(cOMBS_1912792529l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1721100032l_bool(X0,X2),hAPP_f448129468l_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2116]) ).

tff(f2116,plain,
    ! [X0: fun_fu989146164l_bool,X1: fun_fu819804446l_bool,X2: fun_int_bool] : ( hAPP_f448129468l_bool(cOMBS_1912792529l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1721100032l_bool(X0,X2),hAPP_f448129468l_bool(X1,X2)) ),
    inference(rectify,[],[f1273]) ).

tff(f1273,axiom,
    ! [X156: fun_fu989146164l_bool,X157: fun_fu819804446l_bool,X158: fun_int_bool] : ( hAPP_f448129468l_bool(cOMBS_1912792529l_bool(X156,X157),X158) = hAPP_bool_bool(hAPP_f1721100032l_bool(X156,X158),hAPP_f448129468l_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obo) ).

tff(f11740,plain,
    spl250_570,
    inference(avatar_split_clause,[],[f5739,f11738]) ).

tff(f5739,plain,
    ! [X2: fun_a_bool,X0: fun_fu554186387l_bool,X1: fun_fun_a_bool_bool] : ( hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f198738859l_bool(X0,X2),hAPP_fun_a_bool_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2115]) ).

tff(f2115,plain,
    ! [X0: fun_fu554186387l_bool,X1: fun_fun_a_bool_bool,X2: fun_a_bool] : ( hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f198738859l_bool(X0,X2),hAPP_fun_a_bool_bool(X1,X2)) ),
    inference(rectify,[],[f1261]) ).

tff(f1261,axiom,
    ! [X156: fun_fu554186387l_bool,X157: fun_fun_a_bool_bool,X158: fun_a_bool] : ( hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X156,X157),X158) = hAPP_bool_bool(hAPP_f198738859l_bool(X156,X158),hAPP_fun_a_bool_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_) ).

tff(f11736,plain,
    spl250_569,
    inference(avatar_split_clause,[],[f5738,f11734]) ).

tff(f11734,plain,
    ( spl250_569
  <=> ! [X2: fun_pname_bool,X0: fun_fu31783638l_bool,X1: fun_fu1430349052l_bool] : ( hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1476298914l_bool(X0,X2),hAPP_f1664156314l_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_569])]) ).

tff(f5738,plain,
    ! [X2: fun_pname_bool,X0: fun_fu31783638l_bool,X1: fun_fu1430349052l_bool] : ( hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1476298914l_bool(X0,X2),hAPP_f1664156314l_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2114]) ).

tff(f2114,plain,
    ! [X0: fun_fu31783638l_bool,X1: fun_fu1430349052l_bool,X2: fun_pname_bool] : ( hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_f1476298914l_bool(X0,X2),hAPP_f1664156314l_bool(X1,X2)) ),
    inference(rectify,[],[f1278]) ).

tff(f1278,axiom,
    ! [X156: fun_fu31783638l_bool,X157: fun_fu1430349052l_bool,X158: fun_pname_bool] : ( hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X156,X157),X158) = hAPP_bool_bool(hAPP_f1476298914l_bool(X156,X158),hAPP_f1664156314l_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O) ).

tff(f11732,plain,
    spl250_568,
    inference(avatar_split_clause,[],[f5737,f11730]) ).

tff(f5737,plain,
    ! [X2: x_a,X0: fun_a_fun_bool_bool,X1: fun_a_bool] : ( hAPP_a_bool(cOMBS_a_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X0,X2),hAPP_a_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2113]) ).

tff(f2113,plain,
    ! [X0: fun_a_fun_bool_bool,X1: fun_a_bool,X2: x_a] : ( hAPP_a_bool(cOMBS_a_bool_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X0,X2),hAPP_a_bool(X1,X2)) ),
    inference(rectify,[],[f1235]) ).

tff(f1235,axiom,
    ! [X156: fun_a_fun_bool_bool,X157: fun_a_bool,X158: x_a] : ( hAPP_a_bool(cOMBS_a_bool_bool(X156,X157),X158) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X156,X158),hAPP_a_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

tff(f11727,plain,
    ( spl250_567
    | spl250_9
    | ~ spl250_320 ),
    inference(avatar_split_clause,[],[f9505,f9109,f7354,f11724]) ).

tff(f11724,plain,
    ( spl250_567
  <=> ( one_one_int = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(one_one_int)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_567])]) ).

tff(f9109,plain,
    ( spl250_320
  <=> ! [X0: int] :
        ( hBOOL(hAPP_int_bool(nat_neg,X0))
        | ( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_320])]) ).

tff(f9505,plain,
    ( ( one_one_int = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(one_one_int)) )
    | spl250_9
    | ~ spl250_320 ),
    inference(resolution,[],[f9110,f7356]) ).

tff(f9110,plain,
    ( ! [X0: int] :
        ( hBOOL(hAPP_int_bool(nat_neg,X0))
        | ( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0)) = X0 ) )
    | ~ spl250_320 ),
    inference(avatar_component_clause,[],[f9109]) ).

tff(f11722,plain,
    spl250_566,
    inference(avatar_split_clause,[],[f5736,f11720]) ).

tff(f11720,plain,
    ( spl250_566
  <=> ! [X2: pname,X0: fun_pn250273176l_bool,X1: fun_pname_bool] : ( hAPP_pname_bool(cOMBS_568398431l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_p393069232l_bool(X0,X2),hAPP_pname_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_566])]) ).

tff(f5736,plain,
    ! [X2: pname,X0: fun_pn250273176l_bool,X1: fun_pname_bool] : ( hAPP_pname_bool(cOMBS_568398431l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_p393069232l_bool(X0,X2),hAPP_pname_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2112]) ).

tff(f2112,plain,
    ! [X0: fun_pn250273176l_bool,X1: fun_pname_bool,X2: pname] : ( hAPP_pname_bool(cOMBS_568398431l_bool(X0,X1),X2) = hAPP_bool_bool(hAPP_p393069232l_bool(X0,X2),hAPP_pname_bool(X1,X2)) ),
    inference(rectify,[],[f1252]) ).

tff(f1252,axiom,
    ! [X156: fun_pn250273176l_bool,X157: fun_pname_bool,X158: pname] : ( hAPP_pname_bool(cOMBS_568398431l_bool(X156,X157),X158) = hAPP_bool_bool(hAPP_p393069232l_bool(X156,X158),hAPP_pname_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

tff(f11718,plain,
    spl250_565,
    inference(avatar_split_clause,[],[f5540,f11716]) ).

tff(f11716,plain,
    ( spl250_565
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
        | ( zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_565])]) ).

tff(f5540,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | ( zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) ) ),
    inference(cnf_transformation,[],[f4102]) ).

tff(f4102,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
        | ( zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) ) ) ),
    inference(nnf_transformation,[],[f2000]) ).

tff(f2000,plain,
    ! [X0: nat,X1: nat] :
      ( ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) )
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(rectify,[],[f956]) ).

tff(f956,axiom,
    ! [X22: nat,X14: nat] :
      ( ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X22),X14) )
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X14)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_955_diff__is__0__eq) ).

tff(f11714,plain,
    spl250_564,
    inference(avatar_split_clause,[],[f5537,f11712]) ).

tff(f11712,plain,
    ( spl250_564
  <=> ! [X0: nat,X1: nat] :
        ( ( zero_zero_nat = X1 )
        | ( zero_zero_nat = X0 )
        | ( zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_564])]) ).

tff(f5537,plain,
    ! [X0: nat,X1: nat] :
      ( ( zero_zero_nat = X1 )
      | ( zero_zero_nat = X0 )
      | ( zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) ) ),
    inference(cnf_transformation,[],[f4101]) ).

tff(f4101,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) )
        | ( ( zero_zero_nat != X1 )
          & ( zero_zero_nat != X0 ) ) )
      & ( ( zero_zero_nat = X1 )
        | ( zero_zero_nat = X0 )
        | ( zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) ) ) ),
    inference(flattening,[],[f4100]) ).

tff(f4100,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) )
        | ( ( zero_zero_nat != X1 )
          & ( zero_zero_nat != X0 ) ) )
      & ( ( zero_zero_nat = X1 )
        | ( zero_zero_nat = X0 )
        | ( zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) ) ) ),
    inference(nnf_transformation,[],[f1999]) ).

tff(f1999,plain,
    ! [X0: nat,X1: nat] :
      ( ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) )
    <=> ( ( zero_zero_nat = X1 )
        | ( zero_zero_nat = X0 ) ) ),
    inference(rectify,[],[f981]) ).

tff(f981,axiom,
    ! [X22: nat,X14: nat] :
      ( ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X22),X14) )
    <=> ( ( zero_zero_nat = X14 )
        | ( zero_zero_nat = X22 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_980_mult__is__0) ).

tff(f11710,plain,
    spl250_563,
    inference(avatar_split_clause,[],[f5386,f11708]) ).

tff(f11708,plain,
    ( spl250_563
  <=> ! [X0: pname,X1: pname] :
        ( ( X0 = X1 )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_563])]) ).

tff(f5386,plain,
    ! [X0: pname,X1: pname] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool))) ),
    inference(cnf_transformation,[],[f3032]) ).

tff(f3032,plain,
    ! [X0: pname,X1: pname] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool))) ),
    inference(ennf_transformation,[],[f1929]) ).

tff(f1929,plain,
    ! [X0: pname,X1: pname] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool)))
     => ( X0 = X1 ) ),
    inference(rectify,[],[f596]) ).

tff(f596,axiom,
    ! [X28: pname,X5: pname] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X28),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5),bot_bo844097828e_bool)))
     => ( X5 = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_595_singletonE) ).

tff(f11706,plain,
    spl250_562,
    inference(avatar_split_clause,[],[f5371,f11704]) ).

tff(f11704,plain,
    ( spl250_562
  <=> ! [X0: nat,X1: nat] :
        ( ( zero_zero_nat = X0 )
        | ( one_one_nat = X1 )
        | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_562])]) ).

tff(f5371,plain,
    ! [X0: nat,X1: nat] :
      ( ( zero_zero_nat = X0 )
      | ( one_one_nat = X1 )
      | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != X0 ) ),
    inference(cnf_transformation,[],[f3012]) ).

tff(f3012,plain,
    ! [X0: nat,X1: nat] :
      ( ( zero_zero_nat = X0 )
      | ( one_one_nat = X1 )
      | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != X0 ) ),
    inference(flattening,[],[f3011]) ).

tff(f3011,plain,
    ! [X0: nat,X1: nat] :
      ( ( zero_zero_nat = X0 )
      | ( one_one_nat = X1 )
      | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) != X0 ) ),
    inference(ennf_transformation,[],[f1915]) ).

tff(f1915,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) = X0 )
     => ( ( zero_zero_nat = X0 )
        | ( one_one_nat = X1 ) ) ),
    inference(rectify,[],[f1008]) ).

tff(f1008,axiom,
    ! [X12: nat,X11: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X12),X11) = X12 )
     => ( ( zero_zero_nat = X12 )
        | ( one_one_nat = X11 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1007_mult__eq__self__implies__10) ).

tff(f11702,plain,
    spl250_561,
    inference(avatar_split_clause,[],[f5354,f11700]) ).

tff(f11700,plain,
    ( spl250_561
  <=> ! [X0: nat,X1: nat] :
        ( ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_561])]) ).

tff(f5354,plain,
    ! [X0: nat,X1: nat] :
      ( ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2992]) ).

tff(f2992,plain,
    ! [X0: nat,X1: nat] :
      ( ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1900]) ).

tff(f1900,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
     => ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1) ) ),
    inference(rectify,[],[f957]) ).

tff(f957,axiom,
    ! [X12: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X11))
     => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X12),X11) = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_956_diff__is__0__eq_H) ).

tff(f11698,plain,
    spl250_560,
    inference(avatar_split_clause,[],[f5325,f11696]) ).

tff(f11696,plain,
    ( spl250_560
  <=> ! [X0: nat,X1: fun_nat_bool] :
        ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = X1 )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_560])]) ).

tff(f5325,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = X1 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2958]) ).

tff(f2958,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = X1 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1875]) ).

tff(f1875,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
     => ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) = X1 ) ),
    inference(rectify,[],[f400]) ).

tff(f400,axiom,
    ! [X5: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5),X2))
     => ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5),X2) = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_399_insert__absorb) ).

tff(f11694,plain,
    spl250_559,
    inference(avatar_split_clause,[],[f5317,f11692]) ).

tff(f11692,plain,
    ( spl250_559
  <=> ! [X0: int,X1: fun_int_bool] :
        ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = X1 )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_559])]) ).

tff(f5317,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = X1 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ),
    inference(cnf_transformation,[],[f2947]) ).

tff(f2947,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = X1 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ),
    inference(ennf_transformation,[],[f1868]) ).

tff(f1868,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
     => ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) = X1 ) ),
    inference(rectify,[],[f399]) ).

tff(f399,axiom,
    ! [X5: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5),X2))
     => ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5),X2) = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_398_insert__absorb) ).

tff(f11690,plain,
    spl250_558,
    inference(avatar_split_clause,[],[f5308,f11688]) ).

tff(f11688,plain,
    ( spl250_558
  <=> ! [X0: x_a,X1: fun_a_bool] :
        ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = X1 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_558])]) ).

tff(f5308,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = X1 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ),
    inference(cnf_transformation,[],[f2935]) ).

tff(f2935,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = X1 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ),
    inference(ennf_transformation,[],[f1861]) ).

tff(f1861,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
     => ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) = X1 ) ),
    inference(rectify,[],[f398]) ).

tff(f398,axiom,
    ! [X5: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5),X2))
     => ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),X2) = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_397_insert__absorb) ).

tff(f11686,plain,
    spl250_557,
    inference(avatar_split_clause,[],[f5306,f11684]) ).

tff(f11684,plain,
    ( spl250_557
  <=> ! [X0: pname,X1: fun_pname_bool] :
        ( ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1) = X1 )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_557])]) ).

tff(f5306,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1) = X1 )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ),
    inference(cnf_transformation,[],[f2933]) ).

tff(f2933,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1) = X1 )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ),
    inference(ennf_transformation,[],[f1859]) ).

tff(f1859,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
     => ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1) = X1 ) ),
    inference(rectify,[],[f401]) ).

tff(f401,axiom,
    ! [X5: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5),X2))
     => ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5),X2) = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_400_insert__absorb) ).

tff(f11682,plain,
    ( spl250_556
    | ~ spl250_137
    | ~ spl250_307 ),
    inference(avatar_split_clause,[],[f9456,f9056,f8033,f11680]) ).

tff(f11680,plain,
    ( spl250_556
  <=> ! [X0: nat] : ~ sP17(hAPP_nat_nat(suc,X0),X0,ord_less_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_556])]) ).

tff(f8033,plain,
    ( spl250_137
  <=> ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_137])]) ).

tff(f9456,plain,
    ( ! [X0: nat] : ~ sP17(hAPP_nat_nat(suc,X0),X0,ord_less_nat)
    | ~ spl250_137
    | ~ spl250_307 ),
    inference(resolution,[],[f9057,f8034]) ).

tff(f8034,plain,
    ( ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X0)))
    | ~ spl250_137 ),
    inference(avatar_component_clause,[],[f8033]) ).

tff(f11678,plain,
    spl250_555,
    inference(avatar_split_clause,[],[f5279,f11676]) ).

tff(f11676,plain,
    ( spl250_555
  <=> ! [X0: fun_nat_bool,X1: nat] :
        ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
        | ~ hBOOL(hAPP_nat_bool(X0,sK120(X0)))
        | ~ hBOOL(hAPP_nat_bool(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_555])]) ).

tff(f5279,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
      | ~ hBOOL(hAPP_nat_bool(X0,sK120(X0)))
      | ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
    inference(cnf_transformation,[],[f3979]) ).

tff(f11674,plain,
    spl250_554,
    inference(avatar_split_clause,[],[f5276,f11672]) ).

tff(f11672,plain,
    ( spl250_554
  <=> ! [X0: nat,X1: fun_nat_bool] :
        ( hBOOL(hAPP_nat_bool(X1,X0))
        | hBOOL(hAPP_nat_bool(X1,sK119(X1)))
        | ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_554])]) ).

tff(f5276,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(X1,X0))
      | hBOOL(hAPP_nat_bool(X1,sK119(X1)))
      | ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
    inference(cnf_transformation,[],[f3977]) ).

tff(f11670,plain,
    spl250_553,
    inference(avatar_split_clause,[],[f4869,f11668]) ).

tff(f11668,plain,
    ( spl250_553
  <=> ! [X0: int] : ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,sK75(X0))),hAPP_nat_int(semiri1621563631at_int,sK76(X0))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_553])]) ).

tff(f4869,plain,
    ! [X0: int] : ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,sK75(X0))),hAPP_nat_int(semiri1621563631at_int,sK76(X0))) = X0 ),
    inference(cnf_transformation,[],[f3904]) ).

tff(f3904,plain,
    ! [X0: int] : ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,sK75(X0))),hAPP_nat_int(semiri1621563631at_int,sK76(X0))) = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK75,sK76])],[f2610,f3903]) ).

tff(f3903,plain,
    ! [X0: int] :
      ( ? [X1: nat,X2: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)) = X0 )
     => ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,sK75(X0))),hAPP_nat_int(semiri1621563631at_int,sK76(X0))) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f2610,plain,
    ! [X0: int] :
    ? [X1: nat,X2: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)) = X0 ),
    inference(ennf_transformation,[],[f1517]) ).

tff(f1517,plain,
    ! [X0: int] :
      ~ ! [X1: nat,X2: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)) != X0 ),
    inference(rectify,[],[f1144]) ).

tff(f1144,axiom,
    ! [X95: int] :
      ~ ! [X32: nat,X26: nat] : ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X32)),hAPP_nat_int(semiri1621563631at_int,X26)) != X95 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1143_int__diff__cases) ).

tff(f11666,plain,
    spl250_552,
    inference(avatar_split_clause,[],[f4688,f11664]) ).

tff(f11664,plain,
    ( spl250_552
  <=> ! [X0: nat] : ( hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X0)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_552])]) ).

tff(f4688,plain,
    ! [X0: nat] : ( hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X0)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,X0)) ),
    inference(cnf_transformation,[],[f1416]) ).

tff(f1416,plain,
    ! [X0: nat] : ( hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X0)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,X0)) ),
    inference(rectify,[],[f1125]) ).

tff(f1125,axiom,
    ! [X12: nat] : ( hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X12)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,X12)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1124_int__Suc) ).

tff(f11631,plain,
    ( spl250_551
    | ~ spl250_136
    | ~ spl250_307 ),
    inference(avatar_split_clause,[],[f9455,f9056,f8029,f11629]) ).

tff(f11629,plain,
    ( spl250_551
  <=> ! [X0: nat] : ~ sP17(hAPP_nat_nat(suc,X0),zero_zero_nat,ord_less_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_551])]) ).

tff(f8029,plain,
    ( spl250_136
  <=> ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_136])]) ).

tff(f9455,plain,
    ( ! [X0: nat] : ~ sP17(hAPP_nat_nat(suc,X0),zero_zero_nat,ord_less_nat)
    | ~ spl250_136
    | ~ spl250_307 ),
    inference(resolution,[],[f9057,f8030]) ).

tff(f8030,plain,
    ( ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,X0)))
    | ~ spl250_136 ),
    inference(avatar_component_clause,[],[f8029]) ).

tff(f11569,plain,
    ( spl250_550
    | ~ spl250_114
    | ~ spl250_223 ),
    inference(avatar_split_clause,[],[f9158,f8650,f7869,f11567]) ).

tff(f11567,plain,
    ( spl250_550
  <=> ! [X0: x_a] : ( bot_bot_fun_a_bool != collect_a(hAPP_a_fun_a_bool(fequal_a,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_550])]) ).

tff(f7869,plain,
    ( spl250_114
  <=> ! [X0: x_a,X1: fun_a_bool] : ( bot_bot_fun_a_bool != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_114])]) ).

tff(f8650,plain,
    ( spl250_223
  <=> ! [X0: x_a] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = collect_a(hAPP_a_fun_a_bool(fequal_a,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_223])]) ).

tff(f9158,plain,
    ( ! [X0: x_a] : ( bot_bot_fun_a_bool != collect_a(hAPP_a_fun_a_bool(fequal_a,X0)) )
    | ~ spl250_114
    | ~ spl250_223 ),
    inference(superposition,[],[f7870,f8651]) ).

tff(f8651,plain,
    ( ! [X0: x_a] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = collect_a(hAPP_a_fun_a_bool(fequal_a,X0)) )
    | ~ spl250_223 ),
    inference(avatar_component_clause,[],[f8650]) ).

tff(f7870,plain,
    ( ! [X0: x_a,X1: fun_a_bool] : ( bot_bot_fun_a_bool != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) )
    | ~ spl250_114 ),
    inference(avatar_component_clause,[],[f7869]) ).

tff(f11162,plain,
    ( ~ spl250_549
    | ~ spl250_48
    | ~ spl250_458 ),
    inference(avatar_split_clause,[],[f11061,f10523,f7532,f11159]) ).

tff(f11159,plain,
    ( spl250_549
  <=> sP3(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_549])]) ).

tff(f10523,plain,
    ( spl250_458
  <=> ! [X0: fun_fu425979586l_bool] :
        ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK112(X0)),sK113(X0))))
        | ~ sP3(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_458])]) ).

tff(f11061,plain,
    ( ~ sP3(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool))
    | ~ spl250_48
    | ~ spl250_458 ),
    inference(resolution,[],[f10524,f7533]) ).

tff(f10524,plain,
    ( ! [X0: fun_fu425979586l_bool] :
        ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK112(X0)),sK113(X0))))
        | ~ sP3(X0) )
    | ~ spl250_458 ),
    inference(avatar_component_clause,[],[f10523]) ).

tff(f11123,plain,
    ( ~ spl250_548
    | ~ spl250_47
    | ~ spl250_456 ),
    inference(avatar_split_clause,[],[f11053,f10515,f7528,f11120]) ).

tff(f11120,plain,
    ( spl250_548
  <=> sP2(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_548])]) ).

tff(f10515,plain,
    ( spl250_456
  <=> ! [X0: fun_fu819804446l_bool] :
        ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK105(X0)),sK106(X0))))
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_456])]) ).

tff(f11053,plain,
    ( ~ sP2(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool))
    | ~ spl250_47
    | ~ spl250_456 ),
    inference(resolution,[],[f10516,f7529]) ).

tff(f10516,plain,
    ( ! [X0: fun_fu819804446l_bool] :
        ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK105(X0)),sK106(X0))))
        | ~ sP2(X0) )
    | ~ spl250_456 ),
    inference(avatar_component_clause,[],[f10515]) ).

tff(f11087,plain,
    ( ~ spl250_547
    | ~ spl250_46
    | ~ spl250_454 ),
    inference(avatar_split_clause,[],[f11045,f10507,f7524,f11084]) ).

tff(f11084,plain,
    ( spl250_547
  <=> sP1(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_547])]) ).

tff(f10507,plain,
    ( spl250_454
  <=> ! [X0: fun_fun_a_bool_bool] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK98(X0)),sK99(X0))))
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_454])]) ).

tff(f11045,plain,
    ( ~ sP1(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool))
    | ~ spl250_46
    | ~ spl250_454 ),
    inference(resolution,[],[f10508,f7525]) ).

tff(f10508,plain,
    ( ! [X0: fun_fun_a_bool_bool] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK98(X0)),sK99(X0))))
        | ~ sP1(X0) )
    | ~ spl250_454 ),
    inference(avatar_component_clause,[],[f10507]) ).

tff(f11039,plain,
    ( spl250_546
    | ~ spl250_66
    | ~ spl250_210 ),
    inference(avatar_split_clause,[],[f8622,f8388,f7608,f11037]) ).

tff(f11037,plain,
    ( spl250_546
  <=> ! [X0: bool,X1: int] :
        ( hBOOL(X0)
        | ~ sP12(cOMBK_bool_int(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_546])]) ).

tff(f8388,plain,
    ( spl250_210
  <=> ! [X0: fun_int_bool,X1: int] :
        ( hBOOL(hAPP_int_bool(X0,sK205(X0,X1)))
        | ~ sP12(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_210])]) ).

tff(f8622,plain,
    ( ! [X0: bool,X1: int] :
        ( hBOOL(X0)
        | ~ sP12(cOMBK_bool_int(X0),X1) )
    | ~ spl250_66
    | ~ spl250_210 ),
    inference(superposition,[],[f8389,f7609]) ).

tff(f8389,plain,
    ( ! [X0: fun_int_bool,X1: int] :
        ( hBOOL(hAPP_int_bool(X0,sK205(X0,X1)))
        | ~ sP12(X0,X1) )
    | ~ spl250_210 ),
    inference(avatar_component_clause,[],[f8388]) ).

tff(f10957,plain,
    ( spl250_545
    | ~ spl250_67
    | ~ spl250_167 ),
    inference(avatar_split_clause,[],[f8219,f8156,f7612,f10955]) ).

tff(f7612,plain,
    ( spl250_67
  <=> ! [X0: bool,X1: nat] : ( hAPP_nat_bool(cOMBK_bool_nat(X0),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_67])]) ).

tff(f8156,plain,
    ( spl250_167
  <=> ! [X0: fun_nat_bool] :
        ( ( bot_bot_fun_nat_bool = X0 )
        | hBOOL(hAPP_nat_bool(X0,sK48(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_167])]) ).

tff(f8219,plain,
    ( ! [X0: bool] :
        ( hBOOL(X0)
        | ( bot_bot_fun_nat_bool = cOMBK_bool_nat(X0) ) )
    | ~ spl250_67
    | ~ spl250_167 ),
    inference(superposition,[],[f8157,f7613]) ).

tff(f7613,plain,
    ( ! [X0: bool,X1: nat] : ( hAPP_nat_bool(cOMBK_bool_nat(X0),X1) = X0 )
    | ~ spl250_67 ),
    inference(avatar_component_clause,[],[f7612]) ).

tff(f8157,plain,
    ( ! [X0: fun_nat_bool] :
        ( hBOOL(hAPP_nat_bool(X0,sK48(X0)))
        | ( bot_bot_fun_nat_bool = X0 ) )
    | ~ spl250_167 ),
    inference(avatar_component_clause,[],[f8156]) ).

tff(f10926,plain,
    ( spl250_544
    | ~ spl250_66
    | ~ spl250_165 ),
    inference(avatar_split_clause,[],[f8212,f8148,f7608,f10924]) ).

tff(f8148,plain,
    ( spl250_165
  <=> ! [X0: fun_int_bool] :
        ( ( bot_bot_fun_int_bool = X0 )
        | hBOOL(hAPP_int_bool(X0,sK46(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_165])]) ).

tff(f8212,plain,
    ( ! [X0: bool] :
        ( hBOOL(X0)
        | ( bot_bot_fun_int_bool = cOMBK_bool_int(X0) ) )
    | ~ spl250_66
    | ~ spl250_165 ),
    inference(superposition,[],[f8149,f7609]) ).

tff(f8149,plain,
    ( ! [X0: fun_int_bool] :
        ( hBOOL(hAPP_int_bool(X0,sK46(X0)))
        | ( bot_bot_fun_int_bool = X0 ) )
    | ~ spl250_165 ),
    inference(avatar_component_clause,[],[f8148]) ).

tff(f10890,plain,
    ( spl250_543
    | ~ spl250_20
    | ~ spl250_136 ),
    inference(avatar_split_clause,[],[f8166,f8029,f7406,f10887]) ).

tff(f8166,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat))
    | ~ spl250_20
    | ~ spl250_136 ),
    inference(superposition,[],[f8030,f7408]) ).

tff(f10883,plain,
    spl250_542,
    inference(avatar_split_clause,[],[f7217,f10881]) ).

tff(f10881,plain,
    ( spl250_542
  <=> ! [X2: fun_fun_a_bool_a,X0: x_a,X1: fun_a_fun_a_a] :
        ( ( hAPP_fun_a_bool_a(X2,collect_a(hAPP_a_fun_a_bool(fequal_a,X0))) = X0 )
        | ~ hBOOL(finite_folding_one_a(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_542])]) ).

tff(f7217,plain,
    ! [X2: fun_fun_a_bool_a,X0: x_a,X1: fun_a_fun_a_a] :
      ( ( hAPP_fun_a_bool_a(X2,collect_a(hAPP_a_fun_a_bool(fequal_a,X0))) = X0 )
      | ~ hBOOL(finite_folding_one_a(X1,X2)) ),
    inference(forward_demodulation,[],[f6004,f4680]) ).

tff(f6004,plain,
    ! [X2: fun_fun_a_bool_a,X0: x_a,X1: fun_a_fun_a_a] :
      ( ( hAPP_fun_a_bool_a(X2,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)) = X0 )
      | ~ hBOOL(finite_folding_one_a(X1,X2)) ),
    inference(cnf_transformation,[],[f3280]) ).

tff(f3280,plain,
    ! [X0: x_a,X1: fun_a_fun_a_a,X2: fun_fun_a_bool_a] :
      ( ( hAPP_fun_a_bool_a(X2,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)) = X0 )
      | ~ hBOOL(finite_folding_one_a(X1,X2)) ),
    inference(ennf_transformation,[],[f2263]) ).

tff(f2263,plain,
    ! [X0: x_a,X1: fun_a_fun_a_a,X2: fun_fun_a_bool_a] :
      ( hBOOL(finite_folding_one_a(X1,X2))
     => ( hAPP_fun_a_bool_a(X2,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)) = X0 ) ),
    inference(rectify,[],[f749]) ).

tff(f749,axiom,
    ! [X8: x_a,X6: fun_a_fun_a_a,X4: fun_fun_a_bool_a] :
      ( hBOOL(finite_folding_one_a(X6,X4))
     => ( hAPP_fun_a_bool_a(X4,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),bot_bot_fun_a_bool)) = X8 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_748_folding__one_Osingleton) ).

tff(f10879,plain,
    spl250_541,
    inference(avatar_split_clause,[],[f7190,f10877]) ).

tff(f10877,plain,
    ( spl250_541
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_541])]) ).

tff(f7190,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ),
    inference(forward_demodulation,[],[f7189,f4588]) ).

tff(f7189,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))) ),
    inference(forward_demodulation,[],[f5635,f4588]) ).

tff(f5635,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))) ),
    inference(cnf_transformation,[],[f4159]) ).

tff(f10875,plain,
    spl250_540,
    inference(avatar_split_clause,[],[f7188,f10873]) ).

tff(f10873,plain,
    ( spl250_540
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_540])]) ).

tff(f7188,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(forward_demodulation,[],[f7187,f4588]) ).

tff(f7187,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))) ),
    inference(forward_demodulation,[],[f5636,f4588]) ).

tff(f5636,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X0),X1)))) ),
    inference(cnf_transformation,[],[f4159]) ).

tff(f10871,plain,
    spl250_539,
    inference(avatar_split_clause,[],[f7183,f10869]) ).

tff(f10869,plain,
    ( spl250_539
  <=> ! [X0: fun_int_bool,X1: fun_int_bool] :
        ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))
        | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_539])]) ).

tff(f7183,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ),
    inference(forward_demodulation,[],[f7182,f4586]) ).

tff(f7182,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))) ),
    inference(forward_demodulation,[],[f5632,f4586]) ).

tff(f5632,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))) ),
    inference(cnf_transformation,[],[f4157]) ).

tff(f10867,plain,
    spl250_538,
    inference(avatar_split_clause,[],[f7181,f10865]) ).

tff(f10865,plain,
    ( spl250_538
  <=> ! [X0: fun_int_bool,X1: fun_int_bool] :
        ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))
        | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_538])]) ).

tff(f7181,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(forward_demodulation,[],[f7180,f4586]) ).

tff(f7180,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))) ),
    inference(forward_demodulation,[],[f5633,f4586]) ).

tff(f5633,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X0),X1)))) ),
    inference(cnf_transformation,[],[f4157]) ).

tff(f10863,plain,
    spl250_537,
    inference(avatar_split_clause,[],[f7125,f10861]) ).

tff(f10861,plain,
    ( spl250_537
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_537])]) ).

tff(f7125,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(forward_demodulation,[],[f5488,f4670]) ).

tff(f5488,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4052]) ).

tff(f4052,plain,
    ! [X0: nat,X1: nat] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X0)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X0))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    inference(nnf_transformation,[],[f1977]) ).

tff(f1977,plain,
    ! [X0: nat,X1: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X0)) ),
    inference(rectify,[],[f170]) ).

tff(f170,axiom,
    ! [X22: nat,X14: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X14))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X14)),X22)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_not__less__eq__eq) ).

tff(f10859,plain,
    spl250_536,
    inference(avatar_split_clause,[],[f7124,f10857]) ).

tff(f10857,plain,
    ( spl250_536
  <=> ! [X0: nat,X1: nat] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_536])]) ).

tff(f7124,plain,
    ! [X0: nat,X1: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(forward_demodulation,[],[f5489,f4670]) ).

tff(f5489,plain,
    ! [X0: nat,X1: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X0)) ),
    inference(cnf_transformation,[],[f4052]) ).

tff(f10855,plain,
    spl250_535,
    inference(avatar_split_clause,[],[f7110,f10853]) ).

tff(f7110,plain,
    ! [X0: int,X1: int] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
      | sP5(X0,X1)
      | ~ sP4(X1,X0) ),
    inference(forward_demodulation,[],[f6642,f4587]) ).

tff(f6642,plain,
    ! [X0: int,X1: int] :
      ( sP5(X0,X1)
      | ~ sP4(X1,X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),pls)) ),
    inference(definition_unfolding,[],[f5469,f4550]) ).

tff(f5469,plain,
    ! [X0: int,X1: int] :
      ( sP5(X0,X1)
      | ~ sP4(X1,X0)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int)) ),
    inference(cnf_transformation,[],[f4042]) ).

tff(f10851,plain,
    spl250_534,
    inference(avatar_split_clause,[],[f7102,f10849]) ).

tff(f10849,plain,
    ( spl250_534
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_534])]) ).

tff(f7102,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0))) ),
    inference(forward_demodulation,[],[f7101,f4588]) ).

tff(f7101,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1))) ),
    inference(forward_demodulation,[],[f5412,f4588]) ).

tff(f5412,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1))) ),
    inference(cnf_transformation,[],[f3054]) ).

tff(f3054,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0))))
      | ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0)))
        & ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1))) ) ),
    inference(ennf_transformation,[],[f1948]) ).

tff(f1948,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0)))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1))) )
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0)))) ),
    inference(rectify,[],[f118]) ).

tff(f118,axiom,
    ! [X9: fun_nat_bool,X10: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X9)))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X10))) )
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X10),X9)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_finite__Collect__conjI) ).

tff(f10846,plain,
    spl250_533,
    inference(avatar_split_clause,[],[f7100,f10844]) ).

tff(f10844,plain,
    ( spl250_533
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_533])]) ).

tff(f7100,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0))) ),
    inference(forward_demodulation,[],[f7099,f4588]) ).

tff(f7099,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) ),
    inference(forward_demodulation,[],[f5413,f4588]) ).

tff(f5413,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X0))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X0))) ),
    inference(cnf_transformation,[],[f3054]) ).

tff(f10842,plain,
    spl250_532,
    inference(avatar_split_clause,[],[f7098,f10840]) ).

tff(f10840,plain,
    ( spl250_532
  <=> ! [X0: fun_int_bool,X1: fun_int_bool] :
        ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
        | hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X1),X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_532])]) ).

tff(f7098,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X1),X0))) ),
    inference(forward_demodulation,[],[f7097,f4586]) ).

tff(f7097,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X1),X0)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1))) ),
    inference(forward_demodulation,[],[f5410,f4586]) ).

tff(f5410,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X1),X0))))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1))) ),
    inference(cnf_transformation,[],[f3053]) ).

tff(f3053,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X1),X0))))
      | ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0)))
        & ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1))) ) ),
    inference(ennf_transformation,[],[f1947]) ).

tff(f1947,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0)))
        | hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1))) )
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X1),X0)))) ),
    inference(rectify,[],[f119]) ).

tff(f119,axiom,
    ! [X9: fun_int_bool,X10: fun_int_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X9)))
        | hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X10))) )
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X10),X9)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_finite__Collect__conjI) ).

tff(f10838,plain,
    spl250_531,
    inference(avatar_split_clause,[],[f7096,f10836]) ).

tff(f10836,plain,
    ( spl250_531
  <=> ! [X0: fun_int_bool,X1: fun_int_bool] :
        ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
        | hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X1),X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_531])]) ).

tff(f7096,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X1),X0))) ),
    inference(forward_demodulation,[],[f7095,f4586]) ).

tff(f7095,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X1),X0)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0))) ),
    inference(forward_demodulation,[],[f5411,f4586]) ).

tff(f5411,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X1),X0))))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X0))) ),
    inference(cnf_transformation,[],[f3053]) ).

tff(f10834,plain,
    spl250_530,
    inference(avatar_split_clause,[],[f7084,f10832]) ).

tff(f10832,plain,
    ( spl250_530
  <=> ! [X0: x_a,X1: x_a] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),collect_a(hAPP_a_fun_a_bool(fequal_a,X1))))
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_530])]) ).

tff(f7084,plain,
    ! [X0: x_a,X1: x_a] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),collect_a(hAPP_a_fun_a_bool(fequal_a,X1))))
      | ( X0 = X1 ) ),
    inference(forward_demodulation,[],[f5387,f4680]) ).

tff(f5387,plain,
    ! [X0: x_a,X1: x_a] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))) ),
    inference(cnf_transformation,[],[f3033]) ).

tff(f3033,plain,
    ! [X0: x_a,X1: x_a] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))) ),
    inference(ennf_transformation,[],[f1930]) ).

tff(f1930,plain,
    ! [X0: x_a,X1: x_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)))
     => ( X0 = X1 ) ),
    inference(rectify,[],[f593]) ).

tff(f593,axiom,
    ! [X28: x_a,X5: x_a] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X28),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),bot_bot_fun_a_bool)))
     => ( X5 = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_singletonE) ).

tff(f10830,plain,
    spl250_529,
    inference(avatar_split_clause,[],[f7083,f10828]) ).

tff(f7083,plain,
    ! [X0: nat,X1: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | ( hAPP_nat_nat(suc,sK125(X1)) = X1 ) ),
    inference(forward_demodulation,[],[f5385,f4670]) ).

tff(f5385,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(suc,sK125(X1)) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1)) ),
    inference(cnf_transformation,[],[f3998]) ).

tff(f3998,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(suc,sK125(X1)) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK125])],[f3031,f3997]) ).

tff(f3997,plain,
    ! [X1: nat] :
      ( ? [X2: nat] : ( hAPP_nat_nat(suc,X2) = X1 )
     => ( hAPP_nat_nat(suc,sK125(X1)) = X1 ) ),
    introduced(choice_axiom,[]) ).

tff(f3031,plain,
    ! [X0: nat,X1: nat] :
      ( ? [X2: nat] : ( hAPP_nat_nat(suc,X2) = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1)) ),
    inference(ennf_transformation,[],[f1928]) ).

tff(f1928,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X1))
     => ? [X2: nat] : ( hAPP_nat_nat(suc,X2) = X1 ) ),
    inference(rectify,[],[f301]) ).

tff(f301,axiom,
    ! [X11: nat,X31: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X11)),X31))
     => ? [X32: nat] : ( hAPP_nat_nat(suc,X32) = X31 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_Suc__le__D) ).

tff(f10826,plain,
    spl250_528,
    inference(avatar_split_clause,[],[f6983,f10824]) ).

tff(f10824,plain,
    ( spl250_528
  <=> ! [X0: x_a,X1: fun_pname_bool] :
        ( ( collect_a(hAPP_a_fun_a_bool(fequal_a,X0)) = image_pname_a(cOMBK_a_pname(X0),X1) )
        | ( bot_bo844097828e_bool = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_528])]) ).

tff(f6983,plain,
    ! [X0: x_a,X1: fun_pname_bool] :
      ( ( collect_a(hAPP_a_fun_a_bool(fequal_a,X0)) = image_pname_a(cOMBK_a_pname(X0),X1) )
      | ( bot_bo844097828e_bool = X1 ) ),
    inference(forward_demodulation,[],[f4947,f4680]) ).

tff(f4947,plain,
    ! [X0: x_a,X1: fun_pname_bool] :
      ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = image_pname_a(cOMBK_a_pname(X0),X1) )
      | ( bot_bo844097828e_bool = X1 ) ),
    inference(cnf_transformation,[],[f2611]) ).

tff(f2611,plain,
    ! [X0: x_a,X1: fun_pname_bool] :
      ( ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = image_pname_a(cOMBK_a_pname(X0),X1) )
        | ( bot_bo844097828e_bool = X1 ) )
      & ( ( bot_bot_fun_a_bool = image_pname_a(cOMBK_a_pname(X0),X1) )
        | ( bot_bo844097828e_bool != X1 ) ) ),
    inference(ennf_transformation,[],[f1594]) ).

tff(f1594,plain,
    ! [X0: x_a,X1: fun_pname_bool] :
      ( ( ( bot_bo844097828e_bool != X1 )
       => ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = image_pname_a(cOMBK_a_pname(X0),X1) ) )
      & ( ( bot_bo844097828e_bool = X1 )
       => ( bot_bot_fun_a_bool = image_pname_a(cOMBK_a_pname(X0),X1) ) ) ),
    inference(rectify,[],[f669]) ).

tff(f669,axiom,
    ! [X29: x_a,X2: fun_pname_bool] :
      ( ( ( bot_bo844097828e_bool != X2 )
       => ( image_pname_a(cOMBK_a_pname(X29),X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X29),bot_bot_fun_a_bool) ) )
      & ( ( bot_bo844097828e_bool = X2 )
       => ( bot_bot_fun_a_bool = image_pname_a(cOMBK_a_pname(X29),X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_668_image__constant__conv) ).

tff(f10822,plain,
    spl250_527,
    inference(avatar_split_clause,[],[f6949,f10820]) ).

tff(f10820,plain,
    ( spl250_527
  <=> ! [X0: int] :
        ( ( one_one_nat = hAPP_nat_nat(suc,number_number_of_nat(X0)) )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_527])]) ).

tff(f6949,plain,
    ! [X0: int] :
      ( ( one_one_nat = hAPP_nat_nat(suc,number_number_of_nat(X0)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(forward_demodulation,[],[f4701,f4671]) ).

tff(f4701,plain,
    ! [X0: int] :
      ( ( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X0)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(cnf_transformation,[],[f2579]) ).

tff(f10818,plain,
    spl250_526,
    inference(avatar_split_clause,[],[f6876,f10816]) ).

tff(f10816,plain,
    ( spl250_526
  <=> ! [X4: nat,X0: fun_nat_bool,X2: nat] :
        ( hBOOL(hAPP_nat_bool(X0,X4))
        | ~ sP19(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_526])]) ).

tff(f6876,plain,
    ! [X2: nat,X0: fun_nat_bool,X4: nat] :
      ( hBOOL(hAPP_nat_bool(X0,X4))
      | ~ sP19(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4),X2) ),
    inference(equality_resolution,[],[f6315]) ).

tff(f6315,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: nat,X4: nat] :
      ( hBOOL(hAPP_nat_bool(X0,X4))
      | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4) != X1 )
      | ~ sP19(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4431]) ).

tff(f10814,plain,
    spl250_525,
    inference(avatar_split_clause,[],[f6875,f10812]) ).

tff(f10812,plain,
    ( spl250_525
  <=> ! [X4: nat,X0: fun_nat_bool,X2: nat] :
        ( hBOOL(hAPP_nat_bool(X0,X4))
        | ~ sP18(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_525])]) ).

tff(f6875,plain,
    ! [X2: nat,X0: fun_nat_bool,X4: nat] :
      ( hBOOL(hAPP_nat_bool(X0,X4))
      | ~ sP18(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4),X2) ),
    inference(equality_resolution,[],[f6307]) ).

tff(f6307,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: nat,X4: nat] :
      ( hBOOL(hAPP_nat_bool(X0,X4))
      | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4) != X1 )
      | ~ sP18(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4425]) ).

tff(f10810,plain,
    spl250_524,
    inference(avatar_split_clause,[],[f6803,f10808]) ).

tff(f10808,plain,
    ( spl250_524
  <=> ! [X2: nat,X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_524])]) ).

tff(f6803,plain,
    ! [X2: nat,X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,X2)))),
    inference(equality_resolution,[],[f5518]) ).

tff(f5518,plain,
    ! [X2: nat,X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),hAPP_nat_int(semiri1621563631at_int,X2)) != X1 ) ),
    inference(cnf_transformation,[],[f4082]) ).

tff(f10806,plain,
    ( ~ spl250_523
    | spl250_131
    | ~ spl250_295 ),
    inference(avatar_split_clause,[],[f9396,f9007,f8002,f10803]) ).

tff(f10803,plain,
    ( spl250_523
  <=> hBOOL(hAPP_a_bool(g,hAPP_pname_a(mgt_call,pn))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_523])]) ).

tff(f8002,plain,
    ( spl250_131
  <=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_131])]) ).

tff(f9007,plain,
    ( spl250_295
  <=> ! [X0: x_a,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
        | ~ hBOOL(hAPP_a_bool(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_295])]) ).

tff(f9396,plain,
    ( ~ hBOOL(hAPP_a_bool(g,hAPP_pname_a(mgt_call,pn)))
    | spl250_131
    | ~ spl250_295 ),
    inference(resolution,[],[f9008,f8004]) ).

tff(f8004,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g))
    | spl250_131 ),
    inference(avatar_component_clause,[],[f8002]) ).

tff(f9008,plain,
    ( ! [X0: x_a,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
        | ~ hBOOL(hAPP_a_bool(X1,X0)) )
    | ~ spl250_295 ),
    inference(avatar_component_clause,[],[f9007]) ).

tff(f10801,plain,
    spl250_522,
    inference(avatar_split_clause,[],[f6705,f10799]) ).

tff(f10799,plain,
    ( spl250_522
  <=> ! [X2: nat,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_522])]) ).

tff(f6705,plain,
    ! [X2: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(equality_resolution,[],[f4788]) ).

tff(f4788,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
      | ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1) != X0 ) ),
    inference(cnf_transformation,[],[f3821]) ).

tff(f10797,plain,
    spl250_521,
    inference(avatar_split_clause,[],[f6703,f10795]) ).

tff(f10795,plain,
    ( spl250_521
  <=> ! [X2: int,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_521])]) ).

tff(f6703,plain,
    ! [X2: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(equality_resolution,[],[f4782]) ).

tff(f4782,plain,
    ! [X2: int,X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
      | ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1) != X0 ) ),
    inference(cnf_transformation,[],[f3815]) ).

tff(f10793,plain,
    spl250_520,
    inference(avatar_split_clause,[],[f6701,f10791]) ).

tff(f10791,plain,
    ( spl250_520
  <=> ! [X2: x_a,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_520])]) ).

tff(f6701,plain,
    ! [X2: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(equality_resolution,[],[f4778]) ).

tff(f4778,plain,
    ! [X2: x_a,X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
      | ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1) != X0 ) ),
    inference(cnf_transformation,[],[f3810]) ).

tff(f10789,plain,
    spl250_519,
    inference(avatar_split_clause,[],[f6699,f10787]) ).

tff(f10787,plain,
    ( spl250_519
  <=> ! [X2: pname,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_519])]) ).

tff(f6699,plain,
    ! [X2: pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(equality_resolution,[],[f4774]) ).

tff(f4774,plain,
    ! [X2: pname,X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
      | ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1) != X0 ) ),
    inference(cnf_transformation,[],[f3805]) ).

tff(f10785,plain,
    spl250_518,
    inference(avatar_split_clause,[],[f6606,f10783]) ).

tff(f10783,plain,
    ( spl250_518
  <=> ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_518])]) ).

tff(f6606,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(definition_unfolding,[],[f4821,f4550]) ).

tff(f4821,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
    inference(cnf_transformation,[],[f3845]) ).

tff(f3845,plain,
    ! [X0: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ) ),
    inference(nnf_transformation,[],[f1494]) ).

tff(f1494,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
    inference(rectify,[],[f1037]) ).

tff(f1037,axiom,
    ! [X53: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X53))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X53)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1036_int__one__le__iff__zero__less) ).

tff(f10781,plain,
    spl250_517,
    inference(avatar_split_clause,[],[f6605,f10779]) ).

tff(f10779,plain,
    ( spl250_517
  <=> ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_517])]) ).

tff(f6605,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(definition_unfolding,[],[f4822,f4550]) ).

tff(f4822,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
    inference(cnf_transformation,[],[f3845]) ).

tff(f10777,plain,
    spl250_516,
    inference(avatar_split_clause,[],[f6595,f10775]) ).

tff(f6595,plain,
    ! [X0: int] :
      ( ( hAPP_nat_int(semiri1621563631at_int,sK34(X0)) = X0 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(definition_unfolding,[],[f4728,f4550]) ).

tff(f4728,plain,
    ! [X0: int] :
      ( ( hAPP_nat_int(semiri1621563631at_int,sK34(X0)) = X0 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
    inference(cnf_transformation,[],[f3752]) ).

tff(f3752,plain,
    ! [X0: int] :
      ( ( hAPP_nat_int(semiri1621563631at_int,sK34(X0)) = X0 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK34])],[f2600,f3751]) ).

tff(f3751,plain,
    ! [X0: int] :
      ( ? [X1: nat] : ( hAPP_nat_int(semiri1621563631at_int,X1) = X0 )
     => ( hAPP_nat_int(semiri1621563631at_int,sK34(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f2600,plain,
    ! [X0: int] :
      ( ? [X1: nat] : ( hAPP_nat_int(semiri1621563631at_int,X1) = X0 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
    inference(ennf_transformation,[],[f1451]) ).

tff(f1451,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
     => ? [X1: nat] : ( hAPP_nat_int(semiri1621563631at_int,X1) = X0 ) ),
    inference(rectify,[],[f1143]) ).

tff(f1143,axiom,
    ! [X19: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X19))
     => ? [X26: nat] : ( hAPP_nat_int(semiri1621563631at_int,X26) = X19 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1142_zero__le__imp__eq__int) ).

tff(f10773,plain,
    spl250_515,
    inference(avatar_split_clause,[],[f6594,f10771]) ).

tff(f6594,plain,
    ! [X0: int] :
      ( ( hAPP_nat_int(semiri1621563631at_int,sK33(X0)) = X0 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(definition_unfolding,[],[f4727,f4550]) ).

tff(f4727,plain,
    ! [X0: int] :
      ( ( hAPP_nat_int(semiri1621563631at_int,sK33(X0)) = X0 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
    inference(cnf_transformation,[],[f3750]) ).

tff(f3750,plain,
    ! [X0: int] :
      ( ( hAPP_nat_int(semiri1621563631at_int,sK33(X0)) = X0 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f2599,f3749]) ).

tff(f3749,plain,
    ! [X0: int] :
      ( ? [X1: nat] : ( hAPP_nat_int(semiri1621563631at_int,X1) = X0 )
     => ( hAPP_nat_int(semiri1621563631at_int,sK33(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f2599,plain,
    ! [X0: int] :
      ( ? [X1: nat] : ( hAPP_nat_int(semiri1621563631at_int,X1) = X0 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
    inference(ennf_transformation,[],[f1450]) ).

tff(f1450,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
     => ~ ! [X1: nat] : ( hAPP_nat_int(semiri1621563631at_int,X1) != X0 ) ),
    inference(rectify,[],[f1142]) ).

tff(f1142,axiom,
    ! [X95: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X95))
     => ~ ! [X32: nat] : ( hAPP_nat_int(semiri1621563631at_int,X32) != X95 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1141_nonneg__eq__int) ).

tff(f10769,plain,
    spl250_514,
    inference(avatar_split_clause,[],[f6593,f10767]) ).

tff(f6593,plain,
    ! [X0: int] :
      ( ( hAPP_nat_int(semiri1621563631at_int,sK32(X0)) = X0 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(definition_unfolding,[],[f4726,f4550]) ).

tff(f4726,plain,
    ! [X0: int] :
      ( ( hAPP_nat_int(semiri1621563631at_int,sK32(X0)) = X0 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
    inference(cnf_transformation,[],[f3748]) ).

tff(f3748,plain,
    ! [X0: int] :
      ( ( hAPP_nat_int(semiri1621563631at_int,sK32(X0)) = X0 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f2598,f3747]) ).

tff(f3747,plain,
    ! [X0: int] :
      ( ? [X1: nat] : ( hAPP_nat_int(semiri1621563631at_int,X1) = X0 )
     => ( hAPP_nat_int(semiri1621563631at_int,sK32(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f2598,plain,
    ! [X0: int] :
      ( ? [X1: nat] : ( hAPP_nat_int(semiri1621563631at_int,X1) = X0 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
    inference(ennf_transformation,[],[f1449]) ).

tff(f1449,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
     => ~ ! [X1: nat] : ( hAPP_nat_int(semiri1621563631at_int,X1) != X0 ) ),
    inference(rectify,[],[f1141]) ).

tff(f1141,axiom,
    ! [X19: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X19))
     => ~ ! [X26: nat] : ( hAPP_nat_int(semiri1621563631at_int,X26) != X19 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1140_nonneg__int__cases) ).

tff(f10765,plain,
    spl250_513,
    inference(avatar_split_clause,[],[f6590,f10763]) ).

tff(f6590,plain,
    ! [X0: int] :
      ( ( hAPP_nat_int(semiri1621563631at_int,sK31(X0)) = X0 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
    inference(definition_unfolding,[],[f4724,f4550]) ).

tff(f4724,plain,
    ! [X0: int] :
      ( ( hAPP_nat_int(semiri1621563631at_int,sK31(X0)) = X0 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
    inference(cnf_transformation,[],[f3746]) ).

tff(f10759,plain,
    ( spl250_512
    | ~ spl250_106
    | ~ spl250_345
    | ~ spl250_511 ),
    inference(avatar_split_clause,[],[f10754,f10748,f9590,f7837,f10756]) ).

tff(f10756,plain,
    ( spl250_512
  <=> ( one_one_nat = number_number_of_nat(one_one_int) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_512])]) ).

tff(f7837,plain,
    ( spl250_106
  <=> ! [X0: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),pls) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_106])]) ).

tff(f9590,plain,
    ( spl250_345
  <=> ! [X0: int,X1: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_345])]) ).

tff(f10748,plain,
    ( spl250_511
  <=> ( one_one_nat = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_511])]) ).

tff(f10754,plain,
    ( ( one_one_nat = number_number_of_nat(one_one_int) )
    | ~ spl250_106
    | ~ spl250_345
    | ~ spl250_511 ),
    inference(forward_demodulation,[],[f10753,f7838]) ).

tff(f7838,plain,
    ( ! [X0: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),pls) = X0 )
    | ~ spl250_106 ),
    inference(avatar_component_clause,[],[f7837]) ).

tff(f10753,plain,
    ( ( one_one_nat = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)) )
    | ~ spl250_345
    | ~ spl250_511 ),
    inference(forward_demodulation,[],[f10752,f9591]) ).

tff(f9591,plain,
    ( ! [X0: int,X1: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0) )
    | ~ spl250_345 ),
    inference(avatar_component_clause,[],[f9590]) ).

tff(f10752,plain,
    ( ( one_one_nat = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),one_one_int)) )
    | ~ spl250_511 ),
    inference(forward_demodulation,[],[f10750,f6566]) ).

tff(f10750,plain,
    ( ( one_one_nat = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls)) )
    | ~ spl250_511 ),
    inference(avatar_component_clause,[],[f10748]) ).

tff(f10751,plain,
    spl250_511,
    inference(avatar_split_clause,[],[f6562,f10748]) ).

tff(f6562,plain,
    one_one_nat = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls)),
    inference(definition_unfolding,[],[f4564,f4687]) ).

tff(f4564,plain,
    one_one_nat = number_number_of_nat(bit1(pls)),
    inference(cnf_transformation,[],[f1175]) ).

tff(f1175,axiom,
    one_one_nat = number_number_of_nat(bit1(pls)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1174_nat__numeral__1__eq__1) ).

tff(f10743,plain,
    spl250_510,
    inference(avatar_split_clause,[],[f6561,f10740]) ).

tff(f10740,plain,
    ( spl250_510
  <=> ( one_one_int = number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_510])]) ).

tff(f6561,plain,
    one_one_int = number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls)),
    inference(definition_unfolding,[],[f4561,f4687]) ).

tff(f4561,plain,
    one_one_int = number_number_of_int(bit1(pls)),
    inference(cnf_transformation,[],[f1176]) ).

tff(f1176,axiom,
    one_one_int = number_number_of_int(bit1(pls)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1175_one__is__num__one) ).

tff(f10738,plain,
    spl250_509,
    inference(avatar_split_clause,[],[f6323,f10736]) ).

tff(f10736,plain,
    ( spl250_509
  <=> ! [X2: nat,X0: bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_nat_bool(nat_case_bool(X0,X1),hAPP_nat_nat(suc,X2)))
        | ~ hBOOL(hAPP_nat_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_509])]) ).

tff(f6323,plain,
    ! [X2: nat,X0: bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(nat_case_bool(X0,X1),hAPP_nat_nat(suc,X2)))
      | ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f4433]) ).

tff(f4433,plain,
    ! [X0: bool,X1: fun_nat_bool,X2: nat] :
      ( ( hBOOL(hAPP_nat_bool(nat_case_bool(X0,X1),hAPP_nat_nat(suc,X2)))
        | ~ hBOOL(hAPP_nat_bool(X1,X2)) )
      & ( hBOOL(hAPP_nat_bool(X1,X2))
        | ~ hBOOL(hAPP_nat_bool(nat_case_bool(X0,X1),hAPP_nat_nat(suc,X2))) ) ),
    inference(nnf_transformation,[],[f2477]) ).

tff(f2477,plain,
    ! [X0: bool,X1: fun_nat_bool,X2: nat] :
      ( hBOOL(hAPP_nat_bool(nat_case_bool(X0,X1),hAPP_nat_nat(suc,X2)))
    <=> hBOOL(hAPP_nat_bool(X1,X2)) ),
    inference(rectify,[],[f665]) ).

tff(f665,axiom,
    ! [X73: bool,X74: fun_nat_bool,X17: nat] :
      ( hBOOL(hAPP_nat_bool(nat_case_bool(X73,X74),hAPP_nat_nat(suc,X17)))
    <=> hBOOL(hAPP_nat_bool(X74,X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_664_nat__case__Suc) ).

tff(f10734,plain,
    spl250_508,
    inference(avatar_split_clause,[],[f6322,f10732]) ).

tff(f10732,plain,
    ( spl250_508
  <=> ! [X2: nat,X0: bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_nat_bool(X1,X2))
        | ~ hBOOL(hAPP_nat_bool(nat_case_bool(X0,X1),hAPP_nat_nat(suc,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_508])]) ).

tff(f6322,plain,
    ! [X2: nat,X0: bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(X1,X2))
      | ~ hBOOL(hAPP_nat_bool(nat_case_bool(X0,X1),hAPP_nat_nat(suc,X2))) ),
    inference(cnf_transformation,[],[f4433]) ).

tff(f10730,plain,
    spl250_507,
    inference(avatar_split_clause,[],[f6321,f10728]) ).

tff(f6321,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
      | ~ sP19(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4432]) ).

tff(f4432,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
        | ~ sP19(X0,X1,X2) )
      & ( sP19(X0,X1,X2)
        | ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ) ),
    inference(nnf_transformation,[],[f3722]) ).

tff(f3722,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
    <=> sP19(X0,X1,X2) ),
    inference(definition_folding,[],[f3588,f3721]) ).

tff(f3588,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
    <=> ( ! [X3: nat] :
            ( hBOOL(hAPP_nat_bool(X0,X3))
            | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) != X1 ) )
        & ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) ),
    inference(ennf_transformation,[],[f2476]) ).

tff(f2476,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
    <=> ~ ( ? [X3: nat] :
              ( ~ hBOOL(hAPP_nat_bool(X0,X3))
              & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) = X1 ) )
          | ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) ),
    inference(rectify,[],[f963]) ).

tff(f963,axiom,
    ! [X10: fun_nat_bool,X5: nat,X28: nat] :
      ( hBOOL(hAPP_nat_bool(X10,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5),X28)))
    <=> ~ ( ? [X127: nat] :
              ( ~ hBOOL(hAPP_nat_bool(X10,X127))
              & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X28),X127) = X5 ) )
          | ( ~ hBOOL(hAPP_nat_bool(X10,zero_zero_nat))
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5),X28)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_962_nat__diff__split__asm) ).

tff(f10726,plain,
    spl250_506,
    inference(avatar_split_clause,[],[f6320,f10724]) ).

tff(f6320,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: nat] :
      ( sP19(X0,X1,X2)
      | ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ),
    inference(cnf_transformation,[],[f4432]) ).

tff(f10722,plain,
    spl250_505,
    inference(avatar_split_clause,[],[f6313,f10720]) ).

tff(f6313,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
      | ~ sP18(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4426]) ).

tff(f4426,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
        | ~ sP18(X0,X1,X2) )
      & ( sP18(X0,X1,X2)
        | ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ) ),
    inference(nnf_transformation,[],[f3720]) ).

tff(f3720,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
    <=> sP18(X0,X1,X2) ),
    inference(definition_folding,[],[f3587,f3719]) ).

tff(f3587,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
    <=> ( ! [X3: nat] :
            ( hBOOL(hAPP_nat_bool(X0,X3))
            | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) != X1 ) )
        & ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) ),
    inference(ennf_transformation,[],[f2475]) ).

tff(f2475,plain,
    ! [X0: fun_nat_bool,X1: nat,X2: nat] :
      ( hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
    <=> ( ! [X3: nat] :
            ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) = X1 )
           => hBOOL(hAPP_nat_bool(X0,X3)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
         => hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ) ) ),
    inference(rectify,[],[f962]) ).

tff(f962,axiom,
    ! [X10: fun_nat_bool,X5: nat,X28: nat] :
      ( hBOOL(hAPP_nat_bool(X10,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5),X28)))
    <=> ( ! [X127: nat] :
            ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X28),X127) = X5 )
           => hBOOL(hAPP_nat_bool(X10,X127)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5),X28))
         => hBOOL(hAPP_nat_bool(X10,zero_zero_nat)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_961_nat__diff__split) ).

tff(f10718,plain,
    spl250_504,
    inference(avatar_split_clause,[],[f6312,f10716]) ).

tff(f6312,plain,
    ! [X2: nat,X0: fun_nat_bool,X1: nat] :
      ( sP18(X0,X1,X2)
      | ~ hBOOL(hAPP_nat_bool(X0,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ),
    inference(cnf_transformation,[],[f4426]) ).

tff(f10714,plain,
    ( spl250_503
    | spl250_1
    | ~ spl250_152
    | ~ spl250_210 ),
    inference(avatar_split_clause,[],[f9211,f8388,f8093,f7314,f10712]) ).

tff(f10712,plain,
    ( spl250_503
  <=> ! [X0: int] : ~ sP12(bot_bot_fun_int_bool,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_503])]) ).

tff(f9211,plain,
    ( ! [X0: int] :
        ( hBOOL(fFalse)
        | ~ sP12(bot_bot_fun_int_bool,X0) )
    | ~ spl250_152
    | ~ spl250_210 ),
    inference(superposition,[],[f8389,f8094]) ).

tff(f10710,plain,
    spl250_502,
    inference(avatar_split_clause,[],[f6293,f10708]) ).

tff(f10708,plain,
    ( spl250_502
  <=> ! [X2: x_a,X0: x_a,X1: fun_a_bool] :
        ( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),X2))
        | ~ hBOOL(hAPP_a_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_502])]) ).

tff(f6293,plain,
    ! [X2: x_a,X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),X2))
      | ~ hBOOL(hAPP_a_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f4404]) ).

tff(f10706,plain,
    spl250_501,
    inference(avatar_split_clause,[],[f6046,f10704]) ).

tff(f10704,plain,
    ( spl250_501
  <=> ! [X2: int,X0: fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),sK214(X0,X1,X2)))
        | ~ sP14(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_501])]) ).

tff(f6046,plain,
    ! [X2: int,X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),sK214(X0,X1,X2)))
      | ~ sP14(X0,X1) ),
    inference(cnf_transformation,[],[f4333]) ).

tff(f10702,plain,
    spl250_500,
    inference(avatar_split_clause,[],[f6041,f10700]) ).

tff(f10700,plain,
    ( spl250_500
  <=> ! [X2: int,X0: fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK210(X0,X1,X2)),X2))
        | ~ sP13(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_500])]) ).

tff(f6041,plain,
    ! [X2: int,X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK210(X0,X1,X2)),X2))
      | ~ sP13(X0,X1) ),
    inference(cnf_transformation,[],[f4323]) ).

tff(f10698,plain,
    spl250_499,
    inference(avatar_split_clause,[],[f5735,f10696]) ).

tff(f10696,plain,
    ( spl250_499
  <=> ! [X2: nat,X0: fun_nat_fun_nat_bool,X1: nat] : ( hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1),X2) = hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_499])]) ).

tff(f5735,plain,
    ! [X2: nat,X0: fun_nat_fun_nat_bool,X1: nat] : ( hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1),X2) = hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2111]) ).

tff(f2111,plain,
    ! [X0: fun_nat_fun_nat_bool,X1: nat,X2: nat] : ( hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X0),X1),X2) = hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1) ),
    inference(rectify,[],[f1246]) ).

tff(f1246,axiom,
    ! [X156: fun_nat_fun_nat_bool,X157: nat,X158: nat] : ( hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X156),X157),X158) = hAPP_nat_bool(hAPP_n1699378549t_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) ).

tff(f10694,plain,
    spl250_498,
    inference(avatar_split_clause,[],[f5734,f10692]) ).

tff(f10692,plain,
    ( spl250_498
  <=> ! [X2: nat,X0: fun_na1436237685l_bool,X1: fun_nat_bool] : ( hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_498])]) ).

tff(f5734,plain,
    ! [X2: nat,X0: fun_na1436237685l_bool,X1: fun_nat_bool] : ( hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2110]) ).

tff(f2110,plain,
    ! [X0: fun_na1436237685l_bool,X1: fun_nat_bool,X2: nat] : ( hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X0,X2),X1) ),
    inference(rectify,[],[f1270]) ).

tff(f1270,axiom,
    ! [X156: fun_na1436237685l_bool,X157: fun_nat_bool,X158: nat] : ( hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X156),X157),X158) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).

tff(f10690,plain,
    spl250_497,
    inference(avatar_split_clause,[],[f5733,f10688]) ).

tff(f10688,plain,
    ( spl250_497
  <=> ! [X2: nat,X0: fun_nat_fun_int_bool,X1: int] : ( hAPP_nat_bool(hAPP_i418383825t_bool(cOMBC_nat_int_bool(X0),X1),X2) = hAPP_int_bool(hAPP_n1082236369t_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_497])]) ).

tff(f5733,plain,
    ! [X2: nat,X0: fun_nat_fun_int_bool,X1: int] : ( hAPP_nat_bool(hAPP_i418383825t_bool(cOMBC_nat_int_bool(X0),X1),X2) = hAPP_int_bool(hAPP_n1082236369t_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2109]) ).

tff(f2109,plain,
    ! [X0: fun_nat_fun_int_bool,X1: int,X2: nat] : ( hAPP_nat_bool(hAPP_i418383825t_bool(cOMBC_nat_int_bool(X0),X1),X2) = hAPP_int_bool(hAPP_n1082236369t_bool(X0,X2),X1) ),
    inference(rectify,[],[f1245]) ).

tff(f1245,axiom,
    ! [X156: fun_nat_fun_int_bool,X157: int,X158: nat] : ( hAPP_nat_bool(hAPP_i418383825t_bool(cOMBC_nat_int_bool(X156),X157),X158) = hAPP_int_bool(hAPP_n1082236369t_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Int__Oint_000tc__HOL__Obool_U) ).

tff(f10686,plain,
    spl250_496,
    inference(avatar_split_clause,[],[f5732,f10684]) ).

tff(f10684,plain,
    ( spl250_496
  <=> ! [X2: nat,X0: fun_na1583160273l_bool,X1: fun_int_bool] : ( hAPP_nat_bool(hAPP_f274826591t_bool(cOMBC_620423604l_bool(X0),X1),X2) = hAPP_f448129468l_bool(hAPP_n609083369l_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_496])]) ).

tff(f5732,plain,
    ! [X2: nat,X0: fun_na1583160273l_bool,X1: fun_int_bool] : ( hAPP_nat_bool(hAPP_f274826591t_bool(cOMBC_620423604l_bool(X0),X1),X2) = hAPP_f448129468l_bool(hAPP_n609083369l_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2108]) ).

tff(f2108,plain,
    ! [X0: fun_na1583160273l_bool,X1: fun_int_bool,X2: nat] : ( hAPP_nat_bool(hAPP_f274826591t_bool(cOMBC_620423604l_bool(X0),X1),X2) = hAPP_f448129468l_bool(hAPP_n609083369l_bool(X0,X2),X1) ),
    inference(rectify,[],[f1269]) ).

tff(f1269,axiom,
    ! [X156: fun_na1583160273l_bool,X157: fun_int_bool,X158: nat] : ( hAPP_nat_bool(hAPP_f274826591t_bool(cOMBC_620423604l_bool(X156),X157),X158) = hAPP_f448129468l_bool(hAPP_n609083369l_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_) ).

tff(f10682,plain,
    spl250_495,
    inference(avatar_split_clause,[],[f5731,f10680]) ).

tff(f10680,plain,
    ( spl250_495
  <=> ! [X2: nat,X0: fun_na1632405922l_bool,X1: fun_a_bool] : ( hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_495])]) ).

tff(f5731,plain,
    ! [X2: nat,X0: fun_na1632405922l_bool,X1: fun_a_bool] : ( hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2107]) ).

tff(f2107,plain,
    ! [X0: fun_na1632405922l_bool,X1: fun_a_bool,X2: nat] : ( hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(X0,X2),X1) ),
    inference(rectify,[],[f1259]) ).

tff(f1259,axiom,
    ! [X156: fun_na1632405922l_bool,X157: fun_a_bool,X158: nat] : ( hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(X156),X157),X158) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__) ).

tff(f10678,plain,
    spl250_494,
    inference(avatar_split_clause,[],[f5730,f10676]) ).

tff(f10676,plain,
    ( spl250_494
  <=> ! [X2: nat,X0: fun_na2122364079l_bool,X1: fun_pname_bool] : ( hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_494])]) ).

tff(f5730,plain,
    ! [X2: nat,X0: fun_na2122364079l_bool,X1: fun_pname_bool] : ( hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2106]) ).

tff(f2106,plain,
    ! [X0: fun_na2122364079l_bool,X1: fun_pname_bool,X2: nat] : ( hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(X0,X2),X1) ),
    inference(rectify,[],[f1276]) ).

tff(f1276,axiom,
    ! [X156: fun_na2122364079l_bool,X157: fun_pname_bool,X158: nat] : ( hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(X156),X157),X158) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) ).

tff(f10674,plain,
    spl250_493,
    inference(avatar_split_clause,[],[f5729,f10672]) ).

tff(f10672,plain,
    ( spl250_493
  <=> ! [X2: nat,X0: fun_na35521688t_bool,X1: fun_nat_bool] : ( hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBC_178881787t_bool(X0),X1),X2) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_493])]) ).

tff(f5729,plain,
    ! [X2: nat,X0: fun_na35521688t_bool,X1: fun_nat_bool] : ( hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBC_178881787t_bool(X0),X1),X2) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2105]) ).

tff(f2105,plain,
    ! [X0: fun_na35521688t_bool,X1: fun_nat_bool,X2: nat] : ( hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBC_178881787t_bool(X0),X1),X2) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(X0,X2),X1) ),
    inference(rectify,[],[f1284]) ).

tff(f1284,axiom,
    ! [X156: fun_na35521688t_bool,X157: fun_nat_bool,X158: nat] : ( hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBC_178881787t_bool(X156),X157),X158) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__064) ).

tff(f10666,plain,
    spl250_492,
    inference(avatar_split_clause,[],[f5728,f10664]) ).

tff(f10664,plain,
    ( spl250_492
  <=> ! [X2: int,X0: fun_int_fun_int_bool,X1: int] : ( hAPP_int_bool(hAPP_i1948725293t_bool(cOMBC_int_int_bool(X0),X1),X2) = hAPP_int_bool(hAPP_i1948725293t_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_492])]) ).

tff(f5728,plain,
    ! [X2: int,X0: fun_int_fun_int_bool,X1: int] : ( hAPP_int_bool(hAPP_i1948725293t_bool(cOMBC_int_int_bool(X0),X1),X2) = hAPP_int_bool(hAPP_i1948725293t_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2104]) ).

tff(f2104,plain,
    ! [X0: fun_int_fun_int_bool,X1: int,X2: int] : ( hAPP_int_bool(hAPP_i1948725293t_bool(cOMBC_int_int_bool(X0),X1),X2) = hAPP_int_bool(hAPP_i1948725293t_bool(X0,X2),X1) ),
    inference(rectify,[],[f1244]) ).

tff(f1244,axiom,
    ! [X156: fun_int_fun_int_bool,X157: int,X158: int] : ( hAPP_int_bool(hAPP_i1948725293t_bool(cOMBC_int_int_bool(X156),X157),X158) = hAPP_int_bool(hAPP_i1948725293t_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U) ).

tff(f10662,plain,
    spl250_491,
    inference(avatar_split_clause,[],[f5727,f10660]) ).

tff(f10660,plain,
    ( spl250_491
  <=> ! [X2: int,X0: fun_in938817141l_bool,X1: fun_int_bool] : ( hAPP_int_bool(hAPP_f1805168059t_bool(cOMBC_94739984l_bool(X0),X1),X2) = hAPP_f448129468l_bool(hAPP_i2112223885l_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_491])]) ).

tff(f5727,plain,
    ! [X2: int,X0: fun_in938817141l_bool,X1: fun_int_bool] : ( hAPP_int_bool(hAPP_f1805168059t_bool(cOMBC_94739984l_bool(X0),X1),X2) = hAPP_f448129468l_bool(hAPP_i2112223885l_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2103]) ).

tff(f2103,plain,
    ! [X0: fun_in938817141l_bool,X1: fun_int_bool,X2: int] : ( hAPP_int_bool(hAPP_f1805168059t_bool(cOMBC_94739984l_bool(X0),X1),X2) = hAPP_f448129468l_bool(hAPP_i2112223885l_bool(X0,X2),X1) ),
    inference(rectify,[],[f1267]) ).

tff(f1267,axiom,
    ! [X156: fun_in938817141l_bool,X157: fun_int_bool,X158: int] : ( hAPP_int_bool(hAPP_f1805168059t_bool(cOMBC_94739984l_bool(X156),X157),X158) = hAPP_f448129468l_bool(hAPP_i2112223885l_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_) ).

tff(f10658,plain,
    spl250_490,
    inference(avatar_split_clause,[],[f5726,f10656]) ).

tff(f10656,plain,
    ( spl250_490
  <=> ! [X2: int,X0: fun_in791894553l_bool,X1: fun_nat_bool] : ( hAPP_int_bool(hAPP_f183368031t_bool(cOMBC_1848398772l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_i1718399025l_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_490])]) ).

tff(f5726,plain,
    ! [X2: int,X0: fun_in791894553l_bool,X1: fun_nat_bool] : ( hAPP_int_bool(hAPP_f183368031t_bool(cOMBC_1848398772l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_i1718399025l_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2102]) ).

tff(f2102,plain,
    ! [X0: fun_in791894553l_bool,X1: fun_nat_bool,X2: int] : ( hAPP_int_bool(hAPP_f183368031t_bool(cOMBC_1848398772l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_i1718399025l_bool(X0,X2),X1) ),
    inference(rectify,[],[f1268]) ).

tff(f1268,axiom,
    ! [X156: fun_in791894553l_bool,X157: fun_nat_bool,X158: int] : ( hAPP_int_bool(hAPP_f183368031t_bool(cOMBC_1848398772l_bool(X156),X157),X158) = hAPP_f54304608l_bool(hAPP_i1718399025l_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).

tff(f10654,plain,
    spl250_489,
    inference(avatar_split_clause,[],[f5725,f10652]) ).

tff(f10652,plain,
    ( spl250_489
  <=> ! [X2: int,X0: fun_in1106722302l_bool,X1: fun_a_bool] : ( hAPP_int_bool(hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_i888906320l_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_489])]) ).

tff(f5725,plain,
    ! [X2: int,X0: fun_in1106722302l_bool,X1: fun_a_bool] : ( hAPP_int_bool(hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_i888906320l_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2101]) ).

tff(f2101,plain,
    ! [X0: fun_in1106722302l_bool,X1: fun_a_bool,X2: int] : ( hAPP_int_bool(hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_i888906320l_bool(X0,X2),X1) ),
    inference(rectify,[],[f1258]) ).

tff(f1258,axiom,
    ! [X156: fun_in1106722302l_bool,X157: fun_a_bool,X158: int] : ( hAPP_int_bool(hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(X156),X157),X158) = hAPP_fun_a_bool_bool(hAPP_i888906320l_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__) ).

tff(f10650,plain,
    spl250_488,
    inference(avatar_split_clause,[],[f5724,f10648]) ).

tff(f10648,plain,
    ( spl250_488
  <=> ! [X2: int,X0: fun_in711834963l_bool,X1: fun_pname_bool] : ( hAPP_int_bool(hAPP_f449020825t_bool(cOMBC_316919022l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_i1587699435l_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_488])]) ).

tff(f5724,plain,
    ! [X2: int,X0: fun_in711834963l_bool,X1: fun_pname_bool] : ( hAPP_int_bool(hAPP_f449020825t_bool(cOMBC_316919022l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_i1587699435l_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2100]) ).

tff(f2100,plain,
    ! [X0: fun_in711834963l_bool,X1: fun_pname_bool,X2: int] : ( hAPP_int_bool(hAPP_f449020825t_bool(cOMBC_316919022l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_i1587699435l_bool(X0,X2),X1) ),
    inference(rectify,[],[f1275]) ).

tff(f1275,axiom,
    ! [X156: fun_in711834963l_bool,X157: fun_pname_bool,X158: int] : ( hAPP_int_bool(hAPP_f449020825t_bool(cOMBC_316919022l_bool(X156),X157),X158) = hAPP_f1664156314l_bool(hAPP_i1587699435l_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) ).

tff(f10646,plain,
    spl250_487,
    inference(avatar_split_clause,[],[f5723,f10644]) ).

tff(f10644,plain,
    ( spl250_487
  <=> ! [X2: int,X0: fun_int_fun_a_bool,X1: x_a] : ( hAPP_int_bool(hAPP_a_fun_int_bool(cOMBC_int_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_int_fun_a_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_487])]) ).

tff(f5723,plain,
    ! [X2: int,X0: fun_int_fun_a_bool,X1: x_a] : ( hAPP_int_bool(hAPP_a_fun_int_bool(cOMBC_int_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_int_fun_a_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2099]) ).

tff(f2099,plain,
    ! [X0: fun_int_fun_a_bool,X1: x_a,X2: int] : ( hAPP_int_bool(hAPP_a_fun_int_bool(cOMBC_int_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_int_fun_a_bool(X0,X2),X1) ),
    inference(rectify,[],[f1233]) ).

tff(f1233,axiom,
    ! [X156: fun_int_fun_a_bool,X157: x_a,X158: int] : ( hAPP_int_bool(hAPP_a_fun_int_bool(cOMBC_int_a_bool(X156),X157),X158) = hAPP_a_bool(hAPP_int_fun_a_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000t__a_000tc__HOL__Obool_U) ).

tff(f10642,plain,
    spl250_486,
    inference(avatar_split_clause,[],[f5722,f10640]) ).

tff(f10640,plain,
    ( spl250_486
  <=> ! [X2: fun_nat_bool,X0: fun_fu1217155507l_bool,X1: fun_nat_bool] : ( hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_486])]) ).

tff(f5722,plain,
    ! [X2: fun_nat_bool,X0: fun_fu1217155507l_bool,X1: fun_nat_bool] : ( hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2098]) ).

tff(f2098,plain,
    ! [X0: fun_fu1217155507l_bool,X1: fun_nat_bool,X2: fun_nat_bool] : ( hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X0),X1),X2) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X0,X2),X1) ),
    inference(rectify,[],[f1286]) ).

tff(f1286,axiom,
    ! [X156: fun_fu1217155507l_bool,X157: fun_nat_bool,X158: fun_nat_bool] : ( hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X156),X157),X158) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).

tff(f10638,plain,
    spl250_485,
    inference(avatar_split_clause,[],[f5721,f10636]) ).

tff(f10636,plain,
    ( spl250_485
  <=> ! [X2: fun_int_bool,X0: fun_fu1151772339l_bool,X1: fun_int_bool] : ( hAPP_f448129468l_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(X0),X1),X2) = hAPP_f448129468l_bool(hAPP_f284875647l_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_485])]) ).

tff(f5721,plain,
    ! [X2: fun_int_bool,X0: fun_fu1151772339l_bool,X1: fun_int_bool] : ( hAPP_f448129468l_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(X0),X1),X2) = hAPP_f448129468l_bool(hAPP_f284875647l_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2097]) ).

tff(f2097,plain,
    ! [X0: fun_fu1151772339l_bool,X1: fun_int_bool,X2: fun_int_bool] : ( hAPP_f448129468l_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(X0),X1),X2) = hAPP_f448129468l_bool(hAPP_f284875647l_bool(X0,X2),X1) ),
    inference(rectify,[],[f1285]) ).

tff(f1285,axiom,
    ! [X156: fun_fu1151772339l_bool,X157: fun_int_bool,X158: fun_int_bool] : ( hAPP_f448129468l_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(X156),X157),X158) = hAPP_f448129468l_bool(hAPP_f284875647l_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).

tff(f10634,plain,
    spl250_484,
    inference(avatar_split_clause,[],[f5720,f10632]) ).

tff(f10632,plain,
    ( spl250_484
  <=> ! [X2: fun_a_bool,X0: fun_fu1471507361l_bool,X1: fun_a_bool] : ( hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_484])]) ).

tff(f5720,plain,
    ! [X2: fun_a_bool,X0: fun_fu1471507361l_bool,X1: fun_a_bool] : ( hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2096]) ).

tff(f2096,plain,
    ! [X0: fun_fu1471507361l_bool,X1: fun_a_bool,X2: fun_a_bool] : ( hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X0,X2),X1) ),
    inference(rectify,[],[f1280]) ).

tff(f1280,axiom,
    ! [X156: fun_fu1471507361l_bool,X157: fun_a_bool,X158: fun_a_bool] : ( hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X156),X157),X158) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO) ).

tff(f10630,plain,
    spl250_483,
    inference(avatar_split_clause,[],[f5719,f10628]) ).

tff(f10628,plain,
    ( spl250_483
  <=> ! [X2: fun_pname_bool,X0: fun_fu802393907l_bool,X1: fun_pname_bool] : ( hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_483])]) ).

tff(f5719,plain,
    ! [X2: fun_pname_bool,X0: fun_fu802393907l_bool,X1: fun_pname_bool] : ( hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2095]) ).

tff(f2095,plain,
    ! [X0: fun_fu802393907l_bool,X1: fun_pname_bool,X2: fun_pname_bool] : ( hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X0,X2),X1) ),
    inference(rectify,[],[f1290]) ).

tff(f1290,axiom,
    ! [X156: fun_fu802393907l_bool,X157: fun_pname_bool,X158: fun_pname_bool] : ( hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X156),X157),X158) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).

tff(f10623,plain,
    spl250_482,
    inference(avatar_split_clause,[],[f5718,f10621]) ).

tff(f10621,plain,
    ( spl250_482
  <=> ! [X2: int,X0: fun_in719570932t_bool,X1: fun_int_bool] : ( hAPP_i1948725293t_bool(hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(X0),X1),X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_482])]) ).

tff(f5718,plain,
    ! [X2: int,X0: fun_in719570932t_bool,X1: fun_int_bool] : ( hAPP_i1948725293t_bool(hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(X0),X1),X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2094]) ).

tff(f2094,plain,
    ! [X0: fun_in719570932t_bool,X1: fun_int_bool,X2: int] : ( hAPP_i1948725293t_bool(hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(X0),X1),X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(X0,X2),X1) ),
    inference(rectify,[],[f1283]) ).

tff(f1283,axiom,
    ! [X156: fun_in719570932t_bool,X157: fun_int_bool,X158: int] : ( hAPP_i1948725293t_bool(hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(X156),X157),X158) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool__063) ).

tff(f10619,plain,
    spl250_481,
    inference(avatar_split_clause,[],[f5717,f10617]) ).

tff(f10617,plain,
    ( spl250_481
  <=> ! [X2: fun_fun_a_bool_bool,X0: fun_fu418465139l_bool,X1: fun_fun_a_bool_bool] : ( hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X0),X1),X2) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_481])]) ).

tff(f5717,plain,
    ! [X2: fun_fun_a_bool_bool,X0: fun_fu418465139l_bool,X1: fun_fun_a_bool_bool] : ( hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X0),X1),X2) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2093]) ).

tff(f2093,plain,
    ! [X0: fun_fu418465139l_bool,X1: fun_fun_a_bool_bool,X2: fun_fun_a_bool_bool] : ( hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X0),X1),X2) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X0,X2),X1) ),
    inference(rectify,[],[f1299]) ).

tff(f1299,axiom,
    ! [X156: fun_fu418465139l_bool,X157: fun_fun_a_bool_bool,X158: fun_fun_a_bool_bool] : ( hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X156),X157),X158) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool) ).

tff(f10615,plain,
    spl250_480,
    inference(avatar_split_clause,[],[f5716,f10613]) ).

tff(f10613,plain,
    ( spl250_480
  <=> ! [X2: fun_fu819804446l_bool,X0: fun_fu209342027l_bool,X1: fun_fu819804446l_bool] : ( hAPP_f215623910l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(X0),X1),X2) = hAPP_f215623910l_bool(hAPP_f317860125l_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_480])]) ).

tff(f5716,plain,
    ! [X2: fun_fu819804446l_bool,X0: fun_fu209342027l_bool,X1: fun_fu819804446l_bool] : ( hAPP_f215623910l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(X0),X1),X2) = hAPP_f215623910l_bool(hAPP_f317860125l_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2092]) ).

tff(f2092,plain,
    ! [X0: fun_fu209342027l_bool,X1: fun_fu819804446l_bool,X2: fun_fu819804446l_bool] : ( hAPP_f215623910l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(X0),X1),X2) = hAPP_f215623910l_bool(hAPP_f317860125l_bool(X0,X2),X1) ),
    inference(rectify,[],[f1300]) ).

tff(f1300,axiom,
    ! [X156: fun_fu209342027l_bool,X157: fun_fu819804446l_bool,X158: fun_fu819804446l_bool] : ( hAPP_f215623910l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(X156),X157),X158) = hAPP_f215623910l_bool(hAPP_f317860125l_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__H) ).

tff(f10611,plain,
    spl250_479,
    inference(avatar_split_clause,[],[f5715,f10609]) ).

tff(f10609,plain,
    ( spl250_479
  <=> ! [X2: fun_fu1430349052l_bool,X0: fun_fu1911931399l_bool,X1: fun_fu1430349052l_bool] : ( hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X0),X1),X2) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_479])]) ).

tff(f5715,plain,
    ! [X2: fun_fu1430349052l_bool,X0: fun_fu1911931399l_bool,X1: fun_fu1430349052l_bool] : ( hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X0),X1),X2) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2091]) ).

tff(f2091,plain,
    ! [X0: fun_fu1911931399l_bool,X1: fun_fu1430349052l_bool,X2: fun_fu1430349052l_bool] : ( hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X0),X1),X2) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X0,X2),X1) ),
    inference(rectify,[],[f1302]) ).

tff(f1302,axiom,
    ! [X156: fun_fu1911931399l_bool,X157: fun_fu1430349052l_bool,X158: fun_fu1430349052l_bool] : ( hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X156),X157),X158) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) ).

tff(f10607,plain,
    spl250_478,
    inference(avatar_split_clause,[],[f5714,f10605]) ).

tff(f10605,plain,
    ( spl250_478
  <=> ! [X2: fun_fu425979586l_bool,X0: fun_fu140186515l_bool,X1: fun_fu425979586l_bool] : ( hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X0),X1),X2) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_478])]) ).

tff(f5714,plain,
    ! [X2: fun_fu425979586l_bool,X0: fun_fu140186515l_bool,X1: fun_fu425979586l_bool] : ( hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X0),X1),X2) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2090]) ).

tff(f2090,plain,
    ! [X0: fun_fu140186515l_bool,X1: fun_fu425979586l_bool,X2: fun_fu425979586l_bool] : ( hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X0),X1),X2) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X0,X2),X1) ),
    inference(rectify,[],[f1301]) ).

tff(f1301,axiom,
    ! [X156: fun_fu140186515l_bool,X157: fun_fu425979586l_bool,X158: fun_fu425979586l_bool] : ( hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X156),X157),X158) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H) ).

tff(f10603,plain,
    spl250_477,
    inference(avatar_split_clause,[],[f5713,f10601]) ).

tff(f10601,plain,
    ( spl250_477
  <=> ! [X2: x_a,X0: fun_a_1255737515l_bool,X1: fun_a_bool] : ( hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_477])]) ).

tff(f5713,plain,
    ! [X2: x_a,X0: fun_a_1255737515l_bool,X1: fun_a_bool] : ( hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2089]) ).

tff(f2089,plain,
    ! [X0: fun_a_1255737515l_bool,X1: fun_a_bool,X2: x_a] : ( hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X0),X1),X2) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X0,X2),X1) ),
    inference(rectify,[],[f1256]) ).

tff(f1256,axiom,
    ! [X156: fun_a_1255737515l_bool,X157: fun_a_bool,X158: x_a] : ( hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X156),X157),X158) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo) ).

tff(f10599,plain,
    spl250_476,
    inference(avatar_split_clause,[],[f5712,f10597]) ).

tff(f10597,plain,
    ( spl250_476
  <=> ! [X2: x_a,X0: fun_a_fun_a_bool,X1: x_a] : ( hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_a_fun_a_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_476])]) ).

tff(f5712,plain,
    ! [X2: x_a,X0: fun_a_fun_a_bool,X1: x_a] : ( hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_a_fun_a_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2088]) ).

tff(f2088,plain,
    ! [X0: fun_a_fun_a_bool,X1: x_a,X2: x_a] : ( hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_a_fun_a_bool(X0,X2),X1) ),
    inference(rectify,[],[f1227]) ).

tff(f1227,axiom,
    ! [X156: fun_a_fun_a_bool,X157: x_a,X158: x_a] : ( hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X156),X157),X158) = hAPP_a_bool(hAPP_a_fun_a_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U) ).

tff(f10595,plain,
    spl250_475,
    inference(avatar_split_clause,[],[f5711,f10593]) ).

tff(f10593,plain,
    ( spl250_475
  <=> ! [X2: x_a,X0: fun_a_1752562919a_bool,X1: fun_a_bool] : ( hAPP_a_fun_a_bool(hAPP_f1038053735a_bool(cOMBC_394484100a_bool(X0),X1),X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_475])]) ).

tff(f5711,plain,
    ! [X2: x_a,X0: fun_a_1752562919a_bool,X1: fun_a_bool] : ( hAPP_a_fun_a_bool(hAPP_f1038053735a_bool(cOMBC_394484100a_bool(X0),X1),X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2087]) ).

tff(f2087,plain,
    ! [X0: fun_a_1752562919a_bool,X1: fun_a_bool,X2: x_a] : ( hAPP_a_fun_a_bool(hAPP_f1038053735a_bool(cOMBC_394484100a_bool(X0),X1),X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(X0,X2),X1) ),
    inference(rectify,[],[f1264]) ).

tff(f1264,axiom,
    ! [X156: fun_a_1752562919a_bool,X157: fun_a_bool,X158: x_a] : ( hAPP_a_fun_a_bool(hAPP_f1038053735a_bool(cOMBC_394484100a_bool(X156),X157),X158) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a) ).

tff(f10591,plain,
    spl250_474,
    inference(avatar_split_clause,[],[f5710,f10589]) ).

tff(f10589,plain,
    ( spl250_474
  <=> ! [X2: pname,X0: fun_pn422929397l_bool,X1: fun_pname_bool] : ( hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_474])]) ).

tff(f5710,plain,
    ! [X2: pname,X0: fun_pn422929397l_bool,X1: fun_pname_bool] : ( hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2086]) ).

tff(f2086,plain,
    ! [X0: fun_pn422929397l_bool,X1: fun_pname_bool,X2: pname] : ( hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X0),X1),X2) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X0,X2),X1) ),
    inference(rectify,[],[f1279]) ).

tff(f1279,axiom,
    ! [X156: fun_pn422929397l_bool,X157: fun_pname_bool,X158: pname] : ( hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X156),X157),X158) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).

tff(f10587,plain,
    spl250_473,
    inference(avatar_split_clause,[],[f5709,f10585]) ).

tff(f10585,plain,
    ( spl250_473
  <=> ! [X2: pname,X0: fun_pn800050071e_bool,X1: pname] : ( hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X0),X1),X2) = hAPP_pname_bool(hAPP_p61793385e_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_473])]) ).

tff(f5709,plain,
    ! [X2: pname,X0: fun_pn800050071e_bool,X1: pname] : ( hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X0),X1),X2) = hAPP_pname_bool(hAPP_p61793385e_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2085]) ).

tff(f2085,plain,
    ! [X0: fun_pn800050071e_bool,X1: pname,X2: pname] : ( hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X0),X1),X2) = hAPP_pname_bool(hAPP_p61793385e_bool(X0,X2),X1) ),
    inference(rectify,[],[f1253]) ).

tff(f1253,axiom,
    ! [X156: fun_pn800050071e_bool,X157: pname,X158: pname] : ( hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X156),X157),X158) = hAPP_pname_bool(hAPP_p61793385e_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U) ).

tff(f10581,plain,
    spl250_472,
    inference(avatar_split_clause,[],[f5708,f10579]) ).

tff(f10579,plain,
    ( spl250_472
  <=> ! [X2: pname,X0: fun_pname_fun_a_bool,X1: x_a] : ( hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_p1534023578a_bool(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_472])]) ).

tff(f5708,plain,
    ! [X2: pname,X0: fun_pname_fun_a_bool,X1: x_a] : ( hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_p1534023578a_bool(X0,X2),X1) ),
    inference(cnf_transformation,[],[f2084]) ).

tff(f2084,plain,
    ! [X0: fun_pname_fun_a_bool,X1: x_a,X2: pname] : ( hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X0),X1),X2) = hAPP_a_bool(hAPP_p1534023578a_bool(X0,X2),X1) ),
    inference(rectify,[],[f1236]) ).

tff(f1236,axiom,
    ! [X156: fun_pname_fun_a_bool,X157: x_a,X158: pname] : ( hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X156),X157),X158) = hAPP_a_bool(hAPP_p1534023578a_bool(X156,X158),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U) ).

tff(f10577,plain,
    spl250_471,
    inference(avatar_split_clause,[],[f5565,f10575]) ).

tff(f10575,plain,
    ( spl250_471
  <=> ! [X0: nat,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_471])]) ).

tff(f5565,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1))) ),
    inference(cnf_transformation,[],[f4115]) ).

tff(f4115,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) )
      & ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1))) ) ),
    inference(nnf_transformation,[],[f2012]) ).

tff(f2012,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1)))
    <=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(rectify,[],[f146]) ).

tff(f146,axiom,
    ! [X5: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5),X2)))
    <=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_finite__insert) ).

tff(f10573,plain,
    spl250_470,
    inference(avatar_split_clause,[],[f5563,f10571]) ).

tff(f10571,plain,
    ( spl250_470
  <=> ! [X0: int,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_470])]) ).

tff(f5563,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1))) ),
    inference(cnf_transformation,[],[f4114]) ).

tff(f4114,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) )
      & ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1))) ) ),
    inference(nnf_transformation,[],[f2011]) ).

tff(f2011,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1)))
    <=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(rectify,[],[f147]) ).

tff(f147,axiom,
    ! [X5: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5),X2)))
    <=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_finite__insert) ).

tff(f10569,plain,
    spl250_469,
    inference(avatar_split_clause,[],[f5561,f10567]) ).

tff(f10567,plain,
    ( spl250_469
  <=> ! [X0: x_a,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_469])]) ).

tff(f5561,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1))) ),
    inference(cnf_transformation,[],[f4113]) ).

tff(f4113,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) )
      & ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1))) ) ),
    inference(nnf_transformation,[],[f2010]) ).

tff(f2010,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1)))
    <=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(rectify,[],[f148]) ).

tff(f148,axiom,
    ! [X5: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),X2)))
    <=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_finite__insert) ).

tff(f10565,plain,
    spl250_468,
    inference(avatar_split_clause,[],[f5559,f10563]) ).

tff(f10563,plain,
    ( spl250_468
  <=> ! [X0: pname,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_468])]) ).

tff(f5559,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1))) ),
    inference(cnf_transformation,[],[f4112]) ).

tff(f4112,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) )
      & ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1))) ) ),
    inference(nnf_transformation,[],[f2009]) ).

tff(f2009,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1)))
    <=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(rectify,[],[f145]) ).

tff(f145,axiom,
    ! [X5: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5),X2)))
    <=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_finite__insert) ).

tff(f10561,plain,
    spl250_467,
    inference(avatar_split_clause,[],[f5557,f10559]) ).

tff(f10559,plain,
    ( spl250_467
  <=> ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_467])]) ).

tff(f5557,plain,
    ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1))) ),
    inference(cnf_transformation,[],[f4111]) ).

tff(f4111,plain,
    ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
      ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) )
      & ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1))) ) ),
    inference(nnf_transformation,[],[f2008]) ).

tff(f2008,plain,
    ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1)))
    <=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(rectify,[],[f142]) ).

tff(f142,axiom,
    ! [X5: fun_nat_bool,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X5),X2)))
    <=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_finite__insert) ).

tff(f10557,plain,
    spl250_466,
    inference(avatar_split_clause,[],[f5555,f10555]) ).

tff(f10555,plain,
    ( spl250_466
  <=> ! [X0: fun_int_bool,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_466])]) ).

tff(f5555,plain,
    ! [X0: fun_int_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1))) ),
    inference(cnf_transformation,[],[f4110]) ).

tff(f4110,plain,
    ! [X0: fun_int_bool,X1: fun_fu819804446l_bool] :
      ( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) )
      & ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1))) ) ),
    inference(nnf_transformation,[],[f2007]) ).

tff(f2007,plain,
    ! [X0: fun_int_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1)))
    <=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(rectify,[],[f141]) ).

tff(f141,axiom,
    ! [X5: fun_int_bool,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X5),X2)))
    <=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_finite__insert) ).

tff(f10553,plain,
    spl250_465,
    inference(avatar_split_clause,[],[f5553,f10551]) ).

tff(f10551,plain,
    ( spl250_465
  <=> ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_465])]) ).

tff(f5553,plain,
    ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1))) ),
    inference(cnf_transformation,[],[f4109]) ).

tff(f4109,plain,
    ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) )
      & ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1))) ) ),
    inference(nnf_transformation,[],[f2006]) ).

tff(f2006,plain,
    ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1)))
    <=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(rectify,[],[f143]) ).

tff(f143,axiom,
    ! [X5: fun_pname_bool,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X5),X2)))
    <=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_finite__insert) ).

tff(f10549,plain,
    spl250_464,
    inference(avatar_split_clause,[],[f5551,f10547]) ).

tff(f10547,plain,
    ( spl250_464
  <=> ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_464])]) ).

tff(f5551,plain,
    ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1))) ),
    inference(cnf_transformation,[],[f4108]) ).

tff(f4108,plain,
    ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
      ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) )
      & ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1))) ) ),
    inference(nnf_transformation,[],[f2005]) ).

tff(f2005,plain,
    ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1)))
    <=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(rectify,[],[f144]) ).

tff(f144,axiom,
    ! [X5: fun_a_bool,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X5),X2)))
    <=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_finite__insert) ).

tff(f10545,plain,
    spl250_463,
    inference(avatar_split_clause,[],[f5512,f10543]) ).

tff(f10543,plain,
    ( spl250_463
  <=> ! [X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_463])]) ).

tff(f5512,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4074]) ).

tff(f10541,plain,
    spl250_462,
    inference(avatar_split_clause,[],[f5432,f10539]) ).

tff(f10539,plain,
    ( spl250_462
  <=> ! [X0: nat,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK135(X0,X1)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_462])]) ).

tff(f5432,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK135(X0,X1)),X0)) ),
    inference(cnf_transformation,[],[f4020]) ).

tff(f4020,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK135(X0,X1)),X0))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK135(X0,X1)),X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK135])],[f3065,f4019]) ).

tff(f4019,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( ? [X2: nat] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) )
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK135(X0,X1)),X0))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK135(X0,X1)),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f3065,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
      | ? [X2: nat] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ) ),
    inference(ennf_transformation,[],[f1959]) ).

tff(f1959,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( ! [X2: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X0)) )
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(rectify,[],[f918]) ).

tff(f918,axiom,
    ! [X14: nat,X69: fun_nat_bool] :
      ( ! [X27: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X27),X69))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X27),X14)) )
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X69)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_917_bounded__nat__set__is__finite) ).

tff(f10537,plain,
    spl250_461,
    inference(avatar_split_clause,[],[f5431,f10535]) ).

tff(f10535,plain,
    ( spl250_461
  <=> ! [X0: nat,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK135(X0,X1)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_461])]) ).

tff(f5431,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK135(X0,X1)),X1)) ),
    inference(cnf_transformation,[],[f4020]) ).

tff(f10533,plain,
    spl250_460,
    inference(avatar_split_clause,[],[f5374,f10531]) ).

tff(f10531,plain,
    ( spl250_460
  <=> ! [X0: int,X1: int] :
        ( ( one_one_int = abs_abs_int(X0) )
        | ( one_one_int != abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_460])]) ).

tff(f5374,plain,
    ! [X0: int,X1: int] :
      ( ( one_one_int = abs_abs_int(X0) )
      | ( one_one_int != abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X1)) ) ),
    inference(cnf_transformation,[],[f3016]) ).

tff(f3016,plain,
    ! [X0: int,X1: int] :
      ( ( one_one_int = abs_abs_int(X0) )
      | ( one_one_int != abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X1)) ) ),
    inference(ennf_transformation,[],[f1918]) ).

tff(f1918,plain,
    ! [X0: int,X1: int] :
      ( ( one_one_int = abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X1)) )
     => ( one_one_int = abs_abs_int(X0) ) ),
    inference(rectify,[],[f1151]) ).

tff(f1151,axiom,
    ! [X12: int,X11: int] :
      ( ( one_one_int = abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X12),X11)) )
     => ( one_one_int = abs_abs_int(X12) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1150_abs__zmult__eq__1) ).

tff(f10529,plain,
    spl250_459,
    inference(avatar_split_clause,[],[f5343,f10527]) ).

tff(f10527,plain,
    ( spl250_459
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_459])]) ).

tff(f5343,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f2981]) ).

tff(f2981,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
    inference(ennf_transformation,[],[f1891]) ).

tff(f1891,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(rectify,[],[f890]) ).

tff(f890,axiom,
    ! [X12: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),X11))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X11)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_889_less__imp__le__nat) ).

tff(f10525,plain,
    spl250_458,
    inference(avatar_split_clause,[],[f5256,f10523]) ).

tff(f5256,plain,
    ! [X0: fun_fu425979586l_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK112(X0)),sK113(X0))))
      | ~ sP3(X0) ),
    inference(cnf_transformation,[],[f3968]) ).

tff(f3968,plain,
    ! [X0: fun_fu425979586l_bool] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK112(X0)),sK113(X0))))
        & hBOOL(hAPP_f54304608l_bool(X0,sK113(X0)))
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK112(X0)),sK113(X0)))
        & ( bot_bot_fun_nat_bool != sK113(X0) )
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK113(X0))) )
      | ~ sP3(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK112,sK113])],[f3966,f3967]) ).

tff(f3967,plain,
    ! [X0: fun_fu425979586l_bool] :
      ( ? [X1: nat,X2: fun_nat_bool] :
          ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))
          & hBOOL(hAPP_f54304608l_bool(X0,X2))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
          & ( bot_bot_fun_nat_bool != X2 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) )
     => ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK112(X0)),sK113(X0))))
        & hBOOL(hAPP_f54304608l_bool(X0,sK113(X0)))
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK112(X0)),sK113(X0)))
        & ( bot_bot_fun_nat_bool != sK113(X0) )
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK113(X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f3966,plain,
    ! [X0: fun_fu425979586l_bool] :
      ( ? [X1: nat,X2: fun_nat_bool] :
          ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)))
          & hBOOL(hAPP_f54304608l_bool(X0,X2))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
          & ( bot_bot_fun_nat_bool != X2 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) )
      | ~ sP3(X0) ),
    inference(rectify,[],[f3965]) ).

tff(f3965,plain,
    ! [X0: fun_fu425979586l_bool] :
      ( ? [X3: nat,X4: fun_nat_bool] :
          ( ~ hBOOL(hAPP_f54304608l_bool(X0,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4)))
          & hBOOL(hAPP_f54304608l_bool(X0,X4))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
          & ( bot_bot_fun_nat_bool != X4 )
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4)) )
      | ~ sP3(X0) ),
    inference(nnf_transformation,[],[f3690]) ).

tff(f10521,plain,
    spl250_457,
    inference(avatar_split_clause,[],[f5239,f10519]) ).

tff(f10519,plain,
    ( spl250_457
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X0)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_457])]) ).

tff(f5239,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X0)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f2862]) ).

tff(f2862,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X0)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(ennf_transformation,[],[f1811]) ).

tff(f1811,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X0))) ),
    inference(rectify,[],[f496]) ).

tff(f496,axiom,
    ! [X7: fun_nat_bool,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_495_finite__Diff) ).

tff(f10517,plain,
    spl250_456,
    inference(avatar_split_clause,[],[f5213,f10515]) ).

tff(f5213,plain,
    ! [X0: fun_fu819804446l_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK105(X0)),sK106(X0))))
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f3957]) ).

tff(f3957,plain,
    ! [X0: fun_fu819804446l_bool] :
      ( ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK105(X0)),sK106(X0))))
        & hBOOL(hAPP_f448129468l_bool(X0,sK106(X0)))
        & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK105(X0)),sK106(X0)))
        & ( bot_bot_fun_int_bool != sK106(X0) )
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK106(X0))) )
      | ~ sP2(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK105,sK106])],[f3955,f3956]) ).

tff(f3956,plain,
    ! [X0: fun_fu819804446l_bool] :
      ( ? [X1: int,X2: fun_int_bool] :
          ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))
          & hBOOL(hAPP_f448129468l_bool(X0,X2))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
          & ( bot_bot_fun_int_bool != X2 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) )
     => ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK105(X0)),sK106(X0))))
        & hBOOL(hAPP_f448129468l_bool(X0,sK106(X0)))
        & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK105(X0)),sK106(X0)))
        & ( bot_bot_fun_int_bool != sK106(X0) )
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK106(X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f3955,plain,
    ! [X0: fun_fu819804446l_bool] :
      ( ? [X1: int,X2: fun_int_bool] :
          ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)))
          & hBOOL(hAPP_f448129468l_bool(X0,X2))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
          & ( bot_bot_fun_int_bool != X2 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) )
      | ~ sP2(X0) ),
    inference(rectify,[],[f3954]) ).

tff(f3954,plain,
    ! [X0: fun_fu819804446l_bool] :
      ( ? [X3: int,X4: fun_int_bool] :
          ( ~ hBOOL(hAPP_f448129468l_bool(X0,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4)))
          & hBOOL(hAPP_f448129468l_bool(X0,X4))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
          & ( bot_bot_fun_int_bool != X4 )
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4)) )
      | ~ sP2(X0) ),
    inference(nnf_transformation,[],[f3688]) ).

tff(f10513,plain,
    spl250_455,
    inference(avatar_split_clause,[],[f5197,f10511]) ).

tff(f10511,plain,
    ( spl250_455
  <=> ! [X0: fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X0)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_455])]) ).

tff(f5197,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X0)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f2823]) ).

tff(f2823,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X0)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(ennf_transformation,[],[f1783]) ).

tff(f1783,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X0))) ),
    inference(rectify,[],[f495]) ).

tff(f495,axiom,
    ! [X7: fun_int_bool,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_494_finite__Diff) ).

tff(f10509,plain,
    spl250_454,
    inference(avatar_split_clause,[],[f5174,f10507]) ).

tff(f5174,plain,
    ! [X0: fun_fun_a_bool_bool] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK98(X0)),sK99(X0))))
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f3947]) ).

tff(f3947,plain,
    ! [X0: fun_fun_a_bool_bool] :
      ( ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK98(X0)),sK99(X0))))
        & hBOOL(hAPP_fun_a_bool_bool(X0,sK99(X0)))
        & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK98(X0)),sK99(X0)))
        & ( bot_bot_fun_a_bool != sK99(X0) )
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK99(X0))) )
      | ~ sP1(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK98,sK99])],[f3945,f3946]) ).

tff(f3946,plain,
    ! [X0: fun_fun_a_bool_bool] :
      ( ? [X1: x_a,X2: fun_a_bool] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))
          & hBOOL(hAPP_fun_a_bool_bool(X0,X2))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
          & ( bot_bot_fun_a_bool != X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) )
     => ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK98(X0)),sK99(X0))))
        & hBOOL(hAPP_fun_a_bool_bool(X0,sK99(X0)))
        & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK98(X0)),sK99(X0)))
        & ( bot_bot_fun_a_bool != sK99(X0) )
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK99(X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f3945,plain,
    ! [X0: fun_fun_a_bool_bool] :
      ( ? [X1: x_a,X2: fun_a_bool] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)))
          & hBOOL(hAPP_fun_a_bool_bool(X0,X2))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
          & ( bot_bot_fun_a_bool != X2 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) )
      | ~ sP1(X0) ),
    inference(rectify,[],[f3944]) ).

tff(f3944,plain,
    ! [X0: fun_fun_a_bool_bool] :
      ( ? [X3: x_a,X4: fun_a_bool] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(X0,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4)))
          & hBOOL(hAPP_fun_a_bool_bool(X0,X4))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
          & ( bot_bot_fun_a_bool != X4 )
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4)) )
      | ~ sP1(X0) ),
    inference(nnf_transformation,[],[f3686]) ).

tff(f10505,plain,
    spl250_453,
    inference(avatar_split_clause,[],[f5133,f10503]) ).

tff(f5133,plain,
    ! [X0: fun_fu1430349052l_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK91(X0)),sK92(X0))))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f3936]) ).

tff(f3936,plain,
    ! [X0: fun_fu1430349052l_bool] :
      ( ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK91(X0)),sK92(X0))))
        & hBOOL(hAPP_f1664156314l_bool(X0,sK92(X0)))
        & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK91(X0)),sK92(X0)))
        & ( bot_bo844097828e_bool != sK92(X0) )
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK92(X0))) )
      | ~ sP0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK91,sK92])],[f3934,f3935]) ).

tff(f3935,plain,
    ! [X0: fun_fu1430349052l_bool] :
      ( ? [X1: pname,X2: fun_pname_bool] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))
          & hBOOL(hAPP_f1664156314l_bool(X0,X2))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
          & ( bot_bo844097828e_bool != X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) )
     => ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK91(X0)),sK92(X0))))
        & hBOOL(hAPP_f1664156314l_bool(X0,sK92(X0)))
        & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK91(X0)),sK92(X0)))
        & ( bot_bo844097828e_bool != sK92(X0) )
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK92(X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f3934,plain,
    ! [X0: fun_fu1430349052l_bool] :
      ( ? [X1: pname,X2: fun_pname_bool] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)))
          & hBOOL(hAPP_f1664156314l_bool(X0,X2))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
          & ( bot_bo844097828e_bool != X2 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) )
      | ~ sP0(X0) ),
    inference(rectify,[],[f3933]) ).

tff(f3933,plain,
    ! [X0: fun_fu1430349052l_bool] :
      ( ? [X3: pname,X4: fun_pname_bool] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(X0,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X4)))
          & hBOOL(hAPP_f1664156314l_bool(X0,X4))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4))
          & ( bot_bo844097828e_bool != X4 )
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4)) )
      | ~ sP0(X0) ),
    inference(nnf_transformation,[],[f3684]) ).

tff(f10501,plain,
    spl250_452,
    inference(avatar_split_clause,[],[f5114,f10499]) ).

tff(f10499,plain,
    ( spl250_452
  <=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X0)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_452])]) ).

tff(f5114,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X0)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f2745]) ).

tff(f2745,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X0)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(ennf_transformation,[],[f1727]) ).

tff(f1727,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X0))) ),
    inference(rectify,[],[f497]) ).

tff(f497,axiom,
    ! [X7: fun_pname_bool,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_496_finite__Diff) ).

tff(f10497,plain,
    spl250_451,
    inference(avatar_split_clause,[],[f5068,f10495]) ).

tff(f10495,plain,
    ( spl250_451
  <=> ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_451])]) ).

tff(f5068,plain,
    ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(cnf_transformation,[],[f2687]) ).

tff(f2687,plain,
    ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(ennf_transformation,[],[f1685]) ).

tff(f1685,plain,
    ! [X0: fun_pname_bool,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X0),X1))) ),
    inference(rectify,[],[f43]) ).

tff(f43,axiom,
    ! [X5: fun_pname_bool,X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X5),X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_finite_OinsertI) ).

tff(f10493,plain,
    spl250_450,
    inference(avatar_split_clause,[],[f5067,f10491]) ).

tff(f10491,plain,
    ( spl250_450
  <=> ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_450])]) ).

tff(f5067,plain,
    ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(cnf_transformation,[],[f2686]) ).

tff(f2686,plain,
    ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(ennf_transformation,[],[f1684]) ).

tff(f1684,plain,
    ! [X0: fun_nat_bool,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
     => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X0),X1))) ),
    inference(rectify,[],[f42]) ).

tff(f42,axiom,
    ! [X5: fun_nat_bool,X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
     => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X5),X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_finite_OinsertI) ).

tff(f10489,plain,
    spl250_449,
    inference(avatar_split_clause,[],[f5066,f10487]) ).

tff(f10487,plain,
    ( spl250_449
  <=> ! [X0: fun_int_bool,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_449])]) ).

tff(f5066,plain,
    ! [X0: fun_int_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(cnf_transformation,[],[f2685]) ).

tff(f2685,plain,
    ! [X0: fun_int_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(ennf_transformation,[],[f1683]) ).

tff(f1683,plain,
    ! [X0: fun_int_bool,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
     => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X0),X1))) ),
    inference(rectify,[],[f41]) ).

tff(f41,axiom,
    ! [X5: fun_int_bool,X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
     => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X5),X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_finite_OinsertI) ).

tff(f10485,plain,
    spl250_448,
    inference(avatar_split_clause,[],[f5065,f10483]) ).

tff(f10483,plain,
    ( spl250_448
  <=> ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_448])]) ).

tff(f5065,plain,
    ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(cnf_transformation,[],[f2684]) ).

tff(f2684,plain,
    ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(ennf_transformation,[],[f1682]) ).

tff(f1682,plain,
    ! [X0: fun_a_bool,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
     => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X0),X1))) ),
    inference(rectify,[],[f44]) ).

tff(f44,axiom,
    ! [X5: fun_a_bool,X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
     => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X5),X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_finite_OinsertI) ).

tff(f10481,plain,
    spl250_447,
    inference(avatar_split_clause,[],[f4998,f10479]) ).

tff(f10479,plain,
    ( spl250_447
  <=> ! [X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_447])]) ).

tff(f4998,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f1634]) ).

tff(f1634,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
    inference(rectify,[],[f130]) ).

tff(f130,axiom,
    ! [X12: nat,X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X11),X12))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),X11)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_nat__le__linear) ).

tff(f10477,plain,
    spl250_446,
    inference(avatar_split_clause,[],[f4996,f10475]) ).

tff(f10475,plain,
    ( spl250_446
  <=> ! [X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_446])]) ).

tff(f4996,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(cnf_transformation,[],[f1632]) ).

tff(f1632,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
    inference(rectify,[],[f307]) ).

tff(f307,axiom,
    ! [X34: int,X35: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X35),X34))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X34),X35)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_linorder__linear) ).

tff(f10473,plain,
    spl250_445,
    inference(avatar_split_clause,[],[f4910,f10471]) ).

tff(f10471,plain,
    ( spl250_445
  <=> ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),hAPP_nat_nat(suc,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_445])]) ).

tff(f4910,plain,
    ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),hAPP_nat_nat(suc,X0))),
    inference(cnf_transformation,[],[f1558]) ).

tff(f1558,plain,
    ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),hAPP_nat_nat(suc,X0))),
    inference(rectify,[],[f909]) ).

tff(f909,axiom,
    ! [X12: nat,X11: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X12),X11)),hAPP_nat_nat(suc,X12))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_908_diff__less__Suc) ).

tff(f10469,plain,
    spl250_444,
    inference(avatar_split_clause,[],[f4909,f10467]) ).

tff(f10467,plain,
    ( spl250_444
  <=> ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_444])]) ).

tff(f4909,plain,
    ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0)))),
    inference(cnf_transformation,[],[f1557]) ).

tff(f1557,plain,
    ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0)))),
    inference(rectify,[],[f900]) ).

tff(f900,axiom,
    ! [X20: nat,X12: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X20),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X12),X20)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_899_less__add__Suc2) ).

tff(f10465,plain,
    spl250_443,
    inference(avatar_split_clause,[],[f4908,f10463]) ).

tff(f10463,plain,
    ( spl250_443
  <=> ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_443])]) ).

tff(f4908,plain,
    ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)))),
    inference(cnf_transformation,[],[f1556]) ).

tff(f1556,plain,
    ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)))),
    inference(rectify,[],[f899]) ).

tff(f899,axiom,
    ! [X20: nat,X12: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X20),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X20),X12)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_898_less__add__Suc1) ).

tff(f10461,plain,
    spl250_442,
    inference(avatar_split_clause,[],[f4823,f10459]) ).

tff(f4823,plain,
    ! [X0: nat] :
      ( ( hAPP_nat_nat(suc,sK62(X0)) = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f3849]) ).

tff(f3849,plain,
    ! [X0: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | ! [X1: nat] : ( hAPP_nat_nat(suc,X1) != X0 ) )
      & ( ( hAPP_nat_nat(suc,sK62(X0)) = X0 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK62])],[f3847,f3848]) ).

tff(f3848,plain,
    ! [X0: nat] :
      ( ? [X2: nat] : ( hAPP_nat_nat(suc,X2) = X0 )
     => ( hAPP_nat_nat(suc,sK62(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f3847,plain,
    ! [X0: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | ! [X1: nat] : ( hAPP_nat_nat(suc,X1) != X0 ) )
      & ( ? [X2: nat] : ( hAPP_nat_nat(suc,X2) = X0 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
    inference(rectify,[],[f3846]) ).

tff(f3846,plain,
    ! [X0: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | ! [X1: nat] : ( hAPP_nat_nat(suc,X1) != X0 ) )
      & ( ? [X1: nat] : ( hAPP_nat_nat(suc,X1) = X0 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ) ),
    inference(nnf_transformation,[],[f1495]) ).

tff(f1495,plain,
    ! [X0: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
    <=> ? [X1: nat] : ( hAPP_nat_nat(suc,X1) = X0 ) ),
    inference(rectify,[],[f947]) ).

tff(f947,axiom,
    ! [X14: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X14))
    <=> ? [X32: nat] : ( hAPP_nat_nat(suc,X32) = X14 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_946_gr0__conv__Suc) ).

tff(f10457,plain,
    spl250_441,
    inference(avatar_split_clause,[],[f4794,f10455]) ).

tff(f10455,plain,
    ( spl250_441
  <=> ! [X0: fun_nat_bool,X1: nat] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK60(X0,X1)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_441])]) ).

tff(f4794,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK60(X0,X1)),X1)) ),
    inference(cnf_transformation,[],[f3831]) ).

tff(f10453,plain,
    spl250_440,
    inference(avatar_split_clause,[],[f4793,f10451]) ).

tff(f10451,plain,
    ( spl250_440
  <=> ! [X0: fun_nat_bool,X1: nat] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK60(X0,X1)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_440])]) ).

tff(f4793,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK60(X0,X1)),X0)) ),
    inference(cnf_transformation,[],[f3831]) ).

tff(f10449,plain,
    spl250_439,
    inference(avatar_split_clause,[],[f4791,f10447]) ).

tff(f10447,plain,
    ( spl250_439
  <=> ! [X0: fun_nat_bool,X1: nat] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK58(X0,X1)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_439])]) ).

tff(f4791,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK58(X0,X1)),X1)) ),
    inference(cnf_transformation,[],[f3826]) ).

tff(f10445,plain,
    spl250_438,
    inference(avatar_split_clause,[],[f4790,f10443]) ).

tff(f10443,plain,
    ( spl250_438
  <=> ! [X0: fun_nat_bool,X1: nat] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK58(X0,X1)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_438])]) ).

tff(f4790,plain,
    ! [X0: fun_nat_bool,X1: nat] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK58(X0,X1)),X0)) ),
    inference(cnf_transformation,[],[f3826]) ).

tff(f10441,plain,
    spl250_437,
    inference(avatar_split_clause,[],[f4786,f10439]) ).

tff(f10439,plain,
    ( spl250_437
  <=> ! [X0: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK56(X0)))
        | ( bot_bot_fun_nat_bool = X0 )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_437])]) ).

tff(f4786,plain,
    ! [X0: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK56(X0)))
      | ( bot_bot_fun_nat_bool = X0 )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ),
    inference(cnf_transformation,[],[f3821]) ).

tff(f10437,plain,
    spl250_436,
    inference(avatar_split_clause,[],[f4780,f10435]) ).

tff(f10435,plain,
    ( spl250_436
  <=> ! [X0: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK54(X0)))
        | ( bot_bot_fun_int_bool = X0 )
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_436])]) ).

tff(f4780,plain,
    ! [X0: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK54(X0)))
      | ( bot_bot_fun_int_bool = X0 )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ),
    inference(cnf_transformation,[],[f3815]) ).

tff(f10433,plain,
    spl250_435,
    inference(avatar_split_clause,[],[f4776,f10431]) ).

tff(f10431,plain,
    ( spl250_435
  <=> ! [X0: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK52(X0)))
        | ( bot_bot_fun_a_bool = X0 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_435])]) ).

tff(f4776,plain,
    ! [X0: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK52(X0)))
      | ( bot_bot_fun_a_bool = X0 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ),
    inference(cnf_transformation,[],[f3810]) ).

tff(f10429,plain,
    spl250_434,
    inference(avatar_split_clause,[],[f4772,f10427]) ).

tff(f10427,plain,
    ( spl250_434
  <=> ! [X0: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK50(X0)))
        | ( bot_bo844097828e_bool = X0 )
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_434])]) ).

tff(f4772,plain,
    ! [X0: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK50(X0)))
      | ( bot_bo844097828e_bool = X0 )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ),
    inference(cnf_transformation,[],[f3805]) ).

tff(f10425,plain,
    spl250_433,
    inference(avatar_split_clause,[],[f4744,f10423]) ).

tff(f10423,plain,
    ( spl250_433
  <=> ! [X0: fun_a_bool] :
        ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK42(X0)),sK43(X0)) = X0 )
        | ( bot_bot_fun_a_bool = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_433])]) ).

tff(f4744,plain,
    ! [X0: fun_a_bool] :
      ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK42(X0)),sK43(X0)) = X0 )
      | ( bot_bot_fun_a_bool = X0 ) ),
    inference(cnf_transformation,[],[f3770]) ).

tff(f3770,plain,
    ! [X0: fun_a_bool] :
      ( ( ( bot_bot_fun_a_bool != X0 )
        | ! [X1: x_a,X2: fun_a_bool] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
            | ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2) != X0 ) ) )
      & ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK42(X0)),sK43(X0)))
          & ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK42(X0)),sK43(X0)) = X0 ) )
        | ( bot_bot_fun_a_bool = X0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK42,sK43])],[f3768,f3769]) ).

tff(f3769,plain,
    ! [X0: fun_a_bool] :
      ( ? [X3: x_a,X4: fun_a_bool] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
          & ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4) = X0 ) )
     => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK42(X0)),sK43(X0)))
        & ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK42(X0)),sK43(X0)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f3768,plain,
    ! [X0: fun_a_bool] :
      ( ( ( bot_bot_fun_a_bool != X0 )
        | ! [X1: x_a,X2: fun_a_bool] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
            | ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2) != X0 ) ) )
      & ( ? [X3: x_a,X4: fun_a_bool] :
            ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4))
            & ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X4) = X0 ) )
        | ( bot_bot_fun_a_bool = X0 ) ) ),
    inference(rectify,[],[f3767]) ).

tff(f3767,plain,
    ! [X0: fun_a_bool] :
      ( ( ( bot_bot_fun_a_bool != X0 )
        | ! [X1: x_a,X2: fun_a_bool] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
            | ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2) != X0 ) ) )
      & ( ? [X1: x_a,X2: fun_a_bool] :
            ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
            & ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2) = X0 ) )
        | ( bot_bot_fun_a_bool = X0 ) ) ),
    inference(nnf_transformation,[],[f1461]) ).

tff(f1461,plain,
    ! [X0: fun_a_bool] :
      ( ( bot_bot_fun_a_bool != X0 )
    <=> ? [X1: x_a,X2: fun_a_bool] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
          & ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2) = X0 ) ) ),
    inference(rectify,[],[f700]) ).

tff(f700,axiom,
    ! [X2: fun_a_bool] :
      ( ( bot_bot_fun_a_bool != X2 )
    <=> ? [X27: x_a,X80: fun_a_bool] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X27),X80))
          & ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X27),X80) = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_699_nonempty__iff) ).

tff(f10421,plain,
    ( spl250_432
    | ~ spl250_42
    | ~ spl250_388 ),
    inference(avatar_split_clause,[],[f10284,f9763,f7508,f10419]) ).

tff(f10419,plain,
    ( spl250_432
  <=> ! [X0: fun_fu425979586l_bool] : ~ sP11(X0,bot_bot_fun_nat_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_432])]) ).

tff(f7508,plain,
    ( spl250_42
  <=> ! [X0: nat] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),bot_bot_fun_nat_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_42])]) ).

tff(f9763,plain,
    ( spl250_388
  <=> ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK189(X0,X1)),X1))
        | ~ sP11(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_388])]) ).

tff(f10284,plain,
    ( ! [X0: fun_fu425979586l_bool] : ~ sP11(X0,bot_bot_fun_nat_bool)
    | ~ spl250_42
    | ~ spl250_388 ),
    inference(resolution,[],[f9764,f7509]) ).

tff(f7509,plain,
    ( ! [X0: nat] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),bot_bot_fun_nat_bool))
    | ~ spl250_42 ),
    inference(avatar_component_clause,[],[f7508]) ).

tff(f9764,plain,
    ( ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK189(X0,X1)),X1))
        | ~ sP11(X0,X1) )
    | ~ spl250_388 ),
    inference(avatar_component_clause,[],[f9763]) ).

tff(f10417,plain,
    spl250_431,
    inference(avatar_split_clause,[],[f4741,f10415]) ).

tff(f10415,plain,
    ( spl250_431
  <=> ! [X0: fun_int_bool] :
        ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK40(X0)),sK41(X0)) = X0 )
        | ( bot_bot_fun_int_bool = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_431])]) ).

tff(f4741,plain,
    ! [X0: fun_int_bool] :
      ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK40(X0)),sK41(X0)) = X0 )
      | ( bot_bot_fun_int_bool = X0 ) ),
    inference(cnf_transformation,[],[f3766]) ).

tff(f3766,plain,
    ! [X0: fun_int_bool] :
      ( ( ( bot_bot_fun_int_bool != X0 )
        | ! [X1: int,X2: fun_int_bool] :
            ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
            | ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2) != X0 ) ) )
      & ( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK40(X0)),sK41(X0)))
          & ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK40(X0)),sK41(X0)) = X0 ) )
        | ( bot_bot_fun_int_bool = X0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK40,sK41])],[f3764,f3765]) ).

tff(f3765,plain,
    ! [X0: fun_int_bool] :
      ( ? [X3: int,X4: fun_int_bool] :
          ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
          & ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4) = X0 ) )
     => ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK40(X0)),sK41(X0)))
        & ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK40(X0)),sK41(X0)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f3764,plain,
    ! [X0: fun_int_bool] :
      ( ( ( bot_bot_fun_int_bool != X0 )
        | ! [X1: int,X2: fun_int_bool] :
            ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
            | ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2) != X0 ) ) )
      & ( ? [X3: int,X4: fun_int_bool] :
            ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X4))
            & ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X4) = X0 ) )
        | ( bot_bot_fun_int_bool = X0 ) ) ),
    inference(rectify,[],[f3763]) ).

tff(f3763,plain,
    ! [X0: fun_int_bool] :
      ( ( ( bot_bot_fun_int_bool != X0 )
        | ! [X1: int,X2: fun_int_bool] :
            ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
            | ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2) != X0 ) ) )
      & ( ? [X1: int,X2: fun_int_bool] :
            ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
            & ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2) = X0 ) )
        | ( bot_bot_fun_int_bool = X0 ) ) ),
    inference(nnf_transformation,[],[f1460]) ).

tff(f1460,plain,
    ! [X0: fun_int_bool] :
      ( ( bot_bot_fun_int_bool != X0 )
    <=> ? [X1: int,X2: fun_int_bool] :
          ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
          & ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2) = X0 ) ) ),
    inference(rectify,[],[f701]) ).

tff(f701,axiom,
    ! [X2: fun_int_bool] :
      ( ( bot_bot_fun_int_bool != X2 )
    <=> ? [X27: int,X80: fun_int_bool] :
          ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X27),X80))
          & ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X27),X80) = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_700_nonempty__iff) ).

tff(f10413,plain,
    spl250_430,
    inference(avatar_split_clause,[],[f4738,f10411]) ).

tff(f10411,plain,
    ( spl250_430
  <=> ! [X0: fun_nat_bool] :
        ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK38(X0)),sK39(X0)) = X0 )
        | ( bot_bot_fun_nat_bool = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_430])]) ).

tff(f4738,plain,
    ! [X0: fun_nat_bool] :
      ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK38(X0)),sK39(X0)) = X0 )
      | ( bot_bot_fun_nat_bool = X0 ) ),
    inference(cnf_transformation,[],[f3762]) ).

tff(f3762,plain,
    ! [X0: fun_nat_bool] :
      ( ( ( bot_bot_fun_nat_bool != X0 )
        | ! [X1: nat,X2: fun_nat_bool] :
            ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
            | ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2) != X0 ) ) )
      & ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK38(X0)),sK39(X0)))
          & ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK38(X0)),sK39(X0)) = X0 ) )
        | ( bot_bot_fun_nat_bool = X0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39])],[f3760,f3761]) ).

tff(f3761,plain,
    ! [X0: fun_nat_bool] :
      ( ? [X3: nat,X4: fun_nat_bool] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
          & ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4) = X0 ) )
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK38(X0)),sK39(X0)))
        & ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK38(X0)),sK39(X0)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f3760,plain,
    ! [X0: fun_nat_bool] :
      ( ( ( bot_bot_fun_nat_bool != X0 )
        | ! [X1: nat,X2: fun_nat_bool] :
            ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
            | ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2) != X0 ) ) )
      & ( ? [X3: nat,X4: fun_nat_bool] :
            ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4))
            & ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X4) = X0 ) )
        | ( bot_bot_fun_nat_bool = X0 ) ) ),
    inference(rectify,[],[f3759]) ).

tff(f3759,plain,
    ! [X0: fun_nat_bool] :
      ( ( ( bot_bot_fun_nat_bool != X0 )
        | ! [X1: nat,X2: fun_nat_bool] :
            ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
            | ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2) != X0 ) ) )
      & ( ? [X1: nat,X2: fun_nat_bool] :
            ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
            & ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2) = X0 ) )
        | ( bot_bot_fun_nat_bool = X0 ) ) ),
    inference(nnf_transformation,[],[f1459]) ).

tff(f1459,plain,
    ! [X0: fun_nat_bool] :
      ( ( bot_bot_fun_nat_bool != X0 )
    <=> ? [X1: nat,X2: fun_nat_bool] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
          & ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2) = X0 ) ) ),
    inference(rectify,[],[f702]) ).

tff(f702,axiom,
    ! [X2: fun_nat_bool] :
      ( ( bot_bot_fun_nat_bool != X2 )
    <=> ? [X27: nat,X80: fun_nat_bool] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X27),X80))
          & ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X27),X80) = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_701_nonempty__iff) ).

tff(f10409,plain,
    spl250_429,
    inference(avatar_split_clause,[],[f4735,f10407]) ).

tff(f10407,plain,
    ( spl250_429
  <=> ! [X0: fun_pname_bool] :
        ( ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK36(X0)),sK37(X0)) = X0 )
        | ( bot_bo844097828e_bool = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_429])]) ).

tff(f4735,plain,
    ! [X0: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK36(X0)),sK37(X0)) = X0 )
      | ( bot_bo844097828e_bool = X0 ) ),
    inference(cnf_transformation,[],[f3758]) ).

tff(f10405,plain,
    spl250_428,
    inference(avatar_split_clause,[],[f4732,f10403]) ).

tff(f4732,plain,
    ! [X0: nat] :
      ( ( hAPP_nat_nat(suc,sK35(X0)) = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(cnf_transformation,[],[f3754]) ).

tff(f3754,plain,
    ! [X0: nat] :
      ( ( hAPP_nat_nat(suc,sK35(X0)) = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK35])],[f2604,f3753]) ).

tff(f3753,plain,
    ! [X0: nat] :
      ( ? [X1: nat] : ( hAPP_nat_nat(suc,X1) = X0 )
     => ( hAPP_nat_nat(suc,sK35(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f2604,plain,
    ! [X0: nat] :
      ( ? [X1: nat] : ( hAPP_nat_nat(suc,X1) = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(ennf_transformation,[],[f1455]) ).

tff(f1455,plain,
    ! [X0: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
     => ? [X1: nat] : ( hAPP_nat_nat(suc,X1) = X0 ) ),
    inference(rectify,[],[f973]) ).

tff(f973,axiom,
    ! [X11: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X11))
     => ? [X32: nat] : ( hAPP_nat_nat(suc,X32) = X11 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_972_gr0__implies__Suc) ).

tff(f10401,plain,
    spl250_427,
    inference(avatar_split_clause,[],[f4717,f10399]) ).

tff(f10399,plain,
    ( spl250_427
  <=> ! [X0: fun_nat_bool] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X0))))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_427])]) ).

tff(f4717,plain,
    ! [X0: fun_nat_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X0))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ),
    inference(cnf_transformation,[],[f2590]) ).

tff(f2590,plain,
    ! [X0: fun_nat_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X0))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ),
    inference(ennf_transformation,[],[f1441]) ).

tff(f1441,plain,
    ! [X0: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
     => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X0)))) ),
    inference(rectify,[],[f8]) ).

tff(f8,axiom,
    ! [X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
     => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_finite__Collect__subsets) ).

tff(f10397,plain,
    spl250_426,
    inference(avatar_split_clause,[],[f4716,f10395]) ).

tff(f10395,plain,
    ( spl250_426
  <=> ! [X0: fun_int_bool] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(ord_le951220754t_bool),X0))))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_426])]) ).

tff(f4716,plain,
    ! [X0: fun_int_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(ord_le951220754t_bool),X0))))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ),
    inference(cnf_transformation,[],[f2589]) ).

tff(f2589,plain,
    ! [X0: fun_int_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(ord_le951220754t_bool),X0))))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0)) ),
    inference(ennf_transformation,[],[f1440]) ).

tff(f1440,plain,
    ! [X0: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X0))
     => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(ord_le951220754t_bool),X0)))) ),
    inference(rectify,[],[f9]) ).

tff(f9,axiom,
    ! [X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
     => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(ord_le951220754t_bool),X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_finite__Collect__subsets) ).

tff(f10393,plain,
    spl250_425,
    inference(avatar_split_clause,[],[f4715,f10391]) ).

tff(f10391,plain,
    ( spl250_425
  <=> ! [X0: fun_a_bool] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X0))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_425])]) ).

tff(f4715,plain,
    ! [X0: fun_a_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X0))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ),
    inference(cnf_transformation,[],[f2588]) ).

tff(f2588,plain,
    ! [X0: fun_a_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X0))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0)) ),
    inference(ennf_transformation,[],[f1439]) ).

tff(f1439,plain,
    ! [X0: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X0))
     => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X0)))) ),
    inference(rectify,[],[f6]) ).

tff(f6,axiom,
    ! [X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
     => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_finite__Collect__subsets) ).

tff(f10389,plain,
    spl250_424,
    inference(avatar_split_clause,[],[f4714,f10387]) ).

tff(f10387,plain,
    ( spl250_424
  <=> ! [X0: fun_pname_bool] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X0))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_424])]) ).

tff(f4714,plain,
    ! [X0: fun_pname_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X0))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ),
    inference(cnf_transformation,[],[f2587]) ).

tff(f2587,plain,
    ! [X0: fun_pname_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X0))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0)) ),
    inference(ennf_transformation,[],[f1438]) ).

tff(f1438,plain,
    ! [X0: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X0))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X0)))) ),
    inference(rectify,[],[f7]) ).

tff(f7,axiom,
    ! [X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_finite__Collect__subsets) ).

tff(f10385,plain,
    spl250_423,
    inference(avatar_split_clause,[],[f4713,f10383]) ).

tff(f10383,plain,
    ( spl250_423
  <=> ! [X0: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X0))))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_423])]) ).

tff(f4713,plain,
    ! [X0: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X0))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ),
    inference(cnf_transformation,[],[f2586]) ).

tff(f2586,plain,
    ! [X0: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X0))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0)) ),
    inference(ennf_transformation,[],[f1437]) ).

tff(f1437,plain,
    ! [X0: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X0))
     => hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X0)))) ),
    inference(rectify,[],[f4]) ).

tff(f4,axiom,
    ! [X2: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
     => hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_finite__Collect__subsets) ).

tff(f10381,plain,
    spl250_422,
    inference(avatar_split_clause,[],[f4712,f10379]) ).

tff(f10379,plain,
    ( spl250_422
  <=> ! [X0: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X0))))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_422])]) ).

tff(f4712,plain,
    ! [X0: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X0))))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ),
    inference(cnf_transformation,[],[f2585]) ).

tff(f2585,plain,
    ! [X0: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X0))))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0)) ),
    inference(ennf_transformation,[],[f1436]) ).

tff(f1436,plain,
    ! [X0: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X0))
     => hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X0)))) ),
    inference(rectify,[],[f5]) ).

tff(f5,axiom,
    ! [X2: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
     => hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_finite__Collect__subsets) ).

tff(f10377,plain,
    ( spl250_421
    | ~ spl250_41
    | ~ spl250_387 ),
    inference(avatar_split_clause,[],[f10280,f9759,f7504,f10375]) ).

tff(f10375,plain,
    ( spl250_421
  <=> ! [X0: fun_fu819804446l_bool] : ~ sP10(X0,bot_bot_fun_int_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_421])]) ).

tff(f7504,plain,
    ( spl250_41
  <=> ! [X0: int] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),bot_bot_fun_int_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_41])]) ).

tff(f9759,plain,
    ( spl250_387
  <=> ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK180(X0,X1)),X1))
        | ~ sP10(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_387])]) ).

tff(f10280,plain,
    ( ! [X0: fun_fu819804446l_bool] : ~ sP10(X0,bot_bot_fun_int_bool)
    | ~ spl250_41
    | ~ spl250_387 ),
    inference(resolution,[],[f9760,f7505]) ).

tff(f7505,plain,
    ( ! [X0: int] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),bot_bot_fun_int_bool))
    | ~ spl250_41 ),
    inference(avatar_component_clause,[],[f7504]) ).

tff(f9760,plain,
    ( ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK180(X0,X1)),X1))
        | ~ sP10(X0,X1) )
    | ~ spl250_387 ),
    inference(avatar_component_clause,[],[f9759]) ).

tff(f10373,plain,
    spl250_420,
    inference(avatar_split_clause,[],[f4711,f10371]) ).

tff(f10371,plain,
    ( spl250_420
  <=> ! [X0: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X0))))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_420])]) ).

tff(f4711,plain,
    ! [X0: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X0))))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ),
    inference(cnf_transformation,[],[f2584]) ).

tff(f2584,plain,
    ! [X0: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X0))))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0)) ),
    inference(ennf_transformation,[],[f1435]) ).

tff(f1435,plain,
    ! [X0: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X0))
     => hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X0)))) ),
    inference(rectify,[],[f3]) ).

tff(f3,axiom,
    ! [X2: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
     => hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_finite__Collect__subsets) ).

tff(f10369,plain,
    spl250_419,
    inference(avatar_split_clause,[],[f4710,f10367]) ).

tff(f10367,plain,
    ( spl250_419
  <=> ! [X0: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_f1593524852l_bool(finite2095298929l_bool,collec1409689523l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(ord_le1848167016l_bool),X0))))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_419])]) ).

tff(f4710,plain,
    ! [X0: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f1593524852l_bool(finite2095298929l_bool,collec1409689523l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(ord_le1848167016l_bool),X0))))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0)) ),
    inference(cnf_transformation,[],[f2583]) ).

tff(f2583,plain,
    ! [X0: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f1593524852l_bool(finite2095298929l_bool,collec1409689523l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(ord_le1848167016l_bool),X0))))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0)) ),
    inference(ennf_transformation,[],[f1434]) ).

tff(f1434,plain,
    ! [X0: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X0))
     => hBOOL(hAPP_f1593524852l_bool(finite2095298929l_bool,collec1409689523l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(ord_le1848167016l_bool),X0)))) ),
    inference(rectify,[],[f2]) ).

tff(f2,axiom,
    ! [X2: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
     => hBOOL(hAPP_f1593524852l_bool(finite2095298929l_bool,collec1409689523l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(ord_le1848167016l_bool),X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_finite__Collect__subsets) ).

tff(f10362,plain,
    ( spl250_418
    | ~ spl250_172
    | ~ spl250_417 ),
    inference(avatar_split_clause,[],[f10357,f10353,f8230,f10359]) ).

tff(f10359,plain,
    ( spl250_418
  <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,na),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_418])]) ).

tff(f8230,plain,
    ( spl250_172
  <=> ! [X0: nat] : ( hAPP_n1699378549t_bool(ord_less_nat,X0) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_172])]) ).

tff(f10353,plain,
    ( spl250_417
  <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_417])]) ).

tff(f10357,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,na),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))))
    | ~ spl250_172
    | ~ spl250_417 ),
    inference(forward_demodulation,[],[f10355,f8231]) ).

tff(f8231,plain,
    ( ! [X0: nat] : ( hAPP_n1699378549t_bool(ord_less_nat,X0) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)) )
    | ~ spl250_172 ),
    inference(avatar_component_clause,[],[f8230]) ).

tff(f10355,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))))
    | ~ spl250_417 ),
    inference(avatar_component_clause,[],[f10353]) ).

tff(f10356,plain,
    spl250_417,
    inference(avatar_split_clause,[],[f4545,f10353]) ).

tff(f4545,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))),
    inference(cnf_transformation,[],[f1305]) ).

tff(f1305,axiom,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).

tff(f10337,plain,
    ( spl250_416
    | ~ spl250_40
    | ~ spl250_386 ),
    inference(avatar_split_clause,[],[f10275,f9755,f7500,f10335]) ).

tff(f10335,plain,
    ( spl250_416
  <=> ! [X0: fun_fun_a_bool_bool] : ~ sP9(X0,bot_bot_fun_a_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_416])]) ).

tff(f7500,plain,
    ( spl250_40
  <=> ! [X0: x_a] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),bot_bot_fun_a_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_40])]) ).

tff(f9755,plain,
    ( spl250_386
  <=> ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK170(X0,X1)),X1))
        | ~ sP9(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_386])]) ).

tff(f10275,plain,
    ( ! [X0: fun_fun_a_bool_bool] : ~ sP9(X0,bot_bot_fun_a_bool)
    | ~ spl250_40
    | ~ spl250_386 ),
    inference(resolution,[],[f9756,f7501]) ).

tff(f7501,plain,
    ( ! [X0: x_a] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),bot_bot_fun_a_bool))
    | ~ spl250_40 ),
    inference(avatar_component_clause,[],[f7500]) ).

tff(f9756,plain,
    ( ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK170(X0,X1)),X1))
        | ~ sP9(X0,X1) )
    | ~ spl250_386 ),
    inference(avatar_component_clause,[],[f9755]) ).

tff(f10326,plain,
    ( spl250_415
    | ~ spl250_371
    | ~ spl250_403 ),
    inference(avatar_split_clause,[],[f9826,f9823,f9695,f10324]) ).

tff(f10324,plain,
    ( spl250_415
  <=> ! [X0: nat] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_eq_int,semiri1621563631at_int),X0),pls))
        | ( zero_zero_nat = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_415])]) ).

tff(f9823,plain,
    ( spl250_403
  <=> ! [X0: nat] :
        ( ( zero_zero_nat = X0 )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_403])]) ).

tff(f9826,plain,
    ( ! [X0: nat] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_eq_int,semiri1621563631at_int),X0),pls))
        | ( zero_zero_nat = X0 ) )
    | ~ spl250_371
    | ~ spl250_403 ),
    inference(forward_demodulation,[],[f9824,f9696]) ).

tff(f9824,plain,
    ( ! [X0: nat] :
        ( ( zero_zero_nat = X0 )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls)) )
    | ~ spl250_403 ),
    inference(avatar_component_clause,[],[f9823]) ).

tff(f10273,plain,
    ( spl250_414
    | ~ spl250_39
    | ~ spl250_385 ),
    inference(avatar_split_clause,[],[f10266,f9751,f7496,f10271]) ).

tff(f10271,plain,
    ( spl250_414
  <=> ! [X0: fun_fu1430349052l_bool] : ~ sP8(X0,bot_bo844097828e_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_414])]) ).

tff(f9751,plain,
    ( spl250_385
  <=> ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK160(X0,X1)),X1))
        | ~ sP8(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_385])]) ).

tff(f10266,plain,
    ( ! [X0: fun_fu1430349052l_bool] : ~ sP8(X0,bot_bo844097828e_bool)
    | ~ spl250_39
    | ~ spl250_385 ),
    inference(resolution,[],[f9752,f7497]) ).

tff(f9752,plain,
    ( ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK160(X0,X1)),X1))
        | ~ sP8(X0,X1) )
    | ~ spl250_385 ),
    inference(avatar_component_clause,[],[f9751]) ).

tff(f10216,plain,
    ( spl250_413
    | ~ spl250_49
    | ~ spl250_353 ),
    inference(avatar_split_clause,[],[f10015,f9622,f7536,f10214]) ).

tff(f7536,plain,
    ( spl250_49
  <=> ! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_49])]) ).

tff(f9622,plain,
    ( spl250_353
  <=> ! [X0: fun_a_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(p(X1),X0))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_353])]) ).

tff(f10015,plain,
    ( ! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(p(X0),X0))
    | ~ spl250_49
    | ~ spl250_353 ),
    inference(resolution,[],[f9623,f7537]) ).

tff(f7537,plain,
    ( ! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X0))
    | ~ spl250_49 ),
    inference(avatar_component_clause,[],[f7536]) ).

tff(f9623,plain,
    ( ! [X0: fun_a_bool,X1: fun_a_bool] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
        | hBOOL(hAPP_fun_a_bool_bool(p(X1),X0)) )
    | ~ spl250_353 ),
    inference(avatar_component_clause,[],[f9622]) ).

tff(f10104,plain,
    ( spl250_412
    | ~ spl250_46
    | ~ spl250_353 ),
    inference(avatar_split_clause,[],[f10014,f9622,f7524,f10102]) ).

tff(f10014,plain,
    ( ! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(p(X0),bot_bot_fun_a_bool))
    | ~ spl250_46
    | ~ spl250_353 ),
    inference(resolution,[],[f9623,f7525]) ).

tff(f9903,plain,
    ( spl250_411
    | ~ spl250_38
    | ~ spl250_336 ),
    inference(avatar_split_clause,[],[f9856,f9554,f7491,f9900]) ).

tff(f9554,plain,
    ( spl250_336
  <=> ! [X0: pname] :
        ( hBOOL(wt(the_com(body(X0))))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),u)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_336])]) ).

tff(f9856,plain,
    ( hBOOL(wt(the_com(body(pn))))
    | ~ spl250_38
    | ~ spl250_336 ),
    inference(resolution,[],[f9555,f7493]) ).

tff(f9555,plain,
    ( ! [X0: pname] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),u))
        | hBOOL(wt(the_com(body(X0)))) )
    | ~ spl250_336 ),
    inference(avatar_component_clause,[],[f9554]) ).

tff(f9855,plain,
    spl250_410,
    inference(avatar_split_clause,[],[f7218,f9853]) ).

tff(f9853,plain,
    ( spl250_410
  <=> ! [X2: fun_fun_nat_bool_nat,X0: nat,X1: fun_nat_fun_nat_nat] :
        ( ( hAPP_f22106695ol_nat(X2,hAPP_n1699378549t_bool(fequal_nat,X0)) = X0 )
        | ~ hBOOL(finite988810631ne_nat(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_410])]) ).

tff(f7218,plain,
    ! [X2: fun_fun_nat_bool_nat,X0: nat,X1: fun_nat_fun_nat_nat] :
      ( ( hAPP_f22106695ol_nat(X2,hAPP_n1699378549t_bool(fequal_nat,X0)) = X0 )
      | ~ hBOOL(finite988810631ne_nat(X1,X2)) ),
    inference(forward_demodulation,[],[f6005,f6931]) ).

tff(f6005,plain,
    ! [X2: fun_fun_nat_bool_nat,X0: nat,X1: fun_nat_fun_nat_nat] :
      ( ( hAPP_f22106695ol_nat(X2,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)) = X0 )
      | ~ hBOOL(finite988810631ne_nat(X1,X2)) ),
    inference(cnf_transformation,[],[f3281]) ).

tff(f3281,plain,
    ! [X0: nat,X1: fun_nat_fun_nat_nat,X2: fun_fun_nat_bool_nat] :
      ( ( hAPP_f22106695ol_nat(X2,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)) = X0 )
      | ~ hBOOL(finite988810631ne_nat(X1,X2)) ),
    inference(ennf_transformation,[],[f2264]) ).

tff(f2264,plain,
    ! [X0: nat,X1: fun_nat_fun_nat_nat,X2: fun_fun_nat_bool_nat] :
      ( hBOOL(finite988810631ne_nat(X1,X2))
     => ( hAPP_f22106695ol_nat(X2,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)) = X0 ) ),
    inference(rectify,[],[f750]) ).

tff(f750,axiom,
    ! [X8: nat,X6: fun_nat_fun_nat_nat,X4: fun_fun_nat_bool_nat] :
      ( hBOOL(finite988810631ne_nat(X6,X4))
     => ( hAPP_f22106695ol_nat(X4,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),bot_bot_fun_nat_bool)) = X8 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_749_folding__one_Osingleton) ).

tff(f9851,plain,
    spl250_409,
    inference(avatar_split_clause,[],[f7216,f9849]) ).

tff(f9849,plain,
    ( spl250_409
  <=> ! [X2: fun_fun_int_bool_int,X0: int,X1: fun_int_fun_int_int] :
        ( ( hAPP_f1594865479ol_int(X2,hAPP_i1948725293t_bool(fequal_int,X0)) = X0 )
        | ~ hBOOL(finite1626084323ne_int(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_409])]) ).

tff(f7216,plain,
    ! [X2: fun_fun_int_bool_int,X0: int,X1: fun_int_fun_int_int] :
      ( ( hAPP_f1594865479ol_int(X2,hAPP_i1948725293t_bool(fequal_int,X0)) = X0 )
      | ~ hBOOL(finite1626084323ne_int(X1,X2)) ),
    inference(forward_demodulation,[],[f6003,f6930]) ).

tff(f6003,plain,
    ! [X2: fun_fun_int_bool_int,X0: int,X1: fun_int_fun_int_int] :
      ( ( hAPP_f1594865479ol_int(X2,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)) = X0 )
      | ~ hBOOL(finite1626084323ne_int(X1,X2)) ),
    inference(cnf_transformation,[],[f3279]) ).

tff(f3279,plain,
    ! [X0: int,X1: fun_int_fun_int_int,X2: fun_fun_int_bool_int] :
      ( ( hAPP_f1594865479ol_int(X2,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)) = X0 )
      | ~ hBOOL(finite1626084323ne_int(X1,X2)) ),
    inference(ennf_transformation,[],[f2262]) ).

tff(f2262,plain,
    ! [X0: int,X1: fun_int_fun_int_int,X2: fun_fun_int_bool_int] :
      ( hBOOL(finite1626084323ne_int(X1,X2))
     => ( hAPP_f1594865479ol_int(X2,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)) = X0 ) ),
    inference(rectify,[],[f751]) ).

tff(f751,axiom,
    ! [X8: int,X6: fun_int_fun_int_int,X4: fun_fun_int_bool_int] :
      ( hBOOL(finite1626084323ne_int(X6,X4))
     => ( hAPP_f1594865479ol_int(X4,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),bot_bot_fun_int_bool)) = X8 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_750_folding__one_Osingleton) ).

tff(f9847,plain,
    ( spl250_408
    | ~ spl250_85
    | ~ spl250_333 ),
    inference(avatar_split_clause,[],[f9475,f9419,f7733,f9844]) ).

tff(f9844,plain,
    ( spl250_408
  <=> ( fTrue = hAPP_pname_bool(u,pn) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_408])]) ).

tff(f9419,plain,
    ( spl250_333
  <=> hBOOL(hAPP_pname_bool(u,pn)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_333])]) ).

tff(f9475,plain,
    ( ( fTrue = hAPP_pname_bool(u,pn) )
    | ~ spl250_85
    | ~ spl250_333 ),
    inference(resolution,[],[f9421,f7734]) ).

tff(f9421,plain,
    ( hBOOL(hAPP_pname_bool(u,pn))
    | ~ spl250_333 ),
    inference(avatar_component_clause,[],[f9419]) ).

tff(f9842,plain,
    spl250_407,
    inference(avatar_split_clause,[],[f7090,f9840]) ).

tff(f9840,plain,
    ( spl250_407
  <=> ! [X0: nat,X1: nat] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_n1699378549t_bool(fequal_nat,X1)))
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_407])]) ).

tff(f7090,plain,
    ! [X0: nat,X1: nat] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_n1699378549t_bool(fequal_nat,X1)))
      | ( X0 = X1 ) ),
    inference(forward_demodulation,[],[f5391,f6931]) ).

tff(f5391,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))) ),
    inference(cnf_transformation,[],[f3039]) ).

tff(f3039,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))) ),
    inference(ennf_transformation,[],[f1934]) ).

tff(f1934,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)))
     => ( X0 = X1 ) ),
    inference(rectify,[],[f595]) ).

tff(f595,axiom,
    ! [X28: nat,X5: nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X28),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5),bot_bot_fun_nat_bool)))
     => ( X5 = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_594_singletonE) ).

tff(f9838,plain,
    spl250_406,
    inference(avatar_split_clause,[],[f7087,f9836]) ).

tff(f9836,plain,
    ( spl250_406
  <=> ! [X0: int,X1: int] :
        ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_i1948725293t_bool(fequal_int,X1)))
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_406])]) ).

tff(f7087,plain,
    ! [X0: int,X1: int] :
      ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_i1948725293t_bool(fequal_int,X1)))
      | ( X0 = X1 ) ),
    inference(forward_demodulation,[],[f5389,f6930]) ).

tff(f5389,plain,
    ! [X0: int,X1: int] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))) ),
    inference(cnf_transformation,[],[f3036]) ).

tff(f3036,plain,
    ! [X0: int,X1: int] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))) ),
    inference(ennf_transformation,[],[f1932]) ).

tff(f1932,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)))
     => ( X0 = X1 ) ),
    inference(rectify,[],[f594]) ).

tff(f594,axiom,
    ! [X28: int,X5: int] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X28),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5),bot_bot_fun_int_bool)))
     => ( X5 = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_593_singletonE) ).

tff(f9834,plain,
    spl250_405,
    inference(avatar_split_clause,[],[f6984,f9832]) ).

tff(f9832,plain,
    ( spl250_405
  <=> ! [X0: int,X1: fun_nat_bool] :
        ( ( hAPP_i1948725293t_bool(fequal_int,X0) = image_nat_int(cOMBK_int_nat(X0),X1) )
        | ( bot_bot_fun_nat_bool = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_405])]) ).

tff(f6984,plain,
    ! [X0: int,X1: fun_nat_bool] :
      ( ( hAPP_i1948725293t_bool(fequal_int,X0) = image_nat_int(cOMBK_int_nat(X0),X1) )
      | ( bot_bot_fun_nat_bool = X1 ) ),
    inference(forward_demodulation,[],[f4949,f6930]) ).

tff(f4949,plain,
    ! [X0: int,X1: fun_nat_bool] :
      ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = image_nat_int(cOMBK_int_nat(X0),X1) )
      | ( bot_bot_fun_nat_bool = X1 ) ),
    inference(cnf_transformation,[],[f2612]) ).

tff(f2612,plain,
    ! [X0: int,X1: fun_nat_bool] :
      ( ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = image_nat_int(cOMBK_int_nat(X0),X1) )
        | ( bot_bot_fun_nat_bool = X1 ) )
      & ( ( bot_bot_fun_int_bool = image_nat_int(cOMBK_int_nat(X0),X1) )
        | ( bot_bot_fun_nat_bool != X1 ) ) ),
    inference(ennf_transformation,[],[f1595]) ).

tff(f1595,plain,
    ! [X0: int,X1: fun_nat_bool] :
      ( ( ( bot_bot_fun_nat_bool != X1 )
       => ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = image_nat_int(cOMBK_int_nat(X0),X1) ) )
      & ( ( bot_bot_fun_nat_bool = X1 )
       => ( bot_bot_fun_int_bool = image_nat_int(cOMBK_int_nat(X0),X1) ) ) ),
    inference(rectify,[],[f668]) ).

tff(f668,axiom,
    ! [X29: int,X2: fun_nat_bool] :
      ( ( ( bot_bot_fun_nat_bool != X2 )
       => ( image_nat_int(cOMBK_int_nat(X29),X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X29),bot_bot_fun_int_bool) ) )
      & ( ( bot_bot_fun_nat_bool = X2 )
       => ( bot_bot_fun_int_bool = image_nat_int(cOMBK_int_nat(X29),X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_667_image__constant__conv) ).

tff(f9830,plain,
    spl250_404,
    inference(avatar_split_clause,[],[f6966,f9828]) ).

tff(f9828,plain,
    ( spl250_404
  <=> ! [X0: fun_nat_bool,X1: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X0),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_404])]) ).

tff(f6966,plain,
    ! [X0: fun_nat_bool,X1: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X0),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X1)))),
    inference(forward_demodulation,[],[f4907,f4588]) ).

tff(f4907,plain,
    ! [X0: fun_nat_bool,X1: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X0),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X1))))),
    inference(cnf_transformation,[],[f1555]) ).

tff(f1555,plain,
    ! [X0: fun_nat_bool,X1: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X0),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X1))))),
    inference(rectify,[],[f898]) ).

tff(f898,axiom,
    ! [X10: fun_nat_bool,X30: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X10),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X30))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_897_finite__M__bounded__by__nat) ).

tff(f9825,plain,
    spl250_403,
    inference(avatar_split_clause,[],[f6622,f9823]) ).

tff(f6622,plain,
    ! [X0: nat] :
      ( ( zero_zero_nat = X0 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls)) ),
    inference(definition_unfolding,[],[f4841,f4550]) ).

tff(f4841,plain,
    ! [X0: nat] :
      ( ( zero_zero_nat = X0 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int)) ),
    inference(cnf_transformation,[],[f3858]) ).

tff(f3858,plain,
    ! [X0: nat] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int))
        | ( zero_zero_nat != X0 ) )
      & ( ( zero_zero_nat = X0 )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int)) ) ),
    inference(nnf_transformation,[],[f1504]) ).

tff(f1504,plain,
    ! [X0: nat] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int))
    <=> ( zero_zero_nat = X0 ) ),
    inference(rectify,[],[f1122]) ).

tff(f1122,axiom,
    ! [X14: nat] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X14)),zero_zero_int))
    <=> ( zero_zero_nat = X14 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1121_int__le__0__conv) ).

tff(f9821,plain,
    spl250_402,
    inference(avatar_split_clause,[],[f6574,f9819]) ).

tff(f9819,plain,
    ( spl250_402
  <=> ! [X0: int] : ( pls != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_402])]) ).

tff(f6574,plain,
    ! [X0: int] : ( pls != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0)),X0) ),
    inference(definition_unfolding,[],[f4584,f4687]) ).

tff(f4584,plain,
    ! [X0: int] : ( pls != bit1(X0) ),
    inference(cnf_transformation,[],[f1312]) ).

tff(f1312,plain,
    ! [X0: int] : ( pls != bit1(X0) ),
    inference(rectify,[],[f1183]) ).

tff(f1183,axiom,
    ! [X19: int] : ( pls != bit1(X19) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1182_rel__simps_I46_J) ).

tff(f9817,plain,
    spl250_401,
    inference(avatar_split_clause,[],[f6535,f9815]) ).

tff(f9815,plain,
    ( spl250_401
  <=> ! [X0: x_a,X3: x_a,X2: x_a,X1: x_a] :
        ( ( X0 = X1 )
        | ( X1 = X2 )
        | ~ sP28(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_401])]) ).

tff(f6535,plain,
    ! [X2: x_a,X3: x_a,X0: x_a,X1: x_a] :
      ( ( X0 = X1 )
      | ( X1 = X2 )
      | ~ sP28(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f4532]) ).

tff(f4532,plain,
    ! [X0: x_a,X1: x_a,X2: x_a,X3: x_a] :
      ( ( sP28(X0,X1,X2,X3)
        | ( ( ( X0 != X1 )
            | ( X2 != X3 ) )
          & ( ( X1 != X2 )
            | ( X0 != X3 ) ) ) )
      & ( ( ( X0 = X1 )
          & ( X2 = X3 ) )
        | ( ( X1 = X2 )
          & ( X0 = X3 ) )
        | ~ sP28(X0,X1,X2,X3) ) ),
    inference(rectify,[],[f4531]) ).

tff(f4531,plain,
    ! [X2: x_a,X1: x_a,X3: x_a,X0: x_a] :
      ( ( sP28(X2,X1,X3,X0)
        | ( ( ( X1 != X2 )
            | ( X0 != X3 ) )
          & ( ( X1 != X3 )
            | ( X0 != X2 ) ) ) )
      & ( ( ( X1 = X2 )
          & ( X0 = X3 ) )
        | ( ( X1 = X3 )
          & ( X0 = X2 ) )
        | ~ sP28(X2,X1,X3,X0) ) ),
    inference(flattening,[],[f4530]) ).

tff(f4530,plain,
    ! [X2: x_a,X1: x_a,X3: x_a,X0: x_a] :
      ( ( sP28(X2,X1,X3,X0)
        | ( ( ( X1 != X2 )
            | ( X0 != X3 ) )
          & ( ( X1 != X3 )
            | ( X0 != X2 ) ) ) )
      & ( ( ( X1 = X2 )
          & ( X0 = X3 ) )
        | ( ( X1 = X3 )
          & ( X0 = X2 ) )
        | ~ sP28(X2,X1,X3,X0) ) ),
    inference(nnf_transformation,[],[f3739]) ).

tff(f9813,plain,
    spl250_400,
    inference(avatar_split_clause,[],[f6534,f9811]) ).

tff(f9811,plain,
    ( spl250_400
  <=> ! [X0: x_a,X3: x_a,X2: x_a,X1: x_a] :
        ( ( X0 = X1 )
        | ( X0 = X3 )
        | ~ sP28(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_400])]) ).

tff(f6534,plain,
    ! [X2: x_a,X3: x_a,X0: x_a,X1: x_a] :
      ( ( X0 = X1 )
      | ( X0 = X3 )
      | ~ sP28(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f4532]) ).

tff(f9809,plain,
    spl250_399,
    inference(avatar_split_clause,[],[f6533,f9807]) ).

tff(f9807,plain,
    ( spl250_399
  <=> ! [X2: x_a,X0: x_a,X1: x_a,X3: x_a] :
        ( ( X2 = X3 )
        | ( X1 = X2 )
        | ~ sP28(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_399])]) ).

tff(f6533,plain,
    ! [X2: x_a,X3: x_a,X0: x_a,X1: x_a] :
      ( ( X2 = X3 )
      | ( X1 = X2 )
      | ~ sP28(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f4532]) ).

tff(f9805,plain,
    spl250_398,
    inference(avatar_split_clause,[],[f6532,f9803]) ).

tff(f9803,plain,
    ( spl250_398
  <=> ! [X0: x_a,X3: x_a,X2: x_a,X1: x_a] :
        ( ( X2 = X3 )
        | ( X0 = X3 )
        | ~ sP28(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_398])]) ).

tff(f6532,plain,
    ! [X2: x_a,X3: x_a,X0: x_a,X1: x_a] :
      ( ( X2 = X3 )
      | ( X0 = X3 )
      | ~ sP28(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f4532]) ).

tff(f9801,plain,
    spl250_397,
    inference(avatar_split_clause,[],[f6527,f9799]) ).

tff(f9799,plain,
    ( spl250_397
  <=> ! [X0: nat,X3: nat,X2: nat,X1: nat] :
        ( ( X0 = X1 )
        | ( X1 = X2 )
        | ~ sP27(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_397])]) ).

tff(f6527,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ( X1 = X2 )
      | ~ sP27(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f4528]) ).

tff(f4528,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( sP27(X0,X1,X2,X3)
        | ( ( ( X0 != X1 )
            | ( X2 != X3 ) )
          & ( ( X1 != X2 )
            | ( X0 != X3 ) ) ) )
      & ( ( ( X0 = X1 )
          & ( X2 = X3 ) )
        | ( ( X1 = X2 )
          & ( X0 = X3 ) )
        | ~ sP27(X0,X1,X2,X3) ) ),
    inference(rectify,[],[f4527]) ).

tff(f4527,plain,
    ! [X2: nat,X1: nat,X3: nat,X0: nat] :
      ( ( sP27(X2,X1,X3,X0)
        | ( ( ( X1 != X2 )
            | ( X0 != X3 ) )
          & ( ( X1 != X3 )
            | ( X0 != X2 ) ) ) )
      & ( ( ( X1 = X2 )
          & ( X0 = X3 ) )
        | ( ( X1 = X3 )
          & ( X0 = X2 ) )
        | ~ sP27(X2,X1,X3,X0) ) ),
    inference(flattening,[],[f4526]) ).

tff(f4526,plain,
    ! [X2: nat,X1: nat,X3: nat,X0: nat] :
      ( ( sP27(X2,X1,X3,X0)
        | ( ( ( X1 != X2 )
            | ( X0 != X3 ) )
          & ( ( X1 != X3 )
            | ( X0 != X2 ) ) ) )
      & ( ( ( X1 = X2 )
          & ( X0 = X3 ) )
        | ( ( X1 = X3 )
          & ( X0 = X2 ) )
        | ~ sP27(X2,X1,X3,X0) ) ),
    inference(nnf_transformation,[],[f3737]) ).

tff(f9797,plain,
    spl250_396,
    inference(avatar_split_clause,[],[f6526,f9795]) ).

tff(f9795,plain,
    ( spl250_396
  <=> ! [X0: nat,X3: nat,X2: nat,X1: nat] :
        ( ( X0 = X1 )
        | ( X0 = X3 )
        | ~ sP27(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_396])]) ).

tff(f6526,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ( X0 = X3 )
      | ~ sP27(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f4528]) ).

tff(f9793,plain,
    spl250_395,
    inference(avatar_split_clause,[],[f6525,f9791]) ).

tff(f9791,plain,
    ( spl250_395
  <=> ! [X2: nat,X0: nat,X1: nat,X3: nat] :
        ( ( X2 = X3 )
        | ( X1 = X2 )
        | ~ sP27(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_395])]) ).

tff(f6525,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( ( X2 = X3 )
      | ( X1 = X2 )
      | ~ sP27(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f4528]) ).

tff(f9789,plain,
    spl250_394,
    inference(avatar_split_clause,[],[f6524,f9787]) ).

tff(f9787,plain,
    ( spl250_394
  <=> ! [X0: nat,X3: nat,X2: nat,X1: nat] :
        ( ( X2 = X3 )
        | ( X0 = X3 )
        | ~ sP27(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_394])]) ).

tff(f6524,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( ( X2 = X3 )
      | ( X0 = X3 )
      | ~ sP27(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f4528]) ).

tff(f9785,plain,
    spl250_393,
    inference(avatar_split_clause,[],[f6519,f9783]) ).

tff(f9783,plain,
    ( spl250_393
  <=> ! [X0: int,X3: int,X2: int,X1: int] :
        ( ( X0 = X1 )
        | ( X1 = X2 )
        | ~ sP26(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_393])]) ).

tff(f6519,plain,
    ! [X2: int,X3: int,X0: int,X1: int] :
      ( ( X0 = X1 )
      | ( X1 = X2 )
      | ~ sP26(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f4524]) ).

tff(f4524,plain,
    ! [X0: int,X1: int,X2: int,X3: int] :
      ( ( sP26(X0,X1,X2,X3)
        | ( ( ( X0 != X1 )
            | ( X2 != X3 ) )
          & ( ( X1 != X2 )
            | ( X0 != X3 ) ) ) )
      & ( ( ( X0 = X1 )
          & ( X2 = X3 ) )
        | ( ( X1 = X2 )
          & ( X0 = X3 ) )
        | ~ sP26(X0,X1,X2,X3) ) ),
    inference(rectify,[],[f4523]) ).

tff(f4523,plain,
    ! [X2: int,X1: int,X3: int,X0: int] :
      ( ( sP26(X2,X1,X3,X0)
        | ( ( ( X1 != X2 )
            | ( X0 != X3 ) )
          & ( ( X1 != X3 )
            | ( X0 != X2 ) ) ) )
      & ( ( ( X1 = X2 )
          & ( X0 = X3 ) )
        | ( ( X1 = X3 )
          & ( X0 = X2 ) )
        | ~ sP26(X2,X1,X3,X0) ) ),
    inference(flattening,[],[f4522]) ).

tff(f4522,plain,
    ! [X2: int,X1: int,X3: int,X0: int] :
      ( ( sP26(X2,X1,X3,X0)
        | ( ( ( X1 != X2 )
            | ( X0 != X3 ) )
          & ( ( X1 != X3 )
            | ( X0 != X2 ) ) ) )
      & ( ( ( X1 = X2 )
          & ( X0 = X3 ) )
        | ( ( X1 = X3 )
          & ( X0 = X2 ) )
        | ~ sP26(X2,X1,X3,X0) ) ),
    inference(nnf_transformation,[],[f3735]) ).

tff(f9781,plain,
    spl250_392,
    inference(avatar_split_clause,[],[f6518,f9779]) ).

tff(f9779,plain,
    ( spl250_392
  <=> ! [X0: int,X3: int,X2: int,X1: int] :
        ( ( X0 = X1 )
        | ( X0 = X3 )
        | ~ sP26(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_392])]) ).

tff(f6518,plain,
    ! [X2: int,X3: int,X0: int,X1: int] :
      ( ( X0 = X1 )
      | ( X0 = X3 )
      | ~ sP26(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f4524]) ).

tff(f9777,plain,
    spl250_391,
    inference(avatar_split_clause,[],[f6517,f9775]) ).

tff(f9775,plain,
    ( spl250_391
  <=> ! [X2: int,X0: int,X1: int,X3: int] :
        ( ( X2 = X3 )
        | ( X1 = X2 )
        | ~ sP26(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_391])]) ).

tff(f6517,plain,
    ! [X2: int,X3: int,X0: int,X1: int] :
      ( ( X2 = X3 )
      | ( X1 = X2 )
      | ~ sP26(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f4524]) ).

tff(f9773,plain,
    spl250_390,
    inference(avatar_split_clause,[],[f6516,f9771]) ).

tff(f9771,plain,
    ( spl250_390
  <=> ! [X0: int,X3: int,X2: int,X1: int] :
        ( ( X2 = X3 )
        | ( X0 = X3 )
        | ~ sP26(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_390])]) ).

tff(f6516,plain,
    ! [X2: int,X3: int,X0: int,X1: int] :
      ( ( X2 = X3 )
      | ( X0 = X3 )
      | ~ sP26(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f4524]) ).

tff(f9769,plain,
    spl250_389,
    inference(avatar_split_clause,[],[f6009,f9767]) ).

tff(f9767,plain,
    ( spl250_389
  <=> ! [X0: fun_int_bool,X1: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),sK205(X0,X1)))
        | ~ sP12(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_389])]) ).

tff(f6009,plain,
    ! [X0: fun_int_bool,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),sK205(X0,X1)))
      | ~ sP12(X0,X1) ),
    inference(cnf_transformation,[],[f4299]) ).

tff(f9765,plain,
    spl250_388,
    inference(avatar_split_clause,[],[f5972,f9763]) ).

tff(f5972,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK189(X0,X1)),X1))
      | ~ sP11(X0,X1) ),
    inference(cnf_transformation,[],[f4275]) ).

tff(f9761,plain,
    spl250_387,
    inference(avatar_split_clause,[],[f5938,f9759]) ).

tff(f5938,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK180(X0,X1)),X1))
      | ~ sP10(X0,X1) ),
    inference(cnf_transformation,[],[f4257]) ).

tff(f9757,plain,
    spl250_386,
    inference(avatar_split_clause,[],[f5903,f9755]) ).

tff(f5903,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK170(X0,X1)),X1))
      | ~ sP9(X0,X1) ),
    inference(cnf_transformation,[],[f4237]) ).

tff(f9753,plain,
    spl250_385,
    inference(avatar_split_clause,[],[f5865,f9751]) ).

tff(f5865,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK160(X0,X1)),X1))
      | ~ sP8(X0,X1) ),
    inference(cnf_transformation,[],[f4217]) ).

tff(f9749,plain,
    spl250_384,
    inference(avatar_split_clause,[],[f5707,f9747]) ).

tff(f9747,plain,
    ( spl250_384
  <=> ! [X2: nat,X0: nat,X1: fun_nat_nat] : ( hAPP_nat_nat(X1,X2) = hAPP_nat_nat(nat_case_nat(X0,X1),hAPP_nat_nat(suc,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_384])]) ).

tff(f5707,plain,
    ! [X2: nat,X0: nat,X1: fun_nat_nat] : ( hAPP_nat_nat(X1,X2) = hAPP_nat_nat(nat_case_nat(X0,X1),hAPP_nat_nat(suc,X2)) ),
    inference(cnf_transformation,[],[f2083]) ).

tff(f2083,plain,
    ! [X0: nat,X1: fun_nat_nat,X2: nat] : ( hAPP_nat_nat(X1,X2) = hAPP_nat_nat(nat_case_nat(X0,X1),hAPP_nat_nat(suc,X2)) ),
    inference(rectify,[],[f664]) ).

tff(f664,axiom,
    ! [X73: nat,X74: fun_nat_nat,X17: nat] : ( hAPP_nat_nat(nat_case_nat(X73,X74),hAPP_nat_nat(suc,X17)) = hAPP_nat_nat(X74,X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_663_nat__case__Suc) ).

tff(f9745,plain,
    spl250_383,
    inference(avatar_split_clause,[],[f5706,f9743]) ).

tff(f9743,plain,
    ( spl250_383
  <=> ! [X2: nat,X0: fun_bool_bool,X1: fun_nat_bool] : ( hAPP_nat_bool(cOMBB_bool_bool_nat(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_383])]) ).

tff(f5706,plain,
    ! [X2: nat,X0: fun_bool_bool,X1: fun_nat_bool] : ( hAPP_nat_bool(cOMBB_bool_bool_nat(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2082]) ).

tff(f2082,plain,
    ! [X0: fun_bool_bool,X1: fun_nat_bool,X2: nat] : ( hAPP_nat_bool(cOMBB_bool_bool_nat(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_nat_bool(X1,X2)) ),
    inference(rectify,[],[f1248]) ).

tff(f1248,axiom,
    ! [X156: fun_bool_bool,X157: fun_nat_bool,X158: nat] : ( hAPP_nat_bool(cOMBB_bool_bool_nat(X156,X157),X158) = hAPP_bool_bool(X156,hAPP_nat_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U) ).

tff(f9741,plain,
    spl250_382,
    inference(avatar_split_clause,[],[f5705,f9739]) ).

tff(f9739,plain,
    ( spl250_382
  <=> ! [X2: nat,X0: fun_int_bool,X1: fun_nat_int] : ( hAPP_nat_bool(cOMBB_int_bool_nat(X0,X1),X2) = hAPP_int_bool(X0,hAPP_nat_int(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_382])]) ).

tff(f5705,plain,
    ! [X2: nat,X0: fun_int_bool,X1: fun_nat_int] : ( hAPP_nat_bool(cOMBB_int_bool_nat(X0,X1),X2) = hAPP_int_bool(X0,hAPP_nat_int(X1,X2)) ),
    inference(cnf_transformation,[],[f2081]) ).

tff(f2081,plain,
    ! [X0: fun_int_bool,X1: fun_nat_int,X2: nat] : ( hAPP_nat_bool(cOMBB_int_bool_nat(X0,X1),X2) = hAPP_int_bool(X0,hAPP_nat_int(X1,X2)) ),
    inference(rectify,[],[f1243]) ).

tff(f1243,axiom,
    ! [X156: fun_int_bool,X157: fun_nat_int,X158: nat] : ( hAPP_nat_bool(cOMBB_int_bool_nat(X156,X157),X158) = hAPP_int_bool(X156,hAPP_nat_int(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__HOL__Obool_000tc__Nat__Onat_U) ).

tff(f9737,plain,
    spl250_381,
    inference(avatar_split_clause,[],[f5704,f9735]) ).

tff(f9735,plain,
    ( spl250_381
  <=> ! [X2: nat,X0: fun_fu425979586l_bool,X1: fun_nat_fun_nat_bool] : ( hAPP_nat_bool(cOMBB_955900739ol_nat(X0,X1),X2) = hAPP_f54304608l_bool(X0,hAPP_n1699378549t_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_381])]) ).

tff(f5704,plain,
    ! [X2: nat,X0: fun_fu425979586l_bool,X1: fun_nat_fun_nat_bool] : ( hAPP_nat_bool(cOMBB_955900739ol_nat(X0,X1),X2) = hAPP_f54304608l_bool(X0,hAPP_n1699378549t_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2080]) ).

tff(f2080,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_fun_nat_bool,X2: nat] : ( hAPP_nat_bool(cOMBB_955900739ol_nat(X0,X1),X2) = hAPP_f54304608l_bool(X0,hAPP_n1699378549t_bool(X1,X2)) ),
    inference(rectify,[],[f1266]) ).

tff(f1266,axiom,
    ! [X156: fun_fu425979586l_bool,X157: fun_nat_fun_nat_bool,X158: nat] : ( hAPP_nat_bool(cOMBB_955900739ol_nat(X156,X157),X158) = hAPP_f54304608l_bool(X156,hAPP_n1699378549t_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) ).

tff(f9733,plain,
    spl250_380,
    inference(avatar_split_clause,[],[f5703,f9731]) ).

tff(f9731,plain,
    ( spl250_380
  <=> ! [X2: nat,X0: fun_nat_fun_nat_bool,X1: fun_nat_nat] : ( hAPP_n1699378549t_bool(cOMBB_800536526ol_nat(X0,X1),X2) = hAPP_n1699378549t_bool(X0,hAPP_nat_nat(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_380])]) ).

tff(f5703,plain,
    ! [X2: nat,X0: fun_nat_fun_nat_bool,X1: fun_nat_nat] : ( hAPP_n1699378549t_bool(cOMBB_800536526ol_nat(X0,X1),X2) = hAPP_n1699378549t_bool(X0,hAPP_nat_nat(X1,X2)) ),
    inference(cnf_transformation,[],[f2079]) ).

tff(f2079,plain,
    ! [X0: fun_nat_fun_nat_bool,X1: fun_nat_nat,X2: nat] : ( hAPP_n1699378549t_bool(cOMBB_800536526ol_nat(X0,X1),X2) = hAPP_n1699378549t_bool(X0,hAPP_nat_nat(X1,X2)) ),
    inference(rectify,[],[f1263]) ).

tff(f1263,axiom,
    ! [X156: fun_nat_fun_nat_bool,X157: fun_nat_nat,X158: nat] : ( hAPP_n1699378549t_bool(cOMBB_800536526ol_nat(X156,X157),X158) = hAPP_n1699378549t_bool(X156,hAPP_nat_nat(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).

tff(f9729,plain,
    spl250_379,
    inference(avatar_split_clause,[],[f5702,f9727]) ).

tff(f9727,plain,
    ( spl250_379
  <=> ! [X2: int,X0: fun_bool_bool,X1: fun_int_bool] : ( hAPP_int_bool(cOMBB_bool_bool_int(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_int_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_379])]) ).

tff(f5702,plain,
    ! [X2: int,X0: fun_bool_bool,X1: fun_int_bool] : ( hAPP_int_bool(cOMBB_bool_bool_int(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_int_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2078]) ).

tff(f2078,plain,
    ! [X0: fun_bool_bool,X1: fun_int_bool,X2: int] : ( hAPP_int_bool(cOMBB_bool_bool_int(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_int_bool(X1,X2)) ),
    inference(rectify,[],[f1247]) ).

tff(f1247,axiom,
    ! [X156: fun_bool_bool,X157: fun_int_bool,X158: int] : ( hAPP_int_bool(cOMBB_bool_bool_int(X156,X157),X158) = hAPP_bool_bool(X156,hAPP_int_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Int__Oint_U) ).

tff(f9725,plain,
    spl250_378,
    inference(avatar_split_clause,[],[f5701,f9723]) ).

tff(f9723,plain,
    ( spl250_378
  <=> ! [X2: int,X0: fun_fu819804446l_bool,X1: fun_int_fun_int_bool] : ( hAPP_int_bool(cOMBB_1418110531ol_int(X0,X1),X2) = hAPP_f448129468l_bool(X0,hAPP_i1948725293t_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_378])]) ).

tff(f5701,plain,
    ! [X2: int,X0: fun_fu819804446l_bool,X1: fun_int_fun_int_bool] : ( hAPP_int_bool(cOMBB_1418110531ol_int(X0,X1),X2) = hAPP_f448129468l_bool(X0,hAPP_i1948725293t_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2077]) ).

tff(f2077,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_fun_int_bool,X2: int] : ( hAPP_int_bool(cOMBB_1418110531ol_int(X0,X1),X2) = hAPP_f448129468l_bool(X0,hAPP_i1948725293t_bool(X1,X2)) ),
    inference(rectify,[],[f1265]) ).

tff(f1265,axiom,
    ! [X156: fun_fu819804446l_bool,X157: fun_int_fun_int_bool,X158: int] : ( hAPP_int_bool(cOMBB_1418110531ol_int(X156,X157),X158) = hAPP_f448129468l_bool(X156,hAPP_i1948725293t_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obo) ).

tff(f9721,plain,
    spl250_377,
    inference(avatar_split_clause,[],[f5700,f9719]) ).

tff(f9719,plain,
    ( spl250_377
  <=> ! [X2: nat,X0: fun_na1436237685l_bool,X1: fun_nat_nat] : ( hAPP_n215258509l_bool(cOMBB_1146692694ol_nat(X0,X1),X2) = hAPP_n215258509l_bool(X0,hAPP_nat_nat(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_377])]) ).

tff(f5700,plain,
    ! [X2: nat,X0: fun_na1436237685l_bool,X1: fun_nat_nat] : ( hAPP_n215258509l_bool(cOMBB_1146692694ol_nat(X0,X1),X2) = hAPP_n215258509l_bool(X0,hAPP_nat_nat(X1,X2)) ),
    inference(cnf_transformation,[],[f2076]) ).

tff(f2076,plain,
    ! [X0: fun_na1436237685l_bool,X1: fun_nat_nat,X2: nat] : ( hAPP_n215258509l_bool(cOMBB_1146692694ol_nat(X0,X1),X2) = hAPP_n215258509l_bool(X0,hAPP_nat_nat(X1,X2)) ),
    inference(rectify,[],[f1282]) ).

tff(f1282,axiom,
    ! [X156: fun_na1436237685l_bool,X157: fun_nat_nat,X158: nat] : ( hAPP_n215258509l_bool(cOMBB_1146692694ol_nat(X156,X157),X158) = hAPP_n215258509l_bool(X156,hAPP_nat_nat(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO) ).

tff(f9717,plain,
    spl250_376,
    inference(avatar_split_clause,[],[f5699,f9715]) ).

tff(f9715,plain,
    ( spl250_376
  <=> ! [X2: nat,X0: fun_fu1217155507l_bool,X1: fun_nat_fun_nat_bool] : ( hAPP_n215258509l_bool(cOMBB_2026977092ol_nat(X0,X1),X2) = hAPP_f103356543l_bool(X0,hAPP_n1699378549t_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_376])]) ).

tff(f5699,plain,
    ! [X2: nat,X0: fun_fu1217155507l_bool,X1: fun_nat_fun_nat_bool] : ( hAPP_n215258509l_bool(cOMBB_2026977092ol_nat(X0,X1),X2) = hAPP_f103356543l_bool(X0,hAPP_n1699378549t_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2075]) ).

tff(f2075,plain,
    ! [X0: fun_fu1217155507l_bool,X1: fun_nat_fun_nat_bool,X2: nat] : ( hAPP_n215258509l_bool(cOMBB_2026977092ol_nat(X0,X1),X2) = hAPP_f103356543l_bool(X0,hAPP_n1699378549t_bool(X1,X2)) ),
    inference(rectify,[],[f1296]) ).

tff(f1296,axiom,
    ! [X156: fun_fu1217155507l_bool,X157: fun_nat_fun_nat_bool,X158: nat] : ( hAPP_n215258509l_bool(cOMBB_2026977092ol_nat(X156,X157),X158) = hAPP_f103356543l_bool(X156,hAPP_n1699378549t_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__070) ).

tff(f9713,plain,
    spl250_375,
    inference(avatar_split_clause,[],[f5698,f9711]) ).

tff(f9711,plain,
    ( spl250_375
  <=> ! [X2: int,X0: fun_fu1151772339l_bool,X1: fun_int_fun_int_bool] : ( hAPP_i2112223885l_bool(cOMBB_1761098400ol_int(X0,X1),X2) = hAPP_f284875647l_bool(X0,hAPP_i1948725293t_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_375])]) ).

tff(f5698,plain,
    ! [X2: int,X0: fun_fu1151772339l_bool,X1: fun_int_fun_int_bool] : ( hAPP_i2112223885l_bool(cOMBB_1761098400ol_int(X0,X1),X2) = hAPP_f284875647l_bool(X0,hAPP_i1948725293t_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2074]) ).

tff(f2074,plain,
    ! [X0: fun_fu1151772339l_bool,X1: fun_int_fun_int_bool,X2: int] : ( hAPP_i2112223885l_bool(cOMBB_1761098400ol_int(X0,X1),X2) = hAPP_f284875647l_bool(X0,hAPP_i1948725293t_bool(X1,X2)) ),
    inference(rectify,[],[f1293]) ).

tff(f1293,axiom,
    ! [X156: fun_fu1151772339l_bool,X157: fun_int_fun_int_bool,X158: int] : ( hAPP_i2112223885l_bool(cOMBB_1761098400ol_int(X156,X157),X158) = hAPP_f284875647l_bool(X156,hAPP_i1948725293t_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).

tff(f9709,plain,
    spl250_374,
    inference(avatar_split_clause,[],[f5697,f9707]) ).

tff(f9707,plain,
    ( spl250_374
  <=> ! [X2: x_a,X0: fun_bool_bool,X1: fun_a_bool] : ( hAPP_a_bool(cOMBB_bool_bool_a(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_a_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_374])]) ).

tff(f5697,plain,
    ! [X2: x_a,X0: fun_bool_bool,X1: fun_a_bool] : ( hAPP_a_bool(cOMBB_bool_bool_a(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_a_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2073]) ).

tff(f2073,plain,
    ! [X0: fun_bool_bool,X1: fun_a_bool,X2: x_a] : ( hAPP_a_bool(cOMBB_bool_bool_a(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_a_bool(X1,X2)) ),
    inference(rectify,[],[f1234]) ).

tff(f1234,axiom,
    ! [X156: fun_bool_bool,X157: fun_a_bool,X158: x_a] : ( hAPP_a_bool(cOMBB_bool_bool_a(X156,X157),X158) = hAPP_bool_bool(X156,hAPP_a_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U) ).

tff(f9705,plain,
    spl250_373,
    inference(avatar_split_clause,[],[f5696,f9703]) ).

tff(f9703,plain,
    ( spl250_373
  <=> ! [X2: x_a,X0: fun_fun_a_bool_bool,X1: fun_a_fun_a_bool] : ( hAPP_a_bool(cOMBB_1273333599bool_a(X0,X1),X2) = hAPP_fun_a_bool_bool(X0,hAPP_a_fun_a_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_373])]) ).

tff(f5696,plain,
    ! [X2: x_a,X0: fun_fun_a_bool_bool,X1: fun_a_fun_a_bool] : ( hAPP_a_bool(cOMBB_1273333599bool_a(X0,X1),X2) = hAPP_fun_a_bool_bool(X0,hAPP_a_fun_a_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2072]) ).

tff(f2072,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_fun_a_bool,X2: x_a] : ( hAPP_a_bool(cOMBB_1273333599bool_a(X0,X1),X2) = hAPP_fun_a_bool_bool(X0,hAPP_a_fun_a_bool(X1,X2)) ),
    inference(rectify,[],[f1255]) ).

tff(f1255,axiom,
    ! [X156: fun_fun_a_bool_bool,X157: fun_a_fun_a_bool,X158: x_a] : ( hAPP_a_bool(cOMBB_1273333599bool_a(X156,X157),X158) = hAPP_fun_a_bool_bool(X156,hAPP_a_fun_a_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t__) ).

tff(f9701,plain,
    spl250_372,
    inference(avatar_split_clause,[],[f5695,f9699]) ).

tff(f9699,plain,
    ( spl250_372
  <=> ! [X2: pname,X0: fun_bool_bool,X1: fun_pname_bool] : ( hAPP_pname_bool(cOMBB_647938656_pname(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_pname_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_372])]) ).

tff(f5695,plain,
    ! [X2: pname,X0: fun_bool_bool,X1: fun_pname_bool] : ( hAPP_pname_bool(cOMBB_647938656_pname(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_pname_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2071]) ).

tff(f2071,plain,
    ! [X0: fun_bool_bool,X1: fun_pname_bool,X2: pname] : ( hAPP_pname_bool(cOMBB_647938656_pname(X0,X1),X2) = hAPP_bool_bool(X0,hAPP_pname_bool(X1,X2)) ),
    inference(rectify,[],[f1251]) ).

tff(f1251,axiom,
    ! [X156: fun_bool_bool,X157: fun_pname_bool,X158: pname] : ( hAPP_pname_bool(cOMBB_647938656_pname(X156,X157),X158) = hAPP_bool_bool(X156,hAPP_pname_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U) ).

tff(f9697,plain,
    spl250_371,
    inference(avatar_split_clause,[],[f5694,f9695]) ).

tff(f5694,plain,
    ! [X2: nat,X0: fun_int_fun_int_bool,X1: fun_nat_int] : ( hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(X0,X1),X2) = hAPP_i1948725293t_bool(X0,hAPP_nat_int(X1,X2)) ),
    inference(cnf_transformation,[],[f2070]) ).

tff(f2070,plain,
    ! [X0: fun_int_fun_int_bool,X1: fun_nat_int,X2: nat] : ( hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(X0,X1),X2) = hAPP_i1948725293t_bool(X0,hAPP_nat_int(X1,X2)) ),
    inference(rectify,[],[f1262]) ).

tff(f1262,axiom,
    ! [X156: fun_int_fun_int_bool,X157: fun_nat_int,X158: nat] : ( hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(X156,X157),X158) = hAPP_i1948725293t_bool(X156,hAPP_nat_int(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_) ).

tff(f9693,plain,
    spl250_370,
    inference(avatar_split_clause,[],[f5693,f9691]) ).

tff(f9691,plain,
    ( spl250_370
  <=> ! [X2: int,X0: fun_a_fun_a_bool,X1: fun_int_a] : ( hAPP_int_fun_a_bool(cOMBB_375279840ol_int(X0,X1),X2) = hAPP_a_fun_a_bool(X0,hAPP_int_a(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_370])]) ).

tff(f5693,plain,
    ! [X2: int,X0: fun_a_fun_a_bool,X1: fun_int_a] : ( hAPP_int_fun_a_bool(cOMBB_375279840ol_int(X0,X1),X2) = hAPP_a_fun_a_bool(X0,hAPP_int_a(X1,X2)) ),
    inference(cnf_transformation,[],[f2069]) ).

tff(f2069,plain,
    ! [X0: fun_a_fun_a_bool,X1: fun_int_a,X2: int] : ( hAPP_int_fun_a_bool(cOMBB_375279840ol_int(X0,X1),X2) = hAPP_a_fun_a_bool(X0,hAPP_int_a(X1,X2)) ),
    inference(rectify,[],[f1254]) ).

tff(f1254,axiom,
    ! [X156: fun_a_fun_a_bool,X157: fun_int_a,X158: int] : ( hAPP_int_fun_a_bool(cOMBB_375279840ol_int(X156,X157),X158) = hAPP_a_fun_a_bool(X156,hAPP_int_a(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Int__Oint) ).

tff(f9689,plain,
    spl250_369,
    inference(avatar_split_clause,[],[f5692,f9687]) ).

tff(f5692,plain,
    ! [X2: nat,X0: fun_bo1549164019l_bool,X1: fun_nat_bool] : ( hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_nat_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2068]) ).

tff(f2068,plain,
    ! [X0: fun_bo1549164019l_bool,X1: fun_nat_bool,X2: nat] : ( hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_nat_bool(X1,X2)) ),
    inference(rectify,[],[f1272]) ).

tff(f1272,axiom,
    ! [X156: fun_bo1549164019l_bool,X157: fun_nat_bool,X158: nat] : ( hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X156,X157),X158) = hAPP_b589554111l_bool(X156,hAPP_nat_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_060) ).

tff(f9685,plain,
    spl250_368,
    inference(avatar_split_clause,[],[f5691,f9683]) ).

tff(f5691,plain,
    ! [X2: int,X0: fun_bo1549164019l_bool,X1: fun_int_bool] : ( hAPP_i68813070l_bool(cOMBB_1652995168ol_int(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_int_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2067]) ).

tff(f2067,plain,
    ! [X0: fun_bo1549164019l_bool,X1: fun_int_bool,X2: int] : ( hAPP_i68813070l_bool(cOMBB_1652995168ol_int(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_int_bool(X1,X2)) ),
    inference(rectify,[],[f1271]) ).

tff(f1271,axiom,
    ! [X156: fun_bo1549164019l_bool,X157: fun_int_bool,X158: int] : ( hAPP_i68813070l_bool(cOMBB_1652995168ol_int(X156,X157),X158) = hAPP_b589554111l_bool(X156,hAPP_int_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_059) ).

tff(f9680,plain,
    spl250_367,
    inference(avatar_split_clause,[],[f5690,f9678]) ).

tff(f5690,plain,
    ! [X2: x_a,X0: fun_bo1549164019l_bool,X1: fun_a_bool] : ( hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_a_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2066]) ).

tff(f2066,plain,
    ! [X0: fun_bo1549164019l_bool,X1: fun_a_bool,X2: x_a] : ( hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_a_bool(X1,X2)) ),
    inference(rectify,[],[f1260]) ).

tff(f1260,axiom,
    ! [X156: fun_bo1549164019l_bool,X157: fun_a_bool,X158: x_a] : ( hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X156,X157),X158) = hAPP_b589554111l_bool(X156,hAPP_a_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).

tff(f9676,plain,
    spl250_366,
    inference(avatar_split_clause,[],[f5689,f9674]) ).

tff(f9674,plain,
    ( spl250_366
  <=> ! [X2: pname,X0: fun_bo1549164019l_bool,X1: fun_pname_bool] : ( hAPP_p393069232l_bool(cOMBB_675860798_pname(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_pname_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_366])]) ).

tff(f5689,plain,
    ! [X2: pname,X0: fun_bo1549164019l_bool,X1: fun_pname_bool] : ( hAPP_p393069232l_bool(cOMBB_675860798_pname(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_pname_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2065]) ).

tff(f2065,plain,
    ! [X0: fun_bo1549164019l_bool,X1: fun_pname_bool,X2: pname] : ( hAPP_p393069232l_bool(cOMBB_675860798_pname(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_pname_bool(X1,X2)) ),
    inference(rectify,[],[f1277]) ).

tff(f1277,axiom,
    ! [X156: fun_bo1549164019l_bool,X157: fun_pname_bool,X158: pname] : ( hAPP_p393069232l_bool(cOMBB_675860798_pname(X156,X157),X158) = hAPP_b589554111l_bool(X156,hAPP_pname_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_061) ).

tff(f9672,plain,
    spl250_365,
    inference(avatar_split_clause,[],[f5688,f9670]) ).

tff(f9670,plain,
    ( spl250_365
  <=> ! [X2: fun_nat_bool,X0: fun_bo1549164019l_bool,X1: fun_fu425979586l_bool] : ( hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f54304608l_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_365])]) ).

tff(f5688,plain,
    ! [X2: fun_nat_bool,X0: fun_bo1549164019l_bool,X1: fun_fu425979586l_bool] : ( hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f54304608l_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2064]) ).

tff(f2064,plain,
    ! [X0: fun_bo1549164019l_bool,X1: fun_fu425979586l_bool,X2: fun_nat_bool] : ( hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f54304608l_bool(X1,X2)) ),
    inference(rectify,[],[f1288]) ).

tff(f1288,axiom,
    ! [X156: fun_bo1549164019l_bool,X157: fun_fu425979586l_bool,X158: fun_nat_bool] : ( hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X156,X157),X158) = hAPP_b589554111l_bool(X156,hAPP_f54304608l_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_066) ).

tff(f9668,plain,
    spl250_364,
    inference(avatar_split_clause,[],[f5687,f9666]) ).

tff(f9666,plain,
    ( spl250_364
  <=> ! [X2: fun_int_bool,X0: fun_bo1549164019l_bool,X1: fun_fu819804446l_bool] : ( hAPP_f1721100032l_bool(cOMBB_1974511970t_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f448129468l_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_364])]) ).

tff(f5687,plain,
    ! [X2: fun_int_bool,X0: fun_bo1549164019l_bool,X1: fun_fu819804446l_bool] : ( hAPP_f1721100032l_bool(cOMBB_1974511970t_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f448129468l_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2063]) ).

tff(f2063,plain,
    ! [X0: fun_bo1549164019l_bool,X1: fun_fu819804446l_bool,X2: fun_int_bool] : ( hAPP_f1721100032l_bool(cOMBB_1974511970t_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f448129468l_bool(X1,X2)) ),
    inference(rectify,[],[f1287]) ).

tff(f1287,axiom,
    ! [X156: fun_bo1549164019l_bool,X157: fun_fu819804446l_bool,X158: fun_int_bool] : ( hAPP_f1721100032l_bool(cOMBB_1974511970t_bool(X156,X157),X158) = hAPP_b589554111l_bool(X156,hAPP_f448129468l_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_065) ).

tff(f9664,plain,
    spl250_363,
    inference(avatar_split_clause,[],[f5686,f9662]) ).

tff(f5686,plain,
    ! [X2: fun_a_bool,X0: fun_bo1549164019l_bool,X1: fun_fun_a_bool_bool] : ( hAPP_f198738859l_bool(cOMBB_338059395a_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_fun_a_bool_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2062]) ).

tff(f2062,plain,
    ! [X0: fun_bo1549164019l_bool,X1: fun_fun_a_bool_bool,X2: fun_a_bool] : ( hAPP_f198738859l_bool(cOMBB_338059395a_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_fun_a_bool_bool(X1,X2)) ),
    inference(rectify,[],[f1281]) ).

tff(f1281,axiom,
    ! [X156: fun_bo1549164019l_bool,X157: fun_fun_a_bool_bool,X158: fun_a_bool] : ( hAPP_f198738859l_bool(cOMBB_338059395a_bool(X156,X157),X158) = hAPP_b589554111l_bool(X156,hAPP_fun_a_bool_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_062) ).

tff(f9660,plain,
    spl250_362,
    inference(avatar_split_clause,[],[f5685,f9658]) ).

tff(f9658,plain,
    ( spl250_362
  <=> ! [X2: fun_pname_bool,X0: fun_bo1549164019l_bool,X1: fun_fu1430349052l_bool] : ( hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f1664156314l_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_362])]) ).

tff(f5685,plain,
    ! [X2: fun_pname_bool,X0: fun_bo1549164019l_bool,X1: fun_fu1430349052l_bool] : ( hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f1664156314l_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2061]) ).

tff(f2061,plain,
    ! [X0: fun_bo1549164019l_bool,X1: fun_fu1430349052l_bool,X2: fun_pname_bool] : ( hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X0,X1),X2) = hAPP_b589554111l_bool(X0,hAPP_f1664156314l_bool(X1,X2)) ),
    inference(rectify,[],[f1289]) ).

tff(f1289,axiom,
    ! [X156: fun_bo1549164019l_bool,X157: fun_fu1430349052l_bool,X158: fun_pname_bool] : ( hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X156,X157),X158) = hAPP_b589554111l_bool(X156,hAPP_f1664156314l_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_067) ).

tff(f9656,plain,
    spl250_361,
    inference(avatar_split_clause,[],[f5684,f9654]) ).

tff(f9654,plain,
    ( spl250_361
  <=> ! [X2: nat,X0: fun_fu1471507361l_bool,X1: fun_nat_fun_a_bool] : ( hAPP_n1414589940l_bool(cOMBB_1823939024ol_nat(X0,X1),X2) = hAPP_f1631501043l_bool(X0,hAPP_nat_fun_a_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_361])]) ).

tff(f5684,plain,
    ! [X2: nat,X0: fun_fu1471507361l_bool,X1: fun_nat_fun_a_bool] : ( hAPP_n1414589940l_bool(cOMBB_1823939024ol_nat(X0,X1),X2) = hAPP_f1631501043l_bool(X0,hAPP_nat_fun_a_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2060]) ).

tff(f2060,plain,
    ! [X0: fun_fu1471507361l_bool,X1: fun_nat_fun_a_bool,X2: nat] : ( hAPP_n1414589940l_bool(cOMBB_1823939024ol_nat(X0,X1),X2) = hAPP_f1631501043l_bool(X0,hAPP_nat_fun_a_bool(X1,X2)) ),
    inference(rectify,[],[f1292]) ).

tff(f1292,axiom,
    ! [X156: fun_fu1471507361l_bool,X157: fun_nat_fun_a_bool,X158: nat] : ( hAPP_n1414589940l_bool(cOMBB_1823939024ol_nat(X156,X157),X158) = hAPP_f1631501043l_bool(X156,hAPP_nat_fun_a_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___068) ).

tff(f9652,plain,
    spl250_360,
    inference(avatar_split_clause,[],[f5683,f9650]) ).

tff(f9650,plain,
    ( spl250_360
  <=> ! [X2: int,X0: fun_fu1471507361l_bool,X1: fun_int_fun_a_bool] : ( hAPP_i888906320l_bool(cOMBB_313729068ol_int(X0,X1),X2) = hAPP_f1631501043l_bool(X0,hAPP_int_fun_a_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_360])]) ).

tff(f5683,plain,
    ! [X2: int,X0: fun_fu1471507361l_bool,X1: fun_int_fun_a_bool] : ( hAPP_i888906320l_bool(cOMBB_313729068ol_int(X0,X1),X2) = hAPP_f1631501043l_bool(X0,hAPP_int_fun_a_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2059]) ).

tff(f2059,plain,
    ! [X0: fun_fu1471507361l_bool,X1: fun_int_fun_a_bool,X2: int] : ( hAPP_i888906320l_bool(cOMBB_313729068ol_int(X0,X1),X2) = hAPP_f1631501043l_bool(X0,hAPP_int_fun_a_bool(X1,X2)) ),
    inference(rectify,[],[f1291]) ).

tff(f1291,axiom,
    ! [X156: fun_fu1471507361l_bool,X157: fun_int_fun_a_bool,X158: int] : ( hAPP_i888906320l_bool(cOMBB_313729068ol_int(X156,X157),X158) = hAPP_f1631501043l_bool(X156,hAPP_int_fun_a_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__) ).

tff(f9648,plain,
    spl250_359,
    inference(avatar_split_clause,[],[f5682,f9646]) ).

tff(f9646,plain,
    ( spl250_359
  <=> ! [X2: nat,X0: fun_fu1151772339l_bool,X1: fun_nat_fun_int_bool] : ( hAPP_n609083369l_bool(cOMBB_1123824708ol_nat(X0,X1),X2) = hAPP_f284875647l_bool(X0,hAPP_n1082236369t_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_359])]) ).

tff(f5682,plain,
    ! [X2: nat,X0: fun_fu1151772339l_bool,X1: fun_nat_fun_int_bool] : ( hAPP_n609083369l_bool(cOMBB_1123824708ol_nat(X0,X1),X2) = hAPP_f284875647l_bool(X0,hAPP_n1082236369t_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2058]) ).

tff(f2058,plain,
    ! [X0: fun_fu1151772339l_bool,X1: fun_nat_fun_int_bool,X2: nat] : ( hAPP_n609083369l_bool(cOMBB_1123824708ol_nat(X0,X1),X2) = hAPP_f284875647l_bool(X0,hAPP_n1082236369t_bool(X1,X2)) ),
    inference(rectify,[],[f1294]) ).

tff(f1294,axiom,
    ! [X156: fun_fu1151772339l_bool,X157: fun_nat_fun_int_bool,X158: nat] : ( hAPP_n609083369l_bool(cOMBB_1123824708ol_nat(X156,X157),X158) = hAPP_f284875647l_bool(X156,hAPP_n1082236369t_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc__069) ).

tff(f9644,plain,
    spl250_358,
    inference(avatar_split_clause,[],[f5681,f9642]) ).

tff(f9642,plain,
    ( spl250_358
  <=> ! [X2: int,X0: fun_fu1217155507l_bool,X1: fun_int_fun_nat_bool] : ( hAPP_i1718399025l_bool(cOMBB_516767136ol_int(X0,X1),X2) = hAPP_f103356543l_bool(X0,hAPP_i418383825t_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_358])]) ).

tff(f5681,plain,
    ! [X2: int,X0: fun_fu1217155507l_bool,X1: fun_int_fun_nat_bool] : ( hAPP_i1718399025l_bool(cOMBB_516767136ol_int(X0,X1),X2) = hAPP_f103356543l_bool(X0,hAPP_i418383825t_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2057]) ).

tff(f2057,plain,
    ! [X0: fun_fu1217155507l_bool,X1: fun_int_fun_nat_bool,X2: int] : ( hAPP_i1718399025l_bool(cOMBB_516767136ol_int(X0,X1),X2) = hAPP_f103356543l_bool(X0,hAPP_i418383825t_bool(X1,X2)) ),
    inference(rectify,[],[f1295]) ).

tff(f1295,axiom,
    ! [X156: fun_fu1217155507l_bool,X157: fun_int_fun_nat_bool,X158: int] : ( hAPP_i1718399025l_bool(cOMBB_516767136ol_int(X156,X157),X158) = hAPP_f103356543l_bool(X156,hAPP_i418383825t_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).

tff(f9640,plain,
    ( spl250_357
    | ~ spl250_82
    | ~ spl250_307 ),
    inference(avatar_split_clause,[],[f9453,f9056,f7675,f9638]) ).

tff(f9638,plain,
    ( spl250_357
  <=> ! [X0: nat] : ~ sP17(X0,X0,fequal_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_357])]) ).

tff(f7675,plain,
    ( spl250_82
  <=> ! [X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_82])]) ).

tff(f9453,plain,
    ( ! [X0: nat] : ~ sP17(X0,X0,fequal_nat)
    | ~ spl250_82
    | ~ spl250_307 ),
    inference(resolution,[],[f9057,f7676]) ).

tff(f7676,plain,
    ( ! [X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X1))
    | ~ spl250_82 ),
    inference(avatar_component_clause,[],[f7675]) ).

tff(f9636,plain,
    spl250_356,
    inference(avatar_split_clause,[],[f5680,f9634]) ).

tff(f9634,plain,
    ( spl250_356
  <=> ! [X2: nat,X0: fun_fu802393907l_bool,X1: fun_na936072029e_bool] : ( hAPP_n850744903l_bool(cOMBB_2117322052ol_nat(X0,X1),X2) = hAPP_f434788991l_bool(X0,hAPP_n1025906991e_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_356])]) ).

tff(f5680,plain,
    ! [X2: nat,X0: fun_fu802393907l_bool,X1: fun_na936072029e_bool] : ( hAPP_n850744903l_bool(cOMBB_2117322052ol_nat(X0,X1),X2) = hAPP_f434788991l_bool(X0,hAPP_n1025906991e_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2056]) ).

tff(f2056,plain,
    ! [X0: fun_fu802393907l_bool,X1: fun_na936072029e_bool,X2: nat] : ( hAPP_n850744903l_bool(cOMBB_2117322052ol_nat(X0,X1),X2) = hAPP_f434788991l_bool(X0,hAPP_n1025906991e_bool(X1,X2)) ),
    inference(rectify,[],[f1298]) ).

tff(f1298,axiom,
    ! [X156: fun_fu802393907l_bool,X157: fun_na936072029e_bool,X158: nat] : ( hAPP_n850744903l_bool(cOMBB_2117322052ol_nat(X156,X157),X158) = hAPP_f434788991l_bool(X156,hAPP_n1025906991e_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_071) ).

tff(f9632,plain,
    spl250_355,
    inference(avatar_split_clause,[],[f5679,f9630]) ).

tff(f9630,plain,
    ( spl250_355
  <=> ! [X2: int,X0: fun_fu802393907l_bool,X1: fun_in2065004473e_bool] : ( hAPP_i1587699435l_bool(cOMBB_607112096ol_int(X0,X1),X2) = hAPP_f434788991l_bool(X0,hAPP_i7355787e_bool(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_355])]) ).

tff(f5679,plain,
    ! [X2: int,X0: fun_fu802393907l_bool,X1: fun_in2065004473e_bool] : ( hAPP_i1587699435l_bool(cOMBB_607112096ol_int(X0,X1),X2) = hAPP_f434788991l_bool(X0,hAPP_i7355787e_bool(X1,X2)) ),
    inference(cnf_transformation,[],[f2055]) ).

tff(f2055,plain,
    ! [X0: fun_fu802393907l_bool,X1: fun_in2065004473e_bool,X2: int] : ( hAPP_i1587699435l_bool(cOMBB_607112096ol_int(X0,X1),X2) = hAPP_f434788991l_bool(X0,hAPP_i7355787e_bool(X1,X2)) ),
    inference(rectify,[],[f1297]) ).

tff(f1297,axiom,
    ! [X156: fun_fu802393907l_bool,X157: fun_in2065004473e_bool,X158: int] : ( hAPP_i1587699435l_bool(cOMBB_607112096ol_int(X156,X157),X158) = hAPP_f434788991l_bool(X156,hAPP_i7355787e_bool(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).

tff(f9628,plain,
    spl250_354,
    inference(avatar_split_clause,[],[f5678,f9626]) ).

tff(f9626,plain,
    ( spl250_354
  <=> ! [X2: pname,X0: fun_a_fun_a_bool,X1: fun_pname_a] : ( hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X0,X1),X2) = hAPP_a_fun_a_bool(X0,hAPP_pname_a(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_354])]) ).

tff(f5678,plain,
    ! [X2: pname,X0: fun_a_fun_a_bool,X1: fun_pname_a] : ( hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X0,X1),X2) = hAPP_a_fun_a_bool(X0,hAPP_pname_a(X1,X2)) ),
    inference(cnf_transformation,[],[f2054]) ).

tff(f2054,plain,
    ! [X0: fun_a_fun_a_bool,X1: fun_pname_a,X2: pname] : ( hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X0,X1),X2) = hAPP_a_fun_a_bool(X0,hAPP_pname_a(X1,X2)) ),
    inference(rectify,[],[f1257]) ).

tff(f1257,axiom,
    ! [X156: fun_a_fun_a_bool,X157: fun_pname_a,X158: pname] : ( hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X156,X157),X158) = hAPP_a_fun_a_bool(X156,hAPP_pname_a(X157,X158)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna) ).

tff(f9624,plain,
    spl250_353,
    inference(avatar_split_clause,[],[f5310,f9622]) ).

tff(f5310,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(X1),X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ),
    inference(cnf_transformation,[],[f2937]) ).

tff(f2937,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(X1),X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1)) ),
    inference(ennf_transformation,[],[f1]) ).

tff(f1,axiom,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X1))
     => hBOOL(hAPP_fun_a_bool_bool(p(X1),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).

tff(f9620,plain,
    spl250_352,
    inference(avatar_split_clause,[],[f4906,f9618]) ).

tff(f9618,plain,
    ( spl250_352
  <=> ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_352])]) ).

tff(f4906,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X0) = X1 ),
    inference(cnf_transformation,[],[f1554]) ).

tff(f1554,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X0) = X1 ),
    inference(rectify,[],[f835]) ).

tff(f835,axiom,
    ! [X11: nat,X12: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X11),X12)),X11) = X12 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_834_diff__add__inverse) ).

tff(f9616,plain,
    spl250_351,
    inference(avatar_split_clause,[],[f4905,f9614]) ).

tff(f9614,plain,
    ( spl250_351
  <=> ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_351])]) ).

tff(f4905,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X1) = X0 ),
    inference(cnf_transformation,[],[f1553]) ).

tff(f1553,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X1) = X0 ),
    inference(rectify,[],[f834]) ).

tff(f834,axiom,
    ! [X12: nat,X11: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X12),X11)),X11) = X12 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_833_diff__add__inverse2) ).

tff(f9612,plain,
    spl250_350,
    inference(avatar_split_clause,[],[f4904,f9610]) ).

tff(f9610,plain,
    ( spl250_350
  <=> ! [X0: int,X1: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_350])]) ).

tff(f4904,plain,
    ! [X0: int,X1: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),X1) = X0 ),
    inference(cnf_transformation,[],[f1552]) ).

tff(f1552,plain,
    ! [X0: int,X1: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),X1)),X1) = X0 ),
    inference(rectify,[],[f818]) ).

tff(f818,axiom,
    ! [X112: int,X113: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X112),X113)),X113) = X112 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_817_diff__add__cancel) ).

tff(f9608,plain,
    spl250_349,
    inference(avatar_split_clause,[],[f4903,f9606]) ).

tff(f4903,plain,
    ! [X0: int,X1: int] : ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),X1) = X0 ),
    inference(cnf_transformation,[],[f1551]) ).

tff(f1551,plain,
    ! [X0: int,X1: int] : ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1)),X1) = X0 ),
    inference(rectify,[],[f819]) ).

tff(f819,axiom,
    ! [X114: int,X115: int] : ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X114),X115)),X115) = X114 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_818_add__diff__cancel) ).

tff(f9604,plain,
    spl250_348,
    inference(avatar_split_clause,[],[f4902,f9602]) ).

tff(f9602,plain,
    ( spl250_348
  <=> ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_348])]) ).

tff(f4902,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0) ),
    inference(cnf_transformation,[],[f1550]) ).

tff(f1550,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0) ),
    inference(rectify,[],[f799]) ).

tff(f799,axiom,
    ! [X12: nat,X11: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X12),X11) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X11),X12) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_798_nat__add__commute) ).

tff(f9600,plain,
    spl250_347,
    inference(avatar_split_clause,[],[f4901,f9598]) ).

tff(f9598,plain,
    ( spl250_347
  <=> ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_347])]) ).

tff(f4901,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0) ),
    inference(cnf_transformation,[],[f1549]) ).

tff(f1549,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X0) ),
    inference(rectify,[],[f1017]) ).

tff(f1017,axiom,
    ! [X12: nat,X11: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X12),X11) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X11),X12) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1016_nat__mult__commute) ).

tff(f9596,plain,
    ( spl250_346
    | ~ spl250_74
    | ~ spl250_307 ),
    inference(avatar_split_clause,[],[f9451,f9056,f7643,f9594]) ).

tff(f9594,plain,
    ( spl250_346
  <=> ! [X0: nat] : ~ sP17(X0,zero_zero_nat,ord_less_eq_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_346])]) ).

tff(f9451,plain,
    ( ! [X0: nat] : ~ sP17(X0,zero_zero_nat,ord_less_eq_nat)
    | ~ spl250_74
    | ~ spl250_307 ),
    inference(resolution,[],[f9057,f7644]) ).

tff(f9592,plain,
    spl250_345,
    inference(avatar_split_clause,[],[f4900,f9590]) ).

tff(f9588,plain,
    spl250_344,
    inference(avatar_split_clause,[],[f4899,f9586]) ).

tff(f9586,plain,
    ( spl250_344
  <=> ! [X0: int,X1: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_344])]) ).

tff(f4899,plain,
    ! [X0: int,X1: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0) ),
    inference(cnf_transformation,[],[f1547]) ).

tff(f1547,plain,
    ! [X0: int,X1: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X0) ),
    inference(rectify,[],[f1022]) ).

tff(f1022,axiom,
    ! [X95: int,X132: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X95),X132) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X132),X95) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1021_zmult__commute) ).

tff(f9584,plain,
    spl250_343,
    inference(avatar_split_clause,[],[f4898,f9582]) ).

tff(f9582,plain,
    ( spl250_343
  <=> ! [X0: nat,X1: nat] : ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_343])]) ).

tff(f4898,plain,
    ! [X0: nat,X1: nat] : ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f1546]) ).

tff(f1546,plain,
    ! [X0: nat,X1: nat] : ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)) ),
    inference(rectify,[],[f955]) ).

tff(f955,axiom,
    ! [X11: nat,X12: nat] : ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X11),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X11),X12)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_954_diff__add__0) ).

tff(f9580,plain,
    spl250_342,
    inference(avatar_split_clause,[],[f4868,f9578]) ).

tff(f9578,plain,
    ( spl250_342
  <=> ! [X2: nat,X0: fun_int_bool] :
        ( hBOOL(hAPP_int_bool(X0,sK73(X0)))
        | ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_342])]) ).

tff(f4868,plain,
    ! [X2: nat,X0: fun_int_bool] :
      ( hBOOL(hAPP_int_bool(X0,sK73(X0)))
      | ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
    inference(cnf_transformation,[],[f3902]) ).

tff(f9576,plain,
    spl250_341,
    inference(avatar_split_clause,[],[f4856,f9574]) ).

tff(f9574,plain,
    ( spl250_341
  <=> ! [X0: fun_int_bool,X3: nat] :
        ( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
        | ~ hBOOL(hAPP_int_bool(X0,sK68(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_341])]) ).

tff(f4856,plain,
    ! [X3: nat,X0: fun_int_bool] :
      ( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
      | ~ hBOOL(hAPP_int_bool(X0,sK68(X0))) ),
    inference(cnf_transformation,[],[f3881]) ).

tff(f9572,plain,
    spl250_340,
    inference(avatar_split_clause,[],[f4745,f9570]) ).

tff(f9570,plain,
    ( spl250_340
  <=> ! [X0: fun_a_bool] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK42(X0)),sK43(X0)))
        | ( bot_bot_fun_a_bool = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_340])]) ).

tff(f4745,plain,
    ! [X0: fun_a_bool] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK42(X0)),sK43(X0)))
      | ( bot_bot_fun_a_bool = X0 ) ),
    inference(cnf_transformation,[],[f3770]) ).

tff(f9568,plain,
    spl250_339,
    inference(avatar_split_clause,[],[f4742,f9566]) ).

tff(f9566,plain,
    ( spl250_339
  <=> ! [X0: fun_int_bool] :
        ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK40(X0)),sK41(X0)))
        | ( bot_bot_fun_int_bool = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_339])]) ).

tff(f4742,plain,
    ! [X0: fun_int_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK40(X0)),sK41(X0)))
      | ( bot_bot_fun_int_bool = X0 ) ),
    inference(cnf_transformation,[],[f3766]) ).

tff(f9564,plain,
    spl250_338,
    inference(avatar_split_clause,[],[f4739,f9562]) ).

tff(f9562,plain,
    ( spl250_338
  <=> ! [X0: fun_nat_bool] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK38(X0)),sK39(X0)))
        | ( bot_bot_fun_nat_bool = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_338])]) ).

tff(f4739,plain,
    ! [X0: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK38(X0)),sK39(X0)))
      | ( bot_bot_fun_nat_bool = X0 ) ),
    inference(cnf_transformation,[],[f3762]) ).

tff(f9560,plain,
    spl250_337,
    inference(avatar_split_clause,[],[f4736,f9558]) ).

tff(f9558,plain,
    ( spl250_337
  <=> ! [X0: fun_pname_bool] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK36(X0)),sK37(X0)))
        | ( bot_bo844097828e_bool = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_337])]) ).

tff(f4736,plain,
    ! [X0: fun_pname_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK36(X0)),sK37(X0)))
      | ( bot_bo844097828e_bool = X0 ) ),
    inference(cnf_transformation,[],[f3758]) ).

tff(f9556,plain,
    spl250_336,
    inference(avatar_split_clause,[],[f4719,f9554]) ).

tff(f4719,plain,
    ! [X0: pname] :
      ( hBOOL(wt(the_com(body(X0))))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),u)) ),
    inference(cnf_transformation,[],[f2592]) ).

tff(f2592,plain,
    ! [X0: pname] :
      ( hBOOL(wt(the_com(body(X0))))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),u)) ),
    inference(ennf_transformation,[],[f1443]) ).

tff(f1443,plain,
    ! [X0: pname] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),u))
     => hBOOL(wt(the_com(body(X0)))) ),
    inference(rectify,[],[f704]) ).

tff(f704,axiom,
    ! [X77: pname] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X77),u))
     => hBOOL(wt(the_com(body(X77)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_703_assms_I4_J) ).

tff(f9552,plain,
    ( spl250_335
    | ~ spl250_53
    | ~ spl250_307 ),
    inference(avatar_split_clause,[],[f9450,f9056,f7553,f9550]) ).

tff(f9550,plain,
    ( spl250_335
  <=> ! [X0: nat] : ~ sP17(X0,X0,ord_less_eq_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_335])]) ).

tff(f7553,plain,
    ( spl250_53
  <=> ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_53])]) ).

tff(f9450,plain,
    ( ! [X0: nat] : ~ sP17(X0,X0,ord_less_eq_nat)
    | ~ spl250_53
    | ~ spl250_307 ),
    inference(resolution,[],[f9057,f7554]) ).

tff(f7554,plain,
    ( ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0))
    | ~ spl250_53 ),
    inference(avatar_component_clause,[],[f7553]) ).

tff(f9514,plain,
    ( spl250_334
    | ~ spl250_39
    | ~ spl250_293 ),
    inference(avatar_split_clause,[],[f9383,f8999,f7496,f9512]) ).

tff(f8999,plain,
    ( spl250_293
  <=> ! [X0: pname,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
        | ~ hBOOL(hAPP_pname_bool(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_293])]) ).

tff(f9383,plain,
    ( ! [X0: pname] : ~ hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X0))
    | ~ spl250_39
    | ~ spl250_293 ),
    inference(resolution,[],[f9000,f7497]) ).

tff(f9000,plain,
    ( ! [X0: pname,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
        | ~ hBOOL(hAPP_pname_bool(X1,X0)) )
    | ~ spl250_293 ),
    inference(avatar_component_clause,[],[f8999]) ).

tff(f9422,plain,
    ( spl250_333
    | ~ spl250_38
    | ~ spl250_292 ),
    inference(avatar_split_clause,[],[f9376,f8993,f7491,f9419]) ).

tff(f8993,plain,
    ( spl250_292
  <=> ! [X0: pname,X1: fun_pname_bool] :
        ( hBOOL(hAPP_pname_bool(X1,X0))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_292])]) ).

tff(f9376,plain,
    ( hBOOL(hAPP_pname_bool(u,pn))
    | ~ spl250_38
    | ~ spl250_292 ),
    inference(resolution,[],[f8994,f7493]) ).

tff(f8994,plain,
    ( ! [X0: pname,X1: fun_pname_bool] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
        | hBOOL(hAPP_pname_bool(X1,X0)) )
    | ~ spl250_292 ),
    inference(avatar_component_clause,[],[f8993]) ).

tff(f9175,plain,
    ( spl250_332
    | ~ spl250_14
    | ~ spl250_85 ),
    inference(avatar_split_clause,[],[f7924,f7733,f7379,f9172]) ).

tff(f9172,plain,
    ( spl250_332
  <=> ( hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool) = fTrue ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_332])]) ).

tff(f7379,plain,
    ( spl250_14
  <=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_14])]) ).

tff(f7924,plain,
    ( ( hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool) = fTrue )
    | ~ spl250_14
    | ~ spl250_85 ),
    inference(resolution,[],[f7734,f7381]) ).

tff(f7381,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool))
    | ~ spl250_14 ),
    inference(avatar_component_clause,[],[f7379]) ).

tff(f9156,plain,
    spl250_331,
    inference(avatar_split_clause,[],[f7176,f9154]) ).

tff(f7176,plain,
    ! [X0: nat,X1: nat] :
      ( ( one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) )
      | sP7(X1,X0) ),
    inference(forward_demodulation,[],[f5612,f4566]) ).

tff(f5612,plain,
    ! [X0: nat,X1: nat] :
      ( sP7(X1,X0)
      | ( hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) ) ),
    inference(cnf_transformation,[],[f4143]) ).

tff(f4143,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) )
        | ~ sP7(X1,X0) )
      & ( sP7(X1,X0)
        | ( hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) ) ) ),
    inference(nnf_transformation,[],[f3698]) ).

tff(f3698,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) )
    <=> sP7(X1,X0) ),
    inference(definition_folding,[],[f2027,f3697]) ).

tff(f3697,plain,
    ! [X1: nat,X0: nat] :
      ( sP7(X1,X0)
    <=> ( ( ( hAPP_nat_nat(suc,zero_zero_nat) = X1 )
          & ( zero_zero_nat = X0 ) )
        | ( ( zero_zero_nat = X1 )
          & ( hAPP_nat_nat(suc,zero_zero_nat) = X0 ) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).

tff(f2027,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) )
    <=> ( ( ( hAPP_nat_nat(suc,zero_zero_nat) = X1 )
          & ( zero_zero_nat = X0 ) )
        | ( ( zero_zero_nat = X1 )
          & ( hAPP_nat_nat(suc,zero_zero_nat) = X0 ) ) ) ),
    inference(rectify,[],[f950]) ).

tff(f950,axiom,
    ! [X22: nat,X14: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X22),X14) = hAPP_nat_nat(suc,zero_zero_nat) )
    <=> ( ( ( hAPP_nat_nat(suc,zero_zero_nat) = X14 )
          & ( zero_zero_nat = X22 ) )
        | ( ( zero_zero_nat = X14 )
          & ( hAPP_nat_nat(suc,zero_zero_nat) = X22 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_949_one__is__add) ).

tff(f9152,plain,
    spl250_330,
    inference(avatar_split_clause,[],[f7175,f9150]) ).

tff(f9150,plain,
    ( spl250_330
  <=> ! [X0: nat,X1: nat] :
        ( ( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) )
        | ~ sP7(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_330])]) ).

tff(f7175,plain,
    ! [X0: nat,X1: nat] :
      ( ( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) )
      | ~ sP7(X1,X0) ),
    inference(forward_demodulation,[],[f5613,f4566]) ).

tff(f5613,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) )
      | ~ sP7(X1,X0) ),
    inference(cnf_transformation,[],[f4143]) ).

tff(f9148,plain,
    spl250_329,
    inference(avatar_split_clause,[],[f7168,f9146]) ).

tff(f7168,plain,
    ! [X0: nat,X1: nat] :
      ( ( one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) )
      | sP6(X1,X0) ),
    inference(forward_demodulation,[],[f5604,f4566]) ).

tff(f5604,plain,
    ! [X0: nat,X1: nat] :
      ( sP6(X1,X0)
      | ( hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) ) ),
    inference(cnf_transformation,[],[f4139]) ).

tff(f4139,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) )
        | ~ sP6(X1,X0) )
      & ( sP6(X1,X0)
        | ( hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) ) ) ),
    inference(nnf_transformation,[],[f3696]) ).

tff(f3696,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) )
    <=> sP6(X1,X0) ),
    inference(definition_folding,[],[f2026,f3695]) ).

tff(f3695,plain,
    ! [X1: nat,X0: nat] :
      ( sP6(X1,X0)
    <=> ( ( ( hAPP_nat_nat(suc,zero_zero_nat) = X1 )
          & ( zero_zero_nat = X0 ) )
        | ( ( zero_zero_nat = X1 )
          & ( hAPP_nat_nat(suc,zero_zero_nat) = X0 ) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).

tff(f2026,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) )
    <=> ( ( ( hAPP_nat_nat(suc,zero_zero_nat) = X1 )
          & ( zero_zero_nat = X0 ) )
        | ( ( zero_zero_nat = X1 )
          & ( hAPP_nat_nat(suc,zero_zero_nat) = X0 ) ) ) ),
    inference(rectify,[],[f951]) ).

tff(f951,axiom,
    ! [X22: nat,X14: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X22),X14) = hAPP_nat_nat(suc,zero_zero_nat) )
    <=> ( ( ( hAPP_nat_nat(suc,zero_zero_nat) = X14 )
          & ( zero_zero_nat = X22 ) )
        | ( ( zero_zero_nat = X14 )
          & ( hAPP_nat_nat(suc,zero_zero_nat) = X22 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_950_add__is__1) ).

tff(f9144,plain,
    spl250_328,
    inference(avatar_split_clause,[],[f7167,f9142]) ).

tff(f9142,plain,
    ( spl250_328
  <=> ! [X0: nat,X1: nat] :
        ( ( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) )
        | ~ sP6(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_328])]) ).

tff(f7167,plain,
    ! [X0: nat,X1: nat] :
      ( ( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) )
      | ~ sP6(X1,X0) ),
    inference(forward_demodulation,[],[f5605,f4566]) ).

tff(f5605,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) )
      | ~ sP6(X1,X0) ),
    inference(cnf_transformation,[],[f4139]) ).

tff(f9140,plain,
    spl250_327,
    inference(avatar_split_clause,[],[f7123,f9138]) ).

tff(f9138,plain,
    ( spl250_327
  <=> ! [X0: int,X1: int] :
        ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
        | ( pls = X1 )
        | ~ sP4(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_327])]) ).

tff(f7123,plain,
    ! [X0: int,X1: int] :
      ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
      | ( pls = X1 )
      | ~ sP4(X0,X1) ),
    inference(forward_demodulation,[],[f7122,f4587]) ).

tff(f7122,plain,
    ! [X0: int,X1: int] :
      ( ( pls = X1 )
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
      | ~ sP4(X0,X1) ),
    inference(forward_demodulation,[],[f6647,f4587]) ).

tff(f6647,plain,
    ! [X0: int,X1: int] :
      ( ( pls = number_number_of_int(X1) )
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
      | ~ sP4(X0,X1) ),
    inference(definition_unfolding,[],[f5470,f4550]) ).

tff(f5470,plain,
    ! [X0: int,X1: int] :
      ( ( zero_zero_int = number_number_of_int(X1) )
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
      | ~ sP4(X0,X1) ),
    inference(cnf_transformation,[],[f4045]) ).

tff(f4045,plain,
    ! [X0: int,X1: int] :
      ( ( sP4(X0,X1)
        | ( ( X0 != X1 )
          & ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
        | ( ( zero_zero_int != number_number_of_int(X1) )
          & hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) )
      & ( ( ( ( X0 = X1 )
            | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
          & ( ( zero_zero_int = number_number_of_int(X1) )
            | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) )
        | ~ sP4(X0,X1) ) ),
    inference(rectify,[],[f4044]) ).

tff(f4044,plain,
    ! [X1: int,X0: int] :
      ( ( sP4(X1,X0)
        | ( ( X0 != X1 )
          & ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) )
        | ( ( zero_zero_int != number_number_of_int(X0) )
          & hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ) )
      & ( ( ( ( X0 = X1 )
            | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) )
          & ( ( zero_zero_int = number_number_of_int(X0) )
            | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ) )
        | ~ sP4(X1,X0) ) ),
    inference(flattening,[],[f4043]) ).

tff(f4043,plain,
    ! [X1: int,X0: int] :
      ( ( sP4(X1,X0)
        | ( ( X0 != X1 )
          & ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) )
        | ( ( zero_zero_int != number_number_of_int(X0) )
          & hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ) )
      & ( ( ( ( X0 = X1 )
            | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) )
          & ( ( zero_zero_int = number_number_of_int(X0) )
            | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ) )
        | ~ sP4(X1,X0) ) ),
    inference(nnf_transformation,[],[f3692]) ).

tff(f3692,plain,
    ! [X1: int,X0: int] :
      ( sP4(X1,X0)
    <=> ( ( ( X0 = X1 )
          | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) )
        & ( ( zero_zero_int = number_number_of_int(X0) )
          | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

tff(f9136,plain,
    spl250_326,
    inference(avatar_split_clause,[],[f7121,f9134]) ).

tff(f9134,plain,
    ( spl250_326
  <=> ! [X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(nat_neg,X0))
        | ( X0 = X1 )
        | ~ sP4(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_326])]) ).

tff(f7121,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(nat_neg,X0))
      | ( X0 = X1 )
      | ~ sP4(X0,X1) ),
    inference(forward_demodulation,[],[f5471,f4587]) ).

tff(f5471,plain,
    ! [X0: int,X1: int] :
      ( ( X0 = X1 )
      | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
      | ~ sP4(X0,X1) ),
    inference(cnf_transformation,[],[f4045]) ).

tff(f9132,plain,
    ( spl250_325
    | ~ spl250_13
    | ~ spl250_85 ),
    inference(avatar_split_clause,[],[f7920,f7733,f7374,f9129]) ).

tff(f9129,plain,
    ( spl250_325
  <=> ( hAPP_f448129468l_bool(finite_finite_int,bot_bot_fun_int_bool) = fTrue ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_325])]) ).

tff(f7374,plain,
    ( spl250_13
  <=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,bot_bot_fun_int_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_13])]) ).

tff(f7920,plain,
    ( ( hAPP_f448129468l_bool(finite_finite_int,bot_bot_fun_int_bool) = fTrue )
    | ~ spl250_13
    | ~ spl250_85 ),
    inference(resolution,[],[f7734,f7376]) ).

tff(f7376,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,bot_bot_fun_int_bool))
    | ~ spl250_13 ),
    inference(avatar_component_clause,[],[f7374]) ).

tff(f9127,plain,
    spl250_324,
    inference(avatar_split_clause,[],[f7120,f9125]) ).

tff(f9125,plain,
    ( spl250_324
  <=> ! [X0: int,X1: int] :
        ( ( pls != X1 )
        | ~ hBOOL(hAPP_int_bool(nat_neg,X0))
        | sP4(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_324])]) ).

tff(f7120,plain,
    ! [X0: int,X1: int] :
      ( ( pls != X1 )
      | ~ hBOOL(hAPP_int_bool(nat_neg,X0))
      | sP4(X0,X1) ),
    inference(forward_demodulation,[],[f7119,f4587]) ).

tff(f7119,plain,
    ! [X0: int,X1: int] :
      ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
      | sP4(X0,X1)
      | ( pls != number_number_of_int(X1) ) ),
    inference(forward_demodulation,[],[f6646,f4587]) ).

tff(f6646,plain,
    ! [X0: int,X1: int] :
      ( sP4(X0,X1)
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
      | ( pls != number_number_of_int(X1) ) ),
    inference(definition_unfolding,[],[f5473,f4550]) ).

tff(f5473,plain,
    ! [X0: int,X1: int] :
      ( sP4(X0,X1)
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
      | ( zero_zero_int != number_number_of_int(X1) ) ),
    inference(cnf_transformation,[],[f4045]) ).

tff(f9123,plain,
    spl250_323,
    inference(avatar_split_clause,[],[f7114,f9121]) ).

tff(f9121,plain,
    ( spl250_323
  <=> ! [X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(nat_neg,X0))
        | sP4(X1,X0)
        | ~ sP5(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_323])]) ).

tff(f7114,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(nat_neg,X0))
      | sP4(X1,X0)
      | ~ sP5(X0,X1) ),
    inference(forward_demodulation,[],[f5465,f4587]) ).

tff(f5465,plain,
    ! [X0: int,X1: int] :
      ( sP4(X1,X0)
      | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
      | ~ sP5(X0,X1) ),
    inference(cnf_transformation,[],[f4042]) ).

tff(f9119,plain,
    spl250_322,
    inference(avatar_split_clause,[],[f7111,f9117]) ).

tff(f9117,plain,
    ( spl250_322
  <=> ! [X0: int,X1: int] :
        ( hBOOL(hAPP_int_bool(nat_neg,X0))
        | sP5(X0,X1)
        | ~ sP4(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_322])]) ).

tff(f7111,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(nat_neg,X0))
      | sP5(X0,X1)
      | ~ sP4(X1,X0) ),
    inference(forward_demodulation,[],[f5468,f4587]) ).

tff(f5468,plain,
    ! [X0: int,X1: int] :
      ( sP5(X0,X1)
      | ~ sP4(X1,X0)
      | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
    inference(cnf_transformation,[],[f4042]) ).

tff(f9115,plain,
    spl250_321,
    inference(avatar_split_clause,[],[f6947,f9113]) ).

tff(f9113,plain,
    ( spl250_321
  <=> ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
        | ( pls = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_321])]) ).

tff(f6947,plain,
    ! [X0: int] :
      ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
      | ( pls = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0)) ) ),
    inference(forward_demodulation,[],[f6588,f4587]) ).

tff(f6588,plain,
    ! [X0: int] :
      ( ( pls = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0)) )
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
    inference(definition_unfolding,[],[f4699,f4550]) ).

tff(f4699,plain,
    ! [X0: int] :
      ( ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0)) )
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
    inference(cnf_transformation,[],[f2578]) ).

tff(f2578,plain,
    ! [X0: int] :
      ( ( ( number_number_of_int(X0) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0)) )
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
      & ( ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0)) )
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) ),
    inference(ennf_transformation,[],[f1425]) ).

tff(f1425,plain,
    ! [X0: int] :
      ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
       => ( number_number_of_int(X0) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0)) ) )
      & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
       => ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0)) ) ) ),
    inference(rectify,[],[f1157]) ).

tff(f1157,axiom,
    ! [X130: int] :
      ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X130)))
       => ( number_number_of_int(X130) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X130)) ) )
      & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X130)))
       => ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X130)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1156_int__nat__number__of) ).

tff(f9111,plain,
    spl250_320,
    inference(avatar_split_clause,[],[f6946,f9109]) ).

tff(f6946,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(nat_neg,X0))
      | ( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0)) = X0 ) ),
    inference(forward_demodulation,[],[f6945,f4587]) ).

tff(f6945,plain,
    ! [X0: int] :
      ( ( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0)) = X0 )
      | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
    inference(forward_demodulation,[],[f4700,f4587]) ).

tff(f4700,plain,
    ! [X0: int] :
      ( ( number_number_of_int(X0) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X0)) )
      | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
    inference(cnf_transformation,[],[f2578]) ).

tff(f9107,plain,
    spl250_319,
    inference(avatar_split_clause,[],[f6944,f9105]) ).

tff(f9105,plain,
    ( spl250_319
  <=> ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
        | ( one_one_nat = hAPP_nat_nat(suc,number_number_of_nat(X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_319])]) ).

tff(f6944,plain,
    ! [X0: int] :
      ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
      | ( one_one_nat = hAPP_nat_nat(suc,number_number_of_nat(X0)) ) ),
    inference(forward_demodulation,[],[f4697,f4587]) ).

tff(f4697,plain,
    ! [X0: int] :
      ( ( one_one_nat = hAPP_nat_nat(suc,number_number_of_nat(X0)) )
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
    inference(cnf_transformation,[],[f2577]) ).

tff(f9103,plain,
    spl250_318,
    inference(avatar_split_clause,[],[f6937,f9101]) ).

tff(f9101,plain,
    ( spl250_318
  <=> ! [X0: nat] : ( hAPP_nat_nat(suc,X0) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_318])]) ).

tff(f6937,plain,
    ! [X0: nat] : ( hAPP_nat_nat(suc,X0) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)) ),
    inference(forward_demodulation,[],[f4686,f4588]) ).

tff(f4686,plain,
    ! [X0: nat] : ( hAPP_nat_nat(suc,X0) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0))) ),
    inference(cnf_transformation,[],[f1414]) ).

tff(f1414,plain,
    ! [X0: nat] : ( hAPP_nat_nat(suc,X0) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0))) ),
    inference(rectify,[],[f122]) ).

tff(f122,axiom,
    ! [X14: nat] : ( hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X14))) = hAPP_nat_nat(suc,X14) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_card__Collect__le__nat) ).

tff(f9099,plain,
    spl250_317,
    inference(avatar_split_clause,[],[f6936,f9097]) ).

tff(f9097,plain,
    ( spl250_317
  <=> ! [X0: x_a] : ( collect_a(hAPP_a_fun_a_bool(fequal_a,X0)) = collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_317])]) ).

tff(f6936,plain,
    ! [X0: x_a] : ( collect_a(hAPP_a_fun_a_bool(fequal_a,X0)) = collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)) ),
    inference(forward_demodulation,[],[f4685,f4680]) ).

tff(f4685,plain,
    ! [X0: x_a] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)) ),
    inference(cnf_transformation,[],[f1413]) ).

tff(f1413,plain,
    ! [X0: x_a] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool) = collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X0)) ),
    inference(rectify,[],[f637]) ).

tff(f637,axiom,
    ! [X5: x_a] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),bot_bot_fun_a_bool) = collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_636_singleton__conv) ).

tff(f9095,plain,
    spl250_316,
    inference(avatar_split_clause,[],[f6837,f9093]) ).

tff(f9093,plain,
    ( spl250_316
  <=> ! [X1: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_316])]) ).

tff(f6837,plain,
    ! [X1: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int))),
    inference(equality_resolution,[],[f5650]) ).

tff(f5650,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)))
      | ( X0 != X1 ) ),
    inference(cnf_transformation,[],[f4166]) ).

tff(f9091,plain,
    spl250_315,
    inference(avatar_split_clause,[],[f6682,f9089]) ).

tff(f9089,plain,
    ( spl250_315
  <=> ! [X2: int,X0: bool,X1: bool] :
        ( sP16(X0,X2,X1)
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_315])]) ).

tff(f6682,plain,
    ! [X2: int,X0: bool,X1: bool] :
      ( sP16(X0,X2,X1)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2)) ),
    inference(definition_unfolding,[],[f6259,f4550]) ).

tff(f6259,plain,
    ! [X2: int,X0: bool,X1: bool] :
      ( sP16(X0,X2,X1)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
    inference(cnf_transformation,[],[f4370]) ).

tff(f4370,plain,
    ! [X0: bool,X1: bool,X2: int] :
      ( sP16(X0,X2,X1)
      | ( ( ~ hBOOL(X0)
          | ~ hBOOL(X1) )
        & ( hBOOL(X0)
          | hBOOL(X1) )
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
    inference(flattening,[],[f4369]) ).

tff(f4369,plain,
    ! [X0: bool,X1: bool,X2: int] :
      ( sP16(X0,X2,X1)
      | ( ( ~ hBOOL(X0)
          | ~ hBOOL(X1) )
        & ( hBOOL(X0)
          | hBOOL(X1) )
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
    inference(nnf_transformation,[],[f3716]) ).

tff(f3716,plain,
    ! [X0: bool,X1: bool,X2: int] :
      ( sP16(X0,X2,X1)
      | ( ( hBOOL(X1)
        <~> hBOOL(X0) )
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
    inference(definition_folding,[],[f3561,f3715]) ).

tff(f3561,plain,
    ! [X0: bool,X1: bool,X2: int] :
      ( ( ( hBOOL(X1)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
      <=> ( hBOOL(X0)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
      | ( ( hBOOL(X1)
        <~> hBOOL(X0) )
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
    inference(ennf_transformation,[],[f2455]) ).

tff(f2455,plain,
    ! [X0: bool,X1: bool,X2: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
       => ( hBOOL(X1)
        <=> hBOOL(X0) ) )
     => ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
         => hBOOL(X1) )
      <=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
         => hBOOL(X0) ) ) ),
    inference(rectify,[],[f1091]) ).

tff(f1091,axiom,
    ! [X145: bool,X10: bool,X8: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X8))
       => ( hBOOL(X10)
        <=> hBOOL(X145) ) )
     => ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X8))
         => hBOOL(X10) )
      <=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X8))
         => hBOOL(X145) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1090_imp__le__cong) ).

tff(f9087,plain,
    ( spl250_314
    | ~ spl250_11
    | ~ spl250_85 ),
    inference(avatar_split_clause,[],[f7917,f7733,f7364,f9084]) ).

tff(f9084,plain,
    ( spl250_314
  <=> ( hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool) = fTrue ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_314])]) ).

tff(f7364,plain,
    ( spl250_11
  <=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_11])]) ).

tff(f7917,plain,
    ( ( hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool) = fTrue )
    | ~ spl250_11
    | ~ spl250_85 ),
    inference(resolution,[],[f7734,f7366]) ).

tff(f7366,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool))
    | ~ spl250_11 ),
    inference(avatar_component_clause,[],[f7364]) ).

tff(f9082,plain,
    spl250_313,
    inference(avatar_split_clause,[],[f6677,f9080]) ).

tff(f9080,plain,
    ( spl250_313
  <=> ! [X2: int,X0: bool,X1: bool] :
        ( sP15(X0,X2,X1)
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_313])]) ).

tff(f6677,plain,
    ! [X2: int,X0: bool,X1: bool] :
      ( sP15(X0,X2,X1)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2)) ),
    inference(definition_unfolding,[],[f6252,f4550]) ).

tff(f6252,plain,
    ! [X2: int,X0: bool,X1: bool] :
      ( sP15(X0,X2,X1)
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
    inference(cnf_transformation,[],[f4365]) ).

tff(f4365,plain,
    ! [X0: bool,X1: bool,X2: int] :
      ( sP15(X0,X2,X1)
      | ( ( ~ hBOOL(X0)
          | ~ hBOOL(X1) )
        & ( hBOOL(X0)
          | hBOOL(X1) )
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
    inference(flattening,[],[f4364]) ).

tff(f4364,plain,
    ! [X0: bool,X1: bool,X2: int] :
      ( sP15(X0,X2,X1)
      | ( ( ~ hBOOL(X0)
          | ~ hBOOL(X1) )
        & ( hBOOL(X0)
          | hBOOL(X1) )
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
    inference(nnf_transformation,[],[f3714]) ).

tff(f3714,plain,
    ! [X0: bool,X1: bool,X2: int] :
      ( sP15(X0,X2,X1)
      | ( ( hBOOL(X1)
        <~> hBOOL(X0) )
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
    inference(definition_folding,[],[f3560,f3713]) ).

tff(f3560,plain,
    ! [X0: bool,X1: bool,X2: int] :
      ( ( ( hBOOL(X1)
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
      <=> ( hBOOL(X0)
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
      | ( ( hBOOL(X1)
        <~> hBOOL(X0) )
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
    inference(ennf_transformation,[],[f2454]) ).

tff(f2454,plain,
    ! [X0: bool,X1: bool,X2: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
       => ( hBOOL(X1)
        <=> hBOOL(X0) ) )
     => ( ( hBOOL(X1)
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
      <=> ( hBOOL(X0)
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ) ),
    inference(rectify,[],[f1090]) ).

tff(f1090,axiom,
    ! [X145: bool,X10: bool,X8: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X8))
       => ( hBOOL(X10)
        <=> hBOOL(X145) ) )
     => ( ( hBOOL(X10)
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X8)) )
      <=> ( hBOOL(X145)
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X8)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1089_conj__le__cong) ).

tff(f9078,plain,
    spl250_312,
    inference(avatar_split_clause,[],[f6614,f9076]) ).

tff(f9076,plain,
    ( spl250_312
  <=> ! [X0: int] :
        ( ( pls = X0 )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_312])]) ).

tff(f6614,plain,
    ! [X0: int] :
      ( ( pls = X0 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int)) ),
    inference(definition_unfolding,[],[f4833,f4550]) ).

tff(f4833,plain,
    ! [X0: int] :
      ( ( zero_zero_int = X0 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int)) ),
    inference(cnf_transformation,[],[f3854]) ).

tff(f3854,plain,
    ! [X0: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int))
        | ( zero_zero_int != X0 ) )
      & ( ( zero_zero_int = X0 )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int)) ) ),
    inference(nnf_transformation,[],[f1500]) ).

tff(f1500,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int))
    <=> ( zero_zero_int = X0 ) ),
    inference(rectify,[],[f1146]) ).

tff(f1146,axiom,
    ! [X53: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X53)),one_one_int))
    <=> ( zero_zero_int = X53 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1145_zabs__less__one__iff) ).

tff(f9074,plain,
    spl250_311,
    inference(avatar_split_clause,[],[f6600,f9072]) ).

tff(f9072,plain,
    ( spl250_311
  <=> ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
        | ~ hBOOL(hAPP_int_bool(nat_neg,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_311])]) ).

tff(f6600,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
      | ~ hBOOL(hAPP_int_bool(nat_neg,X0)) ),
    inference(definition_unfolding,[],[f4795,f4550]) ).

tff(f4795,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(nat_neg,X0)) ),
    inference(cnf_transformation,[],[f3832]) ).

tff(f3832,plain,
    ! [X0: int] :
      ( ( hBOOL(hAPP_int_bool(nat_neg,X0))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int))
        | ~ hBOOL(hAPP_int_bool(nat_neg,X0)) ) ),
    inference(nnf_transformation,[],[f1481]) ).

tff(f1481,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(nat_neg,X0))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int)) ),
    inference(rectify,[],[f1147]) ).

tff(f1147,axiom,
    ! [X150: int] :
      ( hBOOL(hAPP_int_bool(nat_neg,X150))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X150),zero_zero_int)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1146_neg__def) ).

tff(f9070,plain,
    spl250_310,
    inference(avatar_split_clause,[],[f6599,f9068]) ).

tff(f9068,plain,
    ( spl250_310
  <=> ! [X0: int] :
        ( hBOOL(hAPP_int_bool(nat_neg,X0))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_310])]) ).

tff(f6599,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(nat_neg,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
    inference(definition_unfolding,[],[f4796,f4550]) ).

tff(f4796,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(nat_neg,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),zero_zero_int)) ),
    inference(cnf_transformation,[],[f3832]) ).

tff(f9066,plain,
    spl250_309,
    inference(avatar_split_clause,[],[f6598,f9064]) ).

tff(f9064,plain,
    ( spl250_309
  <=> ! [X0: int] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
        | hBOOL(hAPP_int_bool(nat_neg,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_309])]) ).

tff(f6598,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
      | hBOOL(hAPP_int_bool(nat_neg,X0)) ),
    inference(definition_unfolding,[],[f4753,f4550]) ).

tff(f4753,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
      | hBOOL(hAPP_int_bool(nat_neg,X0)) ),
    inference(cnf_transformation,[],[f3774]) ).

tff(f3774,plain,
    ! [X0: int] :
      ( ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
        | hBOOL(hAPP_int_bool(nat_neg,X0)) ) ),
    inference(nnf_transformation,[],[f1465]) ).

tff(f1465,plain,
    ! [X0: int] :
      ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
    inference(rectify,[],[f1148]) ).

tff(f1148,axiom,
    ! [X8: int] :
      ( ~ hBOOL(hAPP_int_bool(nat_neg,X8))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1147_not__neg__eq__ge__0) ).

tff(f9062,plain,
    spl250_308,
    inference(avatar_split_clause,[],[f6597,f9060]) ).

tff(f9060,plain,
    ( spl250_308
  <=> ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_308])]) ).

tff(f6597,plain,
    ! [X0: int] :
      ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
    inference(definition_unfolding,[],[f4754,f4550]) ).

tff(f4754,plain,
    ! [X0: int] :
      ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ),
    inference(cnf_transformation,[],[f3774]) ).

tff(f9058,plain,
    spl250_307,
    inference(avatar_split_clause,[],[f6263,f9056]) ).

tff(f6263,plain,
    ! [X2: fun_nat_fun_nat_bool,X0: nat,X1: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X2,X1),X0))
      | ~ sP17(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4372]) ).

tff(f4372,plain,
    ! [X0: nat,X1: nat,X2: fun_nat_fun_nat_bool] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X2,X1),X0))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) )
      | ~ sP17(X0,X1,X2) ),
    inference(rectify,[],[f4371]) ).

tff(f4371,plain,
    ! [X1: nat,X2: nat,X0: fun_nat_fun_nat_bool] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
      | ~ sP17(X1,X2,X0) ),
    inference(nnf_transformation,[],[f3717]) ).

tff(f9054,plain,
    spl250_306,
    inference(avatar_split_clause,[],[f6262,f9052]) ).

tff(f9052,plain,
    ( spl250_306
  <=> ! [X2: fun_nat_fun_nat_bool,X0: nat,X1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
        | ~ sP17(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_306])]) ).

tff(f6262,plain,
    ! [X2: fun_nat_fun_nat_bool,X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
      | ~ sP17(X0,X1,X2) ),
    inference(cnf_transformation,[],[f4372]) ).

tff(f9050,plain,
    spl250_305,
    inference(avatar_split_clause,[],[f5545,f9048]) ).

tff(f9048,plain,
    ( spl250_305
  <=> ! [X0: nat,X1: nat] :
        ( ( X0 = X1 )
        | ( hAPP_nat_int(semiri1621563631at_int,X0) != hAPP_nat_int(semiri1621563631at_int,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_305])]) ).

tff(f5545,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ( hAPP_nat_int(semiri1621563631at_int,X0) != hAPP_nat_int(semiri1621563631at_int,X1) ) ),
    inference(cnf_transformation,[],[f4105]) ).

tff(f4105,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( hAPP_nat_int(semiri1621563631at_int,X0) = hAPP_nat_int(semiri1621563631at_int,X1) )
        | ( X0 != X1 ) )
      & ( ( X0 = X1 )
        | ( hAPP_nat_int(semiri1621563631at_int,X0) != hAPP_nat_int(semiri1621563631at_int,X1) ) ) ),
    inference(nnf_transformation,[],[f2002]) ).

tff(f2002,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_int(semiri1621563631at_int,X0) = hAPP_nat_int(semiri1621563631at_int,X1) )
    <=> ( X0 = X1 ) ),
    inference(rectify,[],[f1133]) ).

tff(f1133,axiom,
    ! [X22: nat,X14: nat] :
      ( ( hAPP_nat_int(semiri1621563631at_int,X14) = hAPP_nat_int(semiri1621563631at_int,X22) )
    <=> ( X14 = X22 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1132_int__int__eq) ).

tff(f9046,plain,
    spl250_304,
    inference(avatar_split_clause,[],[f5543,f9044]) ).

tff(f9044,plain,
    ( spl250_304
  <=> ! [X0: nat,X1: nat] :
        ( ( zero_zero_nat = X1 )
        | ( zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_304])]) ).

tff(f5543,plain,
    ! [X0: nat,X1: nat] :
      ( ( zero_zero_nat = X1 )
      | ( zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) ) ),
    inference(cnf_transformation,[],[f4104]) ).

tff(f4104,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) )
        | ( zero_zero_nat != X1 )
        | ( zero_zero_nat != X0 ) )
      & ( ( ( zero_zero_nat = X1 )
          & ( zero_zero_nat = X0 ) )
        | ( zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) ) ) ),
    inference(flattening,[],[f4103]) ).

tff(f4103,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) )
        | ( zero_zero_nat != X1 )
        | ( zero_zero_nat != X0 ) )
      & ( ( ( zero_zero_nat = X1 )
          & ( zero_zero_nat = X0 ) )
        | ( zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) ) ) ),
    inference(nnf_transformation,[],[f2001]) ).

tff(f2001,plain,
    ! [X0: nat,X1: nat] :
      ( ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) )
    <=> ( ( zero_zero_nat = X1 )
        & ( zero_zero_nat = X0 ) ) ),
    inference(rectify,[],[f933]) ).

tff(f933,axiom,
    ! [X22: nat,X14: nat] :
      ( ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X22),X14) )
    <=> ( ( zero_zero_nat = X14 )
        & ( zero_zero_nat = X22 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_932_add__is__0) ).

tff(f9042,plain,
    ( spl250_303
    | ~ spl250_12
    | ~ spl250_85 ),
    inference(avatar_split_clause,[],[f7912,f7733,f7369,f9039]) ).

tff(f9039,plain,
    ( spl250_303
  <=> ( hAPP_fun_a_bool_bool(finite_finite_a,bot_bot_fun_a_bool) = fTrue ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_303])]) ).

tff(f7369,plain,
    ( spl250_12
  <=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,bot_bot_fun_a_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_12])]) ).

tff(f7912,plain,
    ( ( hAPP_fun_a_bool_bool(finite_finite_a,bot_bot_fun_a_bool) = fTrue )
    | ~ spl250_12
    | ~ spl250_85 ),
    inference(resolution,[],[f7734,f7371]) ).

tff(f7371,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,bot_bot_fun_a_bool))
    | ~ spl250_12 ),
    inference(avatar_component_clause,[],[f7369]) ).

tff(f9037,plain,
    spl250_302,
    inference(avatar_split_clause,[],[f5542,f9035]) ).

tff(f9035,plain,
    ( spl250_302
  <=> ! [X0: nat,X1: nat] :
        ( ( zero_zero_nat = X0 )
        | ( zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_302])]) ).

tff(f5542,plain,
    ! [X0: nat,X1: nat] :
      ( ( zero_zero_nat = X0 )
      | ( zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) ) ),
    inference(cnf_transformation,[],[f4104]) ).

tff(f9033,plain,
    spl250_301,
    inference(avatar_split_clause,[],[f5532,f9031]) ).

tff(f9031,plain,
    ( spl250_301
  <=> ! [X0: nat,X1: nat] :
        ( ( one_one_nat = X1 )
        | ( one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_301])]) ).

tff(f5532,plain,
    ! [X0: nat,X1: nat] :
      ( ( one_one_nat = X1 )
      | ( one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) ) ),
    inference(cnf_transformation,[],[f4097]) ).

tff(f4097,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) )
        | ( one_one_nat != X1 )
        | ( one_one_nat != X0 ) )
      & ( ( ( one_one_nat = X1 )
          & ( one_one_nat = X0 ) )
        | ( one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) ) ) ),
    inference(flattening,[],[f4096]) ).

tff(f4096,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) )
        | ( one_one_nat != X1 )
        | ( one_one_nat != X0 ) )
      & ( ( ( one_one_nat = X1 )
          & ( one_one_nat = X0 ) )
        | ( one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) ) ) ),
    inference(nnf_transformation,[],[f1997]) ).

tff(f1997,plain,
    ! [X0: nat,X1: nat] :
      ( ( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) )
    <=> ( ( one_one_nat = X1 )
        & ( one_one_nat = X0 ) ) ),
    inference(rectify,[],[f996]) ).

tff(f996,axiom,
    ! [X22: nat,X14: nat] :
      ( ( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X22),X14) )
    <=> ( ( one_one_nat = X14 )
        & ( one_one_nat = X22 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_995_nat__1__eq__mult__iff) ).

tff(f9029,plain,
    spl250_300,
    inference(avatar_split_clause,[],[f5531,f9027]) ).

tff(f9027,plain,
    ( spl250_300
  <=> ! [X0: nat,X1: nat] :
        ( ( one_one_nat = X0 )
        | ( one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_300])]) ).

tff(f5531,plain,
    ! [X0: nat,X1: nat] :
      ( ( one_one_nat = X0 )
      | ( one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X1) ) ),
    inference(cnf_transformation,[],[f4097]) ).

tff(f9025,plain,
    spl250_299,
    inference(avatar_split_clause,[],[f5501,f9023]) ).

tff(f9023,plain,
    ( spl250_299
  <=> ! [X0: nat,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
        | ~ hBOOL(hAPP_nat_bool(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_299])]) ).

tff(f5501,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
      | ~ hBOOL(hAPP_nat_bool(X1,X0)) ),
    inference(cnf_transformation,[],[f4064]) ).

tff(f4064,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
        | ~ hBOOL(hAPP_nat_bool(X1,X0)) )
      & ( hBOOL(hAPP_nat_bool(X1,X0))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ) ),
    inference(nnf_transformation,[],[f1983]) ).

tff(f1983,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1))
    <=> hBOOL(hAPP_nat_bool(X1,X0)) ),
    inference(rectify,[],[f378]) ).

tff(f378,axiom,
    ! [X8: nat,X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X2))
    <=> hBOOL(hAPP_nat_bool(X2,X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_377_mem__def) ).

tff(f9021,plain,
    spl250_298,
    inference(avatar_split_clause,[],[f5500,f9019]) ).

tff(f9019,plain,
    ( spl250_298
  <=> ! [X0: nat,X1: fun_nat_bool] :
        ( hBOOL(hAPP_nat_bool(X1,X0))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_298])]) ).

tff(f5500,plain,
    ! [X0: nat,X1: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(X1,X0))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f4064]) ).

tff(f9017,plain,
    spl250_297,
    inference(avatar_split_clause,[],[f5497,f9015]) ).

tff(f9015,plain,
    ( spl250_297
  <=> ! [X0: int,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
        | ~ hBOOL(hAPP_int_bool(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_297])]) ).

tff(f5497,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
      | ~ hBOOL(hAPP_int_bool(X1,X0)) ),
    inference(cnf_transformation,[],[f4059]) ).

tff(f4059,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
        | ~ hBOOL(hAPP_int_bool(X1,X0)) )
      & ( hBOOL(hAPP_int_bool(X1,X0))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ) ),
    inference(nnf_transformation,[],[f1981]) ).

tff(f1981,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1))
    <=> hBOOL(hAPP_int_bool(X1,X0)) ),
    inference(rectify,[],[f377]) ).

tff(f377,axiom,
    ! [X8: int,X2: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X2))
    <=> hBOOL(hAPP_int_bool(X2,X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_376_mem__def) ).

tff(f9013,plain,
    spl250_296,
    inference(avatar_split_clause,[],[f5496,f9011]) ).

tff(f9011,plain,
    ( spl250_296
  <=> ! [X0: int,X1: fun_int_bool] :
        ( hBOOL(hAPP_int_bool(X1,X0))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_296])]) ).

tff(f5496,plain,
    ! [X0: int,X1: fun_int_bool] :
      ( hBOOL(hAPP_int_bool(X1,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4059]) ).

tff(f9009,plain,
    spl250_295,
    inference(avatar_split_clause,[],[f5493,f9007]) ).

tff(f5493,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
      | ~ hBOOL(hAPP_a_bool(X1,X0)) ),
    inference(cnf_transformation,[],[f4054]) ).

tff(f4054,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
        | ~ hBOOL(hAPP_a_bool(X1,X0)) )
      & ( hBOOL(hAPP_a_bool(X1,X0))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ) ),
    inference(nnf_transformation,[],[f1979]) ).

tff(f1979,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1))
    <=> hBOOL(hAPP_a_bool(X1,X0)) ),
    inference(rectify,[],[f379]) ).

tff(f379,axiom,
    ! [X8: x_a,X2: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X2))
    <=> hBOOL(hAPP_a_bool(X2,X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_mem__def) ).

tff(f9005,plain,
    spl250_294,
    inference(avatar_split_clause,[],[f5492,f9003]) ).

tff(f9003,plain,
    ( spl250_294
  <=> ! [X0: x_a,X1: fun_a_bool] :
        ( hBOOL(hAPP_a_bool(X1,X0))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_294])]) ).

tff(f5492,plain,
    ! [X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_a_bool(X1,X0))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),X1)) ),
    inference(cnf_transformation,[],[f4054]) ).

tff(f9001,plain,
    spl250_293,
    inference(avatar_split_clause,[],[f5491,f8999]) ).

tff(f5491,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
      | ~ hBOOL(hAPP_pname_bool(X1,X0)) ),
    inference(cnf_transformation,[],[f4053]) ).

tff(f4053,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
        | ~ hBOOL(hAPP_pname_bool(X1,X0)) )
      & ( hBOOL(hAPP_pname_bool(X1,X0))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ) ),
    inference(nnf_transformation,[],[f1978]) ).

tff(f1978,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1))
    <=> hBOOL(hAPP_pname_bool(X1,X0)) ),
    inference(rectify,[],[f380]) ).

tff(f380,axiom,
    ! [X8: pname,X2: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X2))
    <=> hBOOL(hAPP_pname_bool(X2,X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_mem__def) ).

tff(f8995,plain,
    spl250_292,
    inference(avatar_split_clause,[],[f5490,f8993]) ).

tff(f5490,plain,
    ! [X0: pname,X1: fun_pname_bool] :
      ( hBOOL(hAPP_pname_bool(X1,X0))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),X1)) ),
    inference(cnf_transformation,[],[f4053]) ).

tff(f8991,plain,
    spl250_291,
    inference(avatar_split_clause,[],[f5437,f8989]) ).

tff(f8989,plain,
    ( spl250_291
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( ( X0 = X1 )
        | ( image_nat_int(semiri1621563631at_int,X0) != image_nat_int(semiri1621563631at_int,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_291])]) ).

tff(f5437,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ( X0 = X1 )
      | ( image_nat_int(semiri1621563631at_int,X0) != image_nat_int(semiri1621563631at_int,X1) ) ),
    inference(cnf_transformation,[],[f4023]) ).

tff(f4023,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ( ( X0 = X1 )
        | ( image_nat_int(semiri1621563631at_int,X0) != image_nat_int(semiri1621563631at_int,X1) ) )
      & ( ( image_nat_int(semiri1621563631at_int,X0) = image_nat_int(semiri1621563631at_int,X1) )
        | ( X0 != X1 ) ) ),
    inference(nnf_transformation,[],[f1961]) ).

tff(f1961,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ( X0 = X1 )
    <=> ( image_nat_int(semiri1621563631at_int,X0) = image_nat_int(semiri1621563631at_int,X1) ) ),
    inference(rectify,[],[f1137]) ).

tff(f1137,axiom,
    ! [X2: fun_nat_bool,X7: fun_nat_bool] :
      ( ( X2 = X7 )
    <=> ( image_nat_int(semiri1621563631at_int,X2) = image_nat_int(semiri1621563631at_int,X7) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1136_transfer__nat__int__set__relations_I3_J) ).

tff(f8987,plain,
    spl250_290,
    inference(avatar_split_clause,[],[f5373,f8985]) ).

tff(f8985,plain,
    ( spl250_290
  <=> ! [X0: nat,X1: nat] :
        ( ( zero_zero_nat = X1 )
        | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_290])]) ).

tff(f5373,plain,
    ! [X0: nat,X1: nat] :
      ( ( zero_zero_nat = X1 )
      | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) != X0 ) ),
    inference(cnf_transformation,[],[f3015]) ).

tff(f3015,plain,
    ! [X0: nat,X1: nat] :
      ( ( zero_zero_nat = X1 )
      | ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) != X0 ) ),
    inference(ennf_transformation,[],[f1917]) ).

tff(f1917,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1) = X0 )
     => ( zero_zero_nat = X1 ) ),
    inference(rectify,[],[f932]) ).

tff(f932,axiom,
    ! [X12: nat,X11: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X12),X11) = X12 )
     => ( zero_zero_nat = X11 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_931_add__eq__self__zero) ).

tff(f8983,plain,
    spl250_289,
    inference(avatar_split_clause,[],[f5370,f8981]) ).

tff(f8981,plain,
    ( spl250_289
  <=> ! [X0: nat,X1: nat] :
        ( ( X0 = X1 )
        | ( hAPP_nat_nat(suc,X0) != hAPP_nat_nat(suc,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_289])]) ).

tff(f5370,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ( hAPP_nat_nat(suc,X0) != hAPP_nat_nat(suc,X1) ) ),
    inference(cnf_transformation,[],[f3010]) ).

tff(f3010,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ( hAPP_nat_nat(suc,X0) != hAPP_nat_nat(suc,X1) ) ),
    inference(ennf_transformation,[],[f1914]) ).

tff(f1914,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(suc,X0) = hAPP_nat_nat(suc,X1) )
     => ( X0 = X1 ) ),
    inference(rectify,[],[f123]) ).

tff(f123,axiom,
    ! [X15: nat,X16: nat] :
      ( ( hAPP_nat_nat(suc,X15) = hAPP_nat_nat(suc,X16) )
     => ( X15 = X16 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_Suc__inject) ).

tff(f8979,plain,
    spl250_288,
    inference(avatar_split_clause,[],[f5254,f8977]) ).

tff(f8977,plain,
    ( spl250_288
  <=> ! [X0: fun_fu425979586l_bool] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK112(X0)),sK113(X0)))
        | ~ sP3(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_288])]) ).

tff(f5254,plain,
    ! [X0: fun_fu425979586l_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK112(X0)),sK113(X0)))
      | ~ sP3(X0) ),
    inference(cnf_transformation,[],[f3968]) ).

tff(f8975,plain,
    spl250_287,
    inference(avatar_split_clause,[],[f5238,f8973]) ).

tff(f8973,plain,
    ( spl250_287
  <=> ! [X0: fun_nat_int,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_287])]) ).

tff(f5238,plain,
    ! [X0: fun_nat_int,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f2861]) ).

tff(f2861,plain,
    ! [X0: fun_nat_int,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(ennf_transformation,[],[f1810]) ).

tff(f1810,plain,
    ! [X0: fun_nat_int,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X0,X1))) ),
    inference(rectify,[],[f40]) ).

tff(f40,axiom,
    ! [X3: fun_nat_int,X4: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_finite__imageI) ).

tff(f8971,plain,
    spl250_286,
    inference(avatar_split_clause,[],[f5237,f8969]) ).

tff(f8969,plain,
    ( spl250_286
  <=> ! [X0: fun_nat_a,X1: fun_nat_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_286])]) ).

tff(f5237,plain,
    ! [X0: fun_nat_a,X1: fun_nat_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f2860]) ).

tff(f2860,plain,
    ! [X0: fun_nat_a,X1: fun_nat_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(ennf_transformation,[],[f1809]) ).

tff(f1809,plain,
    ! [X0: fun_nat_a,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
     => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X0,X1))) ),
    inference(rectify,[],[f14]) ).

tff(f14,axiom,
    ! [X3: fun_nat_a,X4: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
     => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_finite__imageI) ).

tff(f8967,plain,
    spl250_285,
    inference(avatar_split_clause,[],[f5236,f8965]) ).

tff(f8965,plain,
    ( spl250_285
  <=> ! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_285])]) ).

tff(f5236,plain,
    ! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f2859]) ).

tff(f2859,plain,
    ! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(ennf_transformation,[],[f1808]) ).

tff(f1808,plain,
    ! [X0: fun_nat_fun_a_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
     => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X0,X1))) ),
    inference(rectify,[],[f18]) ).

tff(f18,axiom,
    ! [X3: fun_nat_fun_a_bool,X4: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
     => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_finite__imageI) ).

tff(f8963,plain,
    spl250_284,
    inference(avatar_split_clause,[],[f5235,f8961]) ).

tff(f8961,plain,
    ( spl250_284
  <=> ! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_284])]) ).

tff(f5235,plain,
    ! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f2858]) ).

tff(f2858,plain,
    ! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(ennf_transformation,[],[f1807]) ).

tff(f1807,plain,
    ! [X0: fun_nat_fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
     => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X0,X1))) ),
    inference(rectify,[],[f16]) ).

tff(f16,axiom,
    ! [X3: fun_nat_fun_nat_bool,X4: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
     => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_finite__imageI) ).

tff(f8959,plain,
    spl250_283,
    inference(avatar_split_clause,[],[f5234,f8957]) ).

tff(f8957,plain,
    ( spl250_283
  <=> ! [X0: fun_nat_fun_int_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_283])]) ).

tff(f5234,plain,
    ! [X0: fun_nat_fun_int_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f2857]) ).

tff(f2857,plain,
    ! [X0: fun_nat_fun_int_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(ennf_transformation,[],[f1806]) ).

tff(f1806,plain,
    ! [X0: fun_nat_fun_int_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
     => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X0,X1))) ),
    inference(rectify,[],[f15]) ).

tff(f15,axiom,
    ! [X3: fun_nat_fun_int_bool,X4: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
     => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_finite__imageI) ).

tff(f8955,plain,
    spl250_282,
    inference(avatar_split_clause,[],[f5233,f8953]) ).

tff(f8953,plain,
    ( spl250_282
  <=> ! [X0: fun_na936072029e_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_282])]) ).

tff(f5233,plain,
    ! [X0: fun_na936072029e_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(cnf_transformation,[],[f2856]) ).

tff(f2856,plain,
    ! [X0: fun_na936072029e_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
    inference(ennf_transformation,[],[f1805]) ).

tff(f1805,plain,
    ! [X0: fun_na936072029e_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X0,X1))) ),
    inference(rectify,[],[f17]) ).

tff(f17,axiom,
    ! [X3: fun_na936072029e_bool,X4: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_finite__imageI) ).

tff(f8951,plain,
    spl250_281,
    inference(avatar_split_clause,[],[f5211,f8949]) ).

tff(f8949,plain,
    ( spl250_281
  <=> ! [X0: fun_fu819804446l_bool] :
        ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK105(X0)),sK106(X0)))
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_281])]) ).

tff(f5211,plain,
    ! [X0: fun_fu819804446l_bool] :
      ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK105(X0)),sK106(X0)))
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f3957]) ).

tff(f8947,plain,
    spl250_280,
    inference(avatar_split_clause,[],[f5196,f8945]) ).

tff(f8945,plain,
    ( spl250_280
  <=> ! [X0: fun_int_a,X1: fun_int_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_280])]) ).

tff(f5196,plain,
    ! [X0: fun_int_a,X1: fun_int_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f2822]) ).

tff(f2822,plain,
    ! [X0: fun_int_a,X1: fun_int_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(ennf_transformation,[],[f1782]) ).

tff(f1782,plain,
    ! [X0: fun_int_a,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
     => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X0,X1))) ),
    inference(rectify,[],[f19]) ).

tff(f19,axiom,
    ! [X3: fun_int_a,X4: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
     => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_finite__imageI) ).

tff(f8943,plain,
    spl250_279,
    inference(avatar_split_clause,[],[f5195,f8941]) ).

tff(f8941,plain,
    ( spl250_279
  <=> ! [X0: fun_in2065004473e_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_279])]) ).

tff(f5195,plain,
    ! [X0: fun_in2065004473e_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f2821]) ).

tff(f2821,plain,
    ! [X0: fun_in2065004473e_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(ennf_transformation,[],[f1781]) ).

tff(f1781,plain,
    ! [X0: fun_in2065004473e_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X0,X1))) ),
    inference(rectify,[],[f22]) ).

tff(f22,axiom,
    ! [X3: fun_in2065004473e_bool,X4: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_finite__imageI) ).

tff(f8939,plain,
    spl250_278,
    inference(avatar_split_clause,[],[f5194,f8937]) ).

tff(f8937,plain,
    ( spl250_278
  <=> ! [X0: fun_int_fun_a_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_278])]) ).

tff(f5194,plain,
    ! [X0: fun_int_fun_a_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f2820]) ).

tff(f2820,plain,
    ! [X0: fun_int_fun_a_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(ennf_transformation,[],[f1780]) ).

tff(f1780,plain,
    ! [X0: fun_int_fun_a_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
     => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X0,X1))) ),
    inference(rectify,[],[f23]) ).

tff(f23,axiom,
    ! [X3: fun_int_fun_a_bool,X4: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
     => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_finite__imageI) ).

tff(f8935,plain,
    spl250_277,
    inference(avatar_split_clause,[],[f5193,f8933]) ).

tff(f8933,plain,
    ( spl250_277
  <=> ! [X0: fun_int_fun_nat_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_277])]) ).

tff(f5193,plain,
    ! [X0: fun_int_fun_nat_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f2819]) ).

tff(f2819,plain,
    ! [X0: fun_int_fun_nat_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(ennf_transformation,[],[f1779]) ).

tff(f1779,plain,
    ! [X0: fun_int_fun_nat_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
     => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X0,X1))) ),
    inference(rectify,[],[f21]) ).

tff(f21,axiom,
    ! [X3: fun_int_fun_nat_bool,X4: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
     => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_finite__imageI) ).

tff(f8931,plain,
    spl250_276,
    inference(avatar_split_clause,[],[f5192,f8929]) ).

tff(f8929,plain,
    ( spl250_276
  <=> ! [X0: fun_int_fun_int_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_276])]) ).

tff(f5192,plain,
    ! [X0: fun_int_fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(cnf_transformation,[],[f2818]) ).

tff(f2818,plain,
    ! [X0: fun_int_fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
    inference(ennf_transformation,[],[f1778]) ).

tff(f1778,plain,
    ! [X0: fun_int_fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
     => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X0,X1))) ),
    inference(rectify,[],[f20]) ).

tff(f20,axiom,
    ! [X3: fun_int_fun_int_bool,X4: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4))
     => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_finite__imageI) ).

tff(f8927,plain,
    spl250_275,
    inference(avatar_split_clause,[],[f5172,f8925]) ).

tff(f8925,plain,
    ( spl250_275
  <=> ! [X0: fun_fun_a_bool_bool] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK98(X0)),sK99(X0)))
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_275])]) ).

tff(f5172,plain,
    ! [X0: fun_fun_a_bool_bool] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK98(X0)),sK99(X0)))
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f3947]) ).

tff(f8923,plain,
    spl250_274,
    inference(avatar_split_clause,[],[f5155,f8921]) ).

tff(f8921,plain,
    ( spl250_274
  <=> ! [X0: fun_a_nat,X1: fun_a_bool] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_274])]) ).

tff(f5155,plain,
    ! [X0: fun_a_nat,X1: fun_a_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(cnf_transformation,[],[f2783]) ).

tff(f2783,plain,
    ! [X0: fun_a_nat,X1: fun_a_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(ennf_transformation,[],[f1754]) ).

tff(f1754,plain,
    ! [X0: fun_a_nat,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X0,X1))) ),
    inference(rectify,[],[f29]) ).

tff(f29,axiom,
    ! [X3: fun_a_nat,X4: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_finite__imageI) ).

tff(f8919,plain,
    spl250_273,
    inference(avatar_split_clause,[],[f5154,f8917]) ).

tff(f8917,plain,
    ( spl250_273
  <=> ! [X0: fun_a_int,X1: fun_a_bool] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_a_int(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_273])]) ).

tff(f5154,plain,
    ! [X0: fun_a_int,X1: fun_a_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_a_int(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(cnf_transformation,[],[f2782]) ).

tff(f2782,plain,
    ! [X0: fun_a_int,X1: fun_a_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_a_int(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(ennf_transformation,[],[f1753]) ).

tff(f1753,plain,
    ! [X0: fun_a_int,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_a_int(X0,X1))) ),
    inference(rectify,[],[f34]) ).

tff(f34,axiom,
    ! [X3: fun_a_int,X4: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_a_int(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_finite__imageI) ).

tff(f8915,plain,
    spl250_272,
    inference(avatar_split_clause,[],[f5153,f8913]) ).

tff(f8913,plain,
    ( spl250_272
  <=> ! [X0: fun_a_pname,X1: fun_a_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X0,X1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_272])]) ).

tff(f5153,plain,
    ! [X0: fun_a_pname,X1: fun_a_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(cnf_transformation,[],[f2781]) ).

tff(f2781,plain,
    ! [X0: fun_a_pname,X1: fun_a_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X0,X1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
    inference(ennf_transformation,[],[f1752]) ).

tff(f1752,plain,
    ! [X0: fun_a_pname,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X0,X1))) ),
    inference(rectify,[],[f24]) ).

tff(f24,axiom,
    ! [X3: fun_a_pname,X4: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_finite__imageI) ).

tff(f8911,plain,
    spl250_271,
    inference(avatar_split_clause,[],[f5131,f8909]) ).

tff(f8909,plain,
    ( spl250_271
  <=> ! [X0: fun_fu1430349052l_bool] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK91(X0)),sK92(X0)))
        | ~ sP0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_271])]) ).

tff(f5131,plain,
    ! [X0: fun_fu1430349052l_bool] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK91(X0)),sK92(X0)))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f3936]) ).

tff(f8907,plain,
    spl250_270,
    inference(avatar_split_clause,[],[f5113,f8905]) ).

tff(f8905,plain,
    ( spl250_270
  <=> ! [X0: fun_pname_a,X1: fun_pname_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_270])]) ).

tff(f5113,plain,
    ! [X0: fun_pname_a,X1: fun_pname_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f2744]) ).

tff(f2744,plain,
    ! [X0: fun_pname_a,X1: fun_pname_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(ennf_transformation,[],[f1726]) ).

tff(f1726,plain,
    ! [X0: fun_pname_a,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
     => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X0,X1))) ),
    inference(rectify,[],[f39]) ).

tff(f39,axiom,
    ! [X3: fun_pname_a,X4: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
     => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_finite__imageI) ).

tff(f8903,plain,
    spl250_269,
    inference(avatar_split_clause,[],[f5112,f8901]) ).

tff(f8901,plain,
    ( spl250_269
  <=> ! [X0: fun_pname_fun_a_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_269])]) ).

tff(f5112,plain,
    ! [X0: fun_pname_fun_a_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f2743]) ).

tff(f2743,plain,
    ! [X0: fun_pname_fun_a_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(ennf_transformation,[],[f1725]) ).

tff(f1725,plain,
    ! [X0: fun_pname_fun_a_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
     => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X0,X1))) ),
    inference(rectify,[],[f13]) ).

tff(f13,axiom,
    ! [X3: fun_pname_fun_a_bool,X4: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
     => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_finite__imageI) ).

tff(f8899,plain,
    spl250_268,
    inference(avatar_split_clause,[],[f5111,f8897]) ).

tff(f8897,plain,
    ( spl250_268
  <=> ! [X0: fun_pn665169337t_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1512837979t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_268])]) ).

tff(f5111,plain,
    ! [X0: fun_pn665169337t_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1512837979t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f2742]) ).

tff(f2742,plain,
    ! [X0: fun_pn665169337t_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1512837979t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(ennf_transformation,[],[f1724]) ).

tff(f1724,plain,
    ! [X0: fun_pn665169337t_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
     => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1512837979t_bool(X0,X1))) ),
    inference(rectify,[],[f10]) ).

tff(f10,axiom,
    ! [X3: fun_pn665169337t_bool,X4: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
     => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1512837979t_bool(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_finite__imageI) ).

tff(f8895,plain,
    spl250_267,
    inference(avatar_split_clause,[],[f5110,f8893]) ).

tff(f8893,plain,
    ( spl250_267
  <=> ! [X0: fun_pn406123357t_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_267])]) ).

tff(f5110,plain,
    ! [X0: fun_pn406123357t_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f2741]) ).

tff(f2741,plain,
    ! [X0: fun_pn406123357t_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(ennf_transformation,[],[f1723]) ).

tff(f1723,plain,
    ! [X0: fun_pn406123357t_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
     => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X0,X1))) ),
    inference(rectify,[],[f11]) ).

tff(f11,axiom,
    ! [X3: fun_pn406123357t_bool,X4: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
     => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_finite__imageI) ).

tff(f8891,plain,
    spl250_266,
    inference(avatar_split_clause,[],[f5109,f8889]) ).

tff(f8889,plain,
    ( spl250_266
  <=> ! [X0: fun_pn800050071e_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X0,X1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_266])]) ).

tff(f5109,plain,
    ! [X0: fun_pn800050071e_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(cnf_transformation,[],[f2740]) ).

tff(f2740,plain,
    ! [X0: fun_pn800050071e_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X0,X1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
    inference(ennf_transformation,[],[f1722]) ).

tff(f1722,plain,
    ! [X0: fun_pn800050071e_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X0,X1))) ),
    inference(rectify,[],[f12]) ).

tff(f12,axiom,
    ! [X3: fun_pn800050071e_bool,X4: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_finite__imageI) ).

tff(f8887,plain,
    spl250_265,
    inference(avatar_split_clause,[],[f5064,f8885]) ).

tff(f8885,plain,
    ( spl250_265
  <=> ! [X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X0,X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_265])]) ).

tff(f5064,plain,
    ! [X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(cnf_transformation,[],[f2683]) ).

tff(f2683,plain,
    ! [X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(ennf_transformation,[],[f1681]) ).

tff(f1681,plain,
    ! [X0: fun_fu1668467777ol_nat,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X0,X1))) ),
    inference(rectify,[],[f32]) ).

tff(f32,axiom,
    ! [X3: fun_fu1668467777ol_nat,X4: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_finite__imageI) ).

tff(f8883,plain,
    spl250_264,
    inference(avatar_split_clause,[],[f5063,f8881]) ).

tff(f8881,plain,
    ( spl250_264
  <=> ! [X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X0,X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_264])]) ).

tff(f5063,plain,
    ! [X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(cnf_transformation,[],[f2682]) ).

tff(f2682,plain,
    ! [X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(ennf_transformation,[],[f1680]) ).

tff(f1680,plain,
    ! [X0: fun_fun_nat_bool_nat,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X0,X1))) ),
    inference(rectify,[],[f31]) ).

tff(f31,axiom,
    ! [X3: fun_fun_nat_bool_nat,X4: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_finite__imageI) ).

tff(f8879,plain,
    spl250_263,
    inference(avatar_split_clause,[],[f5062,f8877]) ).

tff(f8877,plain,
    ( spl250_263
  <=> ! [X0: fun_fun_int_bool_nat,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1431733819ol_nat(X0,X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_263])]) ).

tff(f5062,plain,
    ! [X0: fun_fun_int_bool_nat,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1431733819ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(cnf_transformation,[],[f2681]) ).

tff(f2681,plain,
    ! [X0: fun_fun_int_bool_nat,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1431733819ol_nat(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(ennf_transformation,[],[f1679]) ).

tff(f1679,plain,
    ! [X0: fun_fun_int_bool_nat,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1431733819ol_nat(X0,X1))) ),
    inference(rectify,[],[f30]) ).

tff(f30,axiom,
    ! [X3: fun_fun_int_bool_nat,X4: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1431733819ol_nat(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_finite__imageI) ).

tff(f8875,plain,
    ( spl250_262
    | ~ spl250_113
    | ~ spl250_214 ),
    inference(avatar_split_clause,[],[f8629,f8405,f7865,f8873]) ).

tff(f8873,plain,
    ( spl250_262
  <=> ! [X0: nat] : ( bot_bot_fun_nat_bool != hAPP_n1699378549t_bool(fequal_nat,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_262])]) ).

tff(f7865,plain,
    ( spl250_113
  <=> ! [X0: nat,X1: fun_nat_bool] : ( bot_bot_fun_nat_bool != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_113])]) ).

tff(f8405,plain,
    ( spl250_214
  <=> ! [X0: nat] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) = hAPP_n1699378549t_bool(fequal_nat,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_214])]) ).

tff(f8629,plain,
    ( ! [X0: nat] : ( bot_bot_fun_nat_bool != hAPP_n1699378549t_bool(fequal_nat,X0) )
    | ~ spl250_113
    | ~ spl250_214 ),
    inference(superposition,[],[f7866,f8406]) ).

tff(f8406,plain,
    ( ! [X0: nat] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool) = hAPP_n1699378549t_bool(fequal_nat,X0) )
    | ~ spl250_214 ),
    inference(avatar_component_clause,[],[f8405]) ).

tff(f7866,plain,
    ( ! [X0: nat,X1: fun_nat_bool] : ( bot_bot_fun_nat_bool != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) )
    | ~ spl250_113 ),
    inference(avatar_component_clause,[],[f7865]) ).

tff(f8871,plain,
    spl250_261,
    inference(avatar_split_clause,[],[f5061,f8869]) ).

tff(f8869,plain,
    ( spl250_261
  <=> ! [X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X0,X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_261])]) ).

tff(f5061,plain,
    ! [X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(cnf_transformation,[],[f2680]) ).

tff(f2680,plain,
    ! [X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(ennf_transformation,[],[f1678]) ).

tff(f1678,plain,
    ! [X0: fun_fun_a_bool_nat,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X0,X1))) ),
    inference(rectify,[],[f33]) ).

tff(f33,axiom,
    ! [X3: fun_fun_a_bool_nat,X4: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_finite__imageI) ).

tff(f8867,plain,
    spl250_260,
    inference(avatar_split_clause,[],[f5060,f8865]) ).

tff(f8865,plain,
    ( spl250_260
  <=> ! [X0: fun_fun_nat_bool_int,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_1133522419ol_int(X0,X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_260])]) ).

tff(f5060,plain,
    ! [X0: fun_fun_nat_bool_int,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_1133522419ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(cnf_transformation,[],[f2679]) ).

tff(f2679,plain,
    ! [X0: fun_fun_nat_bool_int,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_1133522419ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(ennf_transformation,[],[f1677]) ).

tff(f1677,plain,
    ! [X0: fun_fun_nat_bool_int,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_1133522419ol_int(X0,X1))) ),
    inference(rectify,[],[f36]) ).

tff(f36,axiom,
    ! [X3: fun_fun_nat_bool_int,X4: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4))
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_1133522419ol_int(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_finite__imageI) ).

tff(f8863,plain,
    spl250_259,
    inference(avatar_split_clause,[],[f5059,f8861]) ).

tff(f8861,plain,
    ( spl250_259
  <=> ! [X0: fun_fun_a_bool_int,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_fun_a_bool_int(X0,X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_259])]) ).

tff(f5059,plain,
    ! [X0: fun_fun_a_bool_int,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_fun_a_bool_int(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(cnf_transformation,[],[f2678]) ).

tff(f2678,plain,
    ! [X0: fun_fun_a_bool_int,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_fun_a_bool_int(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(ennf_transformation,[],[f1676]) ).

tff(f1676,plain,
    ! [X0: fun_fun_a_bool_int,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_fun_a_bool_int(X0,X1))) ),
    inference(rectify,[],[f38]) ).

tff(f38,axiom,
    ! [X3: fun_fun_a_bool_int,X4: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4))
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_fun_a_bool_int(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_finite__imageI) ).

tff(f8859,plain,
    spl250_258,
    inference(avatar_split_clause,[],[f5058,f8857]) ).

tff(f8857,plain,
    ( spl250_258
  <=> ! [X0: fun_fu1830380701ol_int,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_41399353ol_int(X0,X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_258])]) ).

tff(f5058,plain,
    ! [X0: fun_fu1830380701ol_int,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_41399353ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(cnf_transformation,[],[f2677]) ).

tff(f2677,plain,
    ! [X0: fun_fu1830380701ol_int,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_41399353ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(ennf_transformation,[],[f1675]) ).

tff(f1675,plain,
    ! [X0: fun_fu1830380701ol_int,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_41399353ol_int(X0,X1))) ),
    inference(rectify,[],[f37]) ).

tff(f37,axiom,
    ! [X3: fun_fu1830380701ol_int,X4: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4))
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_41399353ol_int(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_finite__imageI) ).

tff(f8855,plain,
    spl250_257,
    inference(avatar_split_clause,[],[f5057,f8853]) ).

tff(f8853,plain,
    ( spl250_257
  <=> ! [X0: fun_fun_int_bool_int,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_2069007511ol_int(X0,X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_257])]) ).

tff(f5057,plain,
    ! [X0: fun_fun_int_bool_int,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_2069007511ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(cnf_transformation,[],[f2676]) ).

tff(f2676,plain,
    ! [X0: fun_fun_int_bool_int,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_2069007511ol_int(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(ennf_transformation,[],[f1674]) ).

tff(f1674,plain,
    ! [X0: fun_fun_int_bool_int,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_2069007511ol_int(X0,X1))) ),
    inference(rectify,[],[f35]) ).

tff(f35,axiom,
    ! [X3: fun_fun_int_bool_int,X4: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4))
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_2069007511ol_int(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_finite__imageI) ).

tff(f8851,plain,
    spl250_256,
    inference(avatar_split_clause,[],[f5056,f8849]) ).

tff(f8849,plain,
    ( spl250_256
  <=> ! [X0: fun_fu1499449723_pname,X1: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_256])]) ).

tff(f5056,plain,
    ! [X0: fun_fu1499449723_pname,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(cnf_transformation,[],[f2675]) ).

tff(f2675,plain,
    ! [X0: fun_fu1499449723_pname,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
    inference(ennf_transformation,[],[f1673]) ).

tff(f1673,plain,
    ! [X0: fun_fu1499449723_pname,X1: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X0,X1))) ),
    inference(rectify,[],[f27]) ).

tff(f27,axiom,
    ! [X3: fun_fu1499449723_pname,X4: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_finite__imageI) ).

tff(f8847,plain,
    spl250_255,
    inference(avatar_split_clause,[],[f5055,f8845]) ).

tff(f8845,plain,
    ( spl250_255
  <=> ! [X0: fun_fun_a_bool_pname,X1: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X0,X1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_255])]) ).

tff(f5055,plain,
    ! [X0: fun_fun_a_bool_pname,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(cnf_transformation,[],[f2674]) ).

tff(f2674,plain,
    ! [X0: fun_fun_a_bool_pname,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X0,X1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
    inference(ennf_transformation,[],[f1672]) ).

tff(f1672,plain,
    ! [X0: fun_fun_a_bool_pname,X1: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X0,X1))) ),
    inference(rectify,[],[f28]) ).

tff(f28,axiom,
    ! [X3: fun_fun_a_bool_pname,X4: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_finite__imageI) ).

tff(f8843,plain,
    spl250_254,
    inference(avatar_split_clause,[],[f5054,f8841]) ).

tff(f8841,plain,
    ( spl250_254
  <=> ! [X0: fun_fu665170229_pname,X1: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X0,X1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_254])]) ).

tff(f5054,plain,
    ! [X0: fun_fu665170229_pname,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(cnf_transformation,[],[f2673]) ).

tff(f2673,plain,
    ! [X0: fun_fu665170229_pname,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X0,X1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
    inference(ennf_transformation,[],[f1671]) ).

tff(f1671,plain,
    ! [X0: fun_fu665170229_pname,X1: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X0,X1))) ),
    inference(rectify,[],[f26]) ).

tff(f26,axiom,
    ! [X3: fun_fu665170229_pname,X4: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_finite__imageI) ).

tff(f8839,plain,
    spl250_253,
    inference(avatar_split_clause,[],[f5053,f8837]) ).

tff(f8837,plain,
    ( spl250_253
  <=> ! [X0: fun_fu953875929_pname,X1: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_62782965_pname(X0,X1)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_253])]) ).

tff(f5053,plain,
    ! [X0: fun_fu953875929_pname,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_62782965_pname(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(cnf_transformation,[],[f2672]) ).

tff(f2672,plain,
    ! [X0: fun_fu953875929_pname,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_62782965_pname(X0,X1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
    inference(ennf_transformation,[],[f1670]) ).

tff(f1670,plain,
    ! [X0: fun_fu953875929_pname,X1: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_62782965_pname(X0,X1))) ),
    inference(rectify,[],[f25]) ).

tff(f25,axiom,
    ! [X3: fun_fu953875929_pname,X4: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_62782965_pname(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_finite__imageI) ).

tff(f8835,plain,
    spl250_252,
    inference(avatar_split_clause,[],[f4986,f8833]) ).

tff(f8833,plain,
    ( spl250_252
  <=> ! [X0: bool,X1: bool] :
        ( hBOOL(X1)
        | hBOOL(X0)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_252])]) ).

tff(f4986,plain,
    ! [X0: bool,X1: bool] :
      ( hBOOL(X1)
      | hBOOL(X0)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1)) ),
    inference(cnf_transformation,[],[f1622]) ).

tff(f1622,plain,
    ! [X0: bool,X1: bool] :
      ( hBOOL(X1)
      | hBOOL(X0)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1)) ),
    inference(rectify,[],[f1207]) ).

tff(f1207,axiom,
    ! [X156: bool,X157: bool] :
      ( hBOOL(X157)
      | hBOOL(X156)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X156),X157)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).

tff(f8831,plain,
    ( spl250_251
    | ~ spl250_112
    | ~ spl250_213 ),
    inference(avatar_split_clause,[],[f8628,f8401,f7861,f8829]) ).

tff(f8829,plain,
    ( spl250_251
  <=> ! [X0: int] : ( bot_bot_fun_int_bool != hAPP_i1948725293t_bool(fequal_int,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_251])]) ).

tff(f7861,plain,
    ( spl250_112
  <=> ! [X0: int,X1: fun_int_bool] : ( bot_bot_fun_int_bool != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_112])]) ).

tff(f8401,plain,
    ( spl250_213
  <=> ! [X0: int] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = hAPP_i1948725293t_bool(fequal_int,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_213])]) ).

tff(f8628,plain,
    ( ! [X0: int] : ( bot_bot_fun_int_bool != hAPP_i1948725293t_bool(fequal_int,X0) )
    | ~ spl250_112
    | ~ spl250_213 ),
    inference(superposition,[],[f7862,f8402]) ).

tff(f8402,plain,
    ( ! [X0: int] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool) = hAPP_i1948725293t_bool(fequal_int,X0) )
    | ~ spl250_213 ),
    inference(avatar_component_clause,[],[f8401]) ).

tff(f7862,plain,
    ( ! [X0: int,X1: fun_int_bool] : ( bot_bot_fun_int_bool != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) )
    | ~ spl250_112 ),
    inference(avatar_component_clause,[],[f7861]) ).

tff(f8827,plain,
    spl250_250,
    inference(avatar_split_clause,[],[f4985,f8825]) ).

tff(f8825,plain,
    ( spl250_250
  <=> ! [X0: bool,X1: bool] :
        ( hBOOL(X1)
        | ~ hBOOL(X0)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_250])]) ).

tff(f4985,plain,
    ! [X0: bool,X1: bool] :
      ( hBOOL(X1)
      | ~ hBOOL(X0)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1)) ),
    inference(cnf_transformation,[],[f1621]) ).

tff(f1621,plain,
    ! [X0: bool,X1: bool] :
      ( hBOOL(X1)
      | ~ hBOOL(X0)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1)) ),
    inference(rectify,[],[f1212]) ).

tff(f1212,axiom,
    ! [X156: bool,X157: bool] :
      ( hBOOL(X157)
      | ~ hBOOL(X156)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X156),X157)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).

tff(f8823,plain,
    spl250_249,
    inference(avatar_split_clause,[],[f4970,f8821]) ).

tff(f8821,plain,
    ( spl250_249
  <=> ! [X0: bool,X1: bool] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X0))
        | ~ hBOOL(X0)
        | ~ hBOOL(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_249])]) ).

tff(f4970,plain,
    ! [X0: bool,X1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X0))
      | ~ hBOOL(X0)
      | ~ hBOOL(X1) ),
    inference(cnf_transformation,[],[f1606]) ).

tff(f1606,plain,
    ! [X0: bool,X1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X0))
      | ~ hBOOL(X0)
      | ~ hBOOL(X1) ),
    inference(rectify,[],[f1202]) ).

tff(f1202,axiom,
    ! [X157: bool,X156: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X156),X157))
      | ~ hBOOL(X157)
      | ~ hBOOL(X156) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).

tff(f8819,plain,
    spl250_248,
    inference(avatar_split_clause,[],[f4897,f8817]) ).

tff(f8817,plain,
    ( spl250_248
  <=> ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_248])]) ).

tff(f4897,plain,
    ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X0)),
    inference(cnf_transformation,[],[f1545]) ).

tff(f1545,plain,
    ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X1)),X0)),
    inference(rectify,[],[f180]) ).

tff(f180,axiom,
    ! [X12: nat,X11: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X12),X11)),X12)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_diff__le__self) ).

tff(f8815,plain,
    spl250_247,
    inference(avatar_split_clause,[],[f4896,f8813]) ).

tff(f8813,plain,
    ( spl250_247
  <=> ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_247])]) ).

tff(f4896,plain,
    ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0))),
    inference(cnf_transformation,[],[f1544]) ).

tff(f1544,plain,
    ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X0))),
    inference(rectify,[],[f823]) ).

tff(f823,axiom,
    ! [X11: nat,X12: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X11),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X12),X11))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_822_le__add2) ).

tff(f8811,plain,
    spl250_246,
    inference(avatar_split_clause,[],[f4895,f8809]) ).

tff(f8809,plain,
    ( spl250_246
  <=> ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_246])]) ).

tff(f4895,plain,
    ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1))),
    inference(cnf_transformation,[],[f1543]) ).

tff(f1543,plain,
    ! [X0: nat,X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1))),
    inference(rectify,[],[f824]) ).

tff(f824,axiom,
    ! [X11: nat,X12: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X11),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X11),X12))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_823_le__add1) ).

tff(f8807,plain,
    spl250_245,
    inference(avatar_split_clause,[],[f4894,f8805]) ).

tff(f8805,plain,
    ( spl250_245
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_245])]) ).

tff(f4894,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1)),X0)),
    inference(cnf_transformation,[],[f1542]) ).

tff(f1542,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X1)),X0)),
    inference(rectify,[],[f588]) ).

tff(f588,axiom,
    ! [X2: fun_nat_bool,X7: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X7)),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_587_Diff__subset) ).

tff(f8803,plain,
    spl250_244,
    inference(avatar_split_clause,[],[f4893,f8801]) ).

tff(f4893,plain,
    ! [X0: fun_nat_bool,X1: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0))),
    inference(cnf_transformation,[],[f1541]) ).

tff(f1541,plain,
    ! [X0: fun_nat_bool,X1: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X0))),
    inference(rectify,[],[f453]) ).

tff(f453,axiom,
    ! [X7: fun_nat_bool,X5: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5),X7))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_452_subset__insertI) ).

tff(f8799,plain,
    spl250_243,
    inference(avatar_split_clause,[],[f4892,f8797]) ).

tff(f8797,plain,
    ( spl250_243
  <=> ! [X0: nat,X1: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_243])]) ).

tff(f4892,plain,
    ! [X0: nat,X1: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1))),
    inference(cnf_transformation,[],[f1540]) ).

tff(f1540,plain,
    ! [X0: nat,X1: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1))),
    inference(rectify,[],[f368]) ).

tff(f368,axiom,
    ! [X5: nat,X7: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5),X7))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_367_insertI1) ).

tff(f8795,plain,
    spl250_242,
    inference(avatar_split_clause,[],[f4891,f8793]) ).

tff(f8793,plain,
    ( spl250_242
  <=> ! [X0: fun_int_bool,X1: fun_int_bool] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_242])]) ).

tff(f4891,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1)),X0)),
    inference(cnf_transformation,[],[f1539]) ).

tff(f1539,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X1)),X0)),
    inference(rectify,[],[f587]) ).

tff(f587,axiom,
    ! [X2: fun_int_bool,X7: fun_int_bool] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X7)),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_586_Diff__subset) ).

tff(f8791,plain,
    spl250_241,
    inference(avatar_split_clause,[],[f4890,f8789]) ).

tff(f4890,plain,
    ! [X0: fun_int_bool,X1: int] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0))),
    inference(cnf_transformation,[],[f1538]) ).

tff(f1538,plain,
    ! [X0: fun_int_bool,X1: int] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X0))),
    inference(rectify,[],[f452]) ).

tff(f452,axiom,
    ! [X7: fun_int_bool,X5: int] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X7),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5),X7))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_451_subset__insertI) ).

tff(f8722,plain,
    spl250_240,
    inference(avatar_split_clause,[],[f4889,f8720]) ).

tff(f8720,plain,
    ( spl250_240
  <=> ! [X0: int,X1: fun_int_bool] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_240])]) ).

tff(f4889,plain,
    ! [X0: int,X1: fun_int_bool] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1))),
    inference(cnf_transformation,[],[f1537]) ).

tff(f1537,plain,
    ! [X0: int,X1: fun_int_bool] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1))),
    inference(rectify,[],[f367]) ).

tff(f367,axiom,
    ! [X5: int,X7: fun_int_bool] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5),X7))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_366_insertI1) ).

tff(f8718,plain,
    spl250_239,
    inference(avatar_split_clause,[],[f4888,f8716]) ).

tff(f8716,plain,
    ( spl250_239
  <=> ! [X0: fun_a_bool,X1: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X1)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_239])]) ).

tff(f4888,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X1)),X0)),
    inference(cnf_transformation,[],[f1536]) ).

tff(f1536,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X1)),X0)),
    inference(rectify,[],[f589]) ).

tff(f589,axiom,
    ! [X2: fun_a_bool,X7: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X7)),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_588_Diff__subset) ).

tff(f8714,plain,
    spl250_238,
    inference(avatar_split_clause,[],[f4887,f8712]) ).

tff(f4887,plain,
    ! [X0: fun_a_bool,X1: x_a] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0))),
    inference(cnf_transformation,[],[f1535]) ).

tff(f1535,plain,
    ! [X0: fun_a_bool,X1: x_a] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X0))),
    inference(rectify,[],[f451]) ).

tff(f451,axiom,
    ! [X7: fun_a_bool,X5: x_a] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),X7))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_450_subset__insertI) ).

tff(f8710,plain,
    spl250_237,
    inference(avatar_split_clause,[],[f4886,f8708]) ).

tff(f8708,plain,
    ( spl250_237
  <=> ! [X0: x_a,X1: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_237])]) ).

tff(f4886,plain,
    ! [X0: x_a,X1: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1))),
    inference(cnf_transformation,[],[f1534]) ).

tff(f1534,plain,
    ! [X0: x_a,X1: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1))),
    inference(rectify,[],[f366]) ).

tff(f366,axiom,
    ! [X5: x_a,X7: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),X7))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_insertI1) ).

tff(f8706,plain,
    spl250_236,
    inference(avatar_split_clause,[],[f4885,f8704]) ).

tff(f8704,plain,
    ( spl250_236
  <=> ! [X0: pname,X1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_236])]) ).

tff(f4885,plain,
    ! [X0: pname,X1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1))),
    inference(cnf_transformation,[],[f1533]) ).

tff(f1533,plain,
    ! [X0: pname,X1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X0),X1))),
    inference(rectify,[],[f369]) ).

tff(f369,axiom,
    ! [X5: pname,X7: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5),X7))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_368_insertI1) ).

tff(f8702,plain,
    spl250_235,
    inference(avatar_split_clause,[],[f4884,f8700]) ).

tff(f8700,plain,
    ( spl250_235
  <=> ! [X0: nat,X1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_235])]) ).

tff(f4884,plain,
    ! [X0: nat,X1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X0)),
    inference(cnf_transformation,[],[f1532]) ).

tff(f1532,plain,
    ! [X0: nat,X1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X0)),
    inference(rectify,[],[f877]) ).

tff(f877,axiom,
    ! [X20: nat,X21: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X20),X21)),X20)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_876_not__add__less1) ).

tff(f8698,plain,
    spl250_234,
    inference(avatar_split_clause,[],[f4883,f8696]) ).

tff(f8696,plain,
    ( spl250_234
  <=> ! [X0: nat,X1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_234])]) ).

tff(f4883,plain,
    ! [X0: nat,X1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X1)),
    inference(cnf_transformation,[],[f1531]) ).

tff(f1531,plain,
    ! [X0: nat,X1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),X1)),X1)),
    inference(rectify,[],[f878]) ).

tff(f878,axiom,
    ! [X21: nat,X20: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X21),X20)),X20)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_877_not__add__less2) ).

tff(f8694,plain,
    spl250_233,
    inference(avatar_split_clause,[],[f4865,f8692]) ).

tff(f8692,plain,
    ( spl250_233
  <=> ! [X0: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK72(X0)),X0))
        | ( bot_bot_fun_nat_bool = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_233])]) ).

tff(f4865,plain,
    ! [X0: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK72(X0)),X0))
      | ( bot_bot_fun_nat_bool = X0 ) ),
    inference(cnf_transformation,[],[f3897]) ).

tff(f3897,plain,
    ! [X0: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK72(X0)),X0))
        | ( bot_bot_fun_nat_bool = X0 ) )
      & ( ( bot_bot_fun_nat_bool != X0 )
        | ! [X2: nat] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK72])],[f3895,f3896]) ).

tff(f3896,plain,
    ! [X0: fun_nat_bool] :
      ( ? [X1: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK72(X0)),X0)) ),
    introduced(choice_axiom,[]) ).

tff(f3895,plain,
    ! [X0: fun_nat_bool] :
      ( ( ? [X1: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
        | ( bot_bot_fun_nat_bool = X0 ) )
      & ( ( bot_bot_fun_nat_bool != X0 )
        | ! [X2: nat] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) ) ),
    inference(rectify,[],[f3894]) ).

tff(f3894,plain,
    ! [X0: fun_nat_bool] :
      ( ( ? [X1: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
        | ( bot_bot_fun_nat_bool = X0 ) )
      & ( ( bot_bot_fun_nat_bool != X0 )
        | ! [X1: nat] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) ) ),
    inference(nnf_transformation,[],[f1515]) ).

tff(f1515,plain,
    ! [X0: fun_nat_bool] :
      ( ? [X1: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
    <=> ( bot_bot_fun_nat_bool != X0 ) ),
    inference(rectify,[],[f529]) ).

tff(f529,axiom,
    ! [X2: fun_nat_bool] :
      ( ? [X27: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X27),X2))
    <=> ( bot_bot_fun_nat_bool != X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_528_ex__in__conv) ).

tff(f8690,plain,
    spl250_232,
    inference(avatar_split_clause,[],[f4863,f8688]) ).

tff(f8688,plain,
    ( spl250_232
  <=> ! [X0: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK71(X0)),X0))
        | ( bot_bot_fun_int_bool = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_232])]) ).

tff(f4863,plain,
    ! [X0: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK71(X0)),X0))
      | ( bot_bot_fun_int_bool = X0 ) ),
    inference(cnf_transformation,[],[f3893]) ).

tff(f3893,plain,
    ! [X0: fun_int_bool] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK71(X0)),X0))
        | ( bot_bot_fun_int_bool = X0 ) )
      & ( ( bot_bot_fun_int_bool != X0 )
        | ! [X2: int] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK71])],[f3891,f3892]) ).

tff(f3892,plain,
    ! [X0: fun_int_bool] :
      ( ? [X1: int] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
     => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK71(X0)),X0)) ),
    introduced(choice_axiom,[]) ).

tff(f3891,plain,
    ! [X0: fun_int_bool] :
      ( ( ? [X1: int] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
        | ( bot_bot_fun_int_bool = X0 ) )
      & ( ( bot_bot_fun_int_bool != X0 )
        | ! [X2: int] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X0)) ) ),
    inference(rectify,[],[f3890]) ).

tff(f3890,plain,
    ! [X0: fun_int_bool] :
      ( ( ? [X1: int] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
        | ( bot_bot_fun_int_bool = X0 ) )
      & ( ( bot_bot_fun_int_bool != X0 )
        | ! [X1: int] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) ) ),
    inference(nnf_transformation,[],[f1514]) ).

tff(f1514,plain,
    ! [X0: fun_int_bool] :
      ( ? [X1: int] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
    <=> ( bot_bot_fun_int_bool != X0 ) ),
    inference(rectify,[],[f528]) ).

tff(f528,axiom,
    ! [X2: fun_int_bool] :
      ( ? [X27: int] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X27),X2))
    <=> ( bot_bot_fun_int_bool != X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_527_ex__in__conv) ).

tff(f8686,plain,
    spl250_231,
    inference(avatar_split_clause,[],[f4861,f8684]) ).

tff(f8684,plain,
    ( spl250_231
  <=> ! [X0: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK70(X0)),X0))
        | ( bot_bot_fun_a_bool = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_231])]) ).

tff(f4861,plain,
    ! [X0: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK70(X0)),X0))
      | ( bot_bot_fun_a_bool = X0 ) ),
    inference(cnf_transformation,[],[f3889]) ).

tff(f3889,plain,
    ! [X0: fun_a_bool] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK70(X0)),X0))
        | ( bot_bot_fun_a_bool = X0 ) )
      & ( ( bot_bot_fun_a_bool != X0 )
        | ! [X2: x_a] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK70])],[f3887,f3888]) ).

tff(f3888,plain,
    ! [X0: fun_a_bool] :
      ( ? [X1: x_a] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK70(X0)),X0)) ),
    introduced(choice_axiom,[]) ).

tff(f3887,plain,
    ! [X0: fun_a_bool] :
      ( ( ? [X1: x_a] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
        | ( bot_bot_fun_a_bool = X0 ) )
      & ( ( bot_bot_fun_a_bool != X0 )
        | ! [X2: x_a] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0)) ) ),
    inference(rectify,[],[f3886]) ).

tff(f3886,plain,
    ! [X0: fun_a_bool] :
      ( ( ? [X1: x_a] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
        | ( bot_bot_fun_a_bool = X0 ) )
      & ( ( bot_bot_fun_a_bool != X0 )
        | ! [X1: x_a] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) ) ),
    inference(nnf_transformation,[],[f1513]) ).

tff(f1513,plain,
    ! [X0: fun_a_bool] :
      ( ? [X1: x_a] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
    <=> ( bot_bot_fun_a_bool != X0 ) ),
    inference(rectify,[],[f530]) ).

tff(f530,axiom,
    ! [X2: fun_a_bool] :
      ( ? [X27: x_a] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X27),X2))
    <=> ( bot_bot_fun_a_bool != X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_529_ex__in__conv) ).

tff(f8680,plain,
    spl250_230,
    inference(avatar_split_clause,[],[f4859,f8678]) ).

tff(f8678,plain,
    ( spl250_230
  <=> ! [X0: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK69(X0)),X0))
        | ( bot_bo844097828e_bool = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_230])]) ).

tff(f4859,plain,
    ! [X0: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK69(X0)),X0))
      | ( bot_bo844097828e_bool = X0 ) ),
    inference(cnf_transformation,[],[f3885]) ).

tff(f3885,plain,
    ! [X0: fun_pname_bool] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK69(X0)),X0))
        | ( bot_bo844097828e_bool = X0 ) )
      & ( ( bot_bo844097828e_bool != X0 )
        | ! [X2: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK69])],[f3883,f3884]) ).

tff(f3884,plain,
    ! [X0: fun_pname_bool] :
      ( ? [X1: pname] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK69(X0)),X0)) ),
    introduced(choice_axiom,[]) ).

tff(f3883,plain,
    ! [X0: fun_pname_bool] :
      ( ( ? [X1: pname] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
        | ( bot_bo844097828e_bool = X0 ) )
      & ( ( bot_bo844097828e_bool != X0 )
        | ! [X2: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X0)) ) ),
    inference(rectify,[],[f3882]) ).

tff(f3882,plain,
    ! [X0: fun_pname_bool] :
      ( ( ? [X1: pname] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
        | ( bot_bo844097828e_bool = X0 ) )
      & ( ( bot_bo844097828e_bool != X0 )
        | ! [X1: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) ) ),
    inference(nnf_transformation,[],[f1512]) ).

tff(f1512,plain,
    ! [X0: fun_pname_bool] :
      ( ? [X1: pname] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
    <=> ( bot_bo844097828e_bool != X0 ) ),
    inference(rectify,[],[f531]) ).

tff(f531,axiom,
    ! [X2: fun_pname_bool] :
      ( ? [X27: pname] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X27),X2))
    <=> ( bot_bo844097828e_bool != X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_530_ex__in__conv) ).

tff(f8676,plain,
    spl250_229,
    inference(avatar_split_clause,[],[f4853,f8674]) ).

tff(f8674,plain,
    ( spl250_229
  <=> ! [X0: fun_nat_bool] :
        ( ( bot_bot_fun_nat_bool = X0 )
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK66(X0)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_229])]) ).

tff(f4853,plain,
    ! [X0: fun_nat_bool] :
      ( ( bot_bot_fun_nat_bool = X0 )
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK66(X0)),X0)) ),
    inference(cnf_transformation,[],[f3876]) ).

tff(f3876,plain,
    ! [X0: fun_nat_bool] :
      ( ( ! [X1: nat] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
        | ( bot_bot_fun_nat_bool != X0 ) )
      & ( ( bot_bot_fun_nat_bool = X0 )
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK66(X0)),X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK66])],[f3874,f3875]) ).

tff(f3875,plain,
    ! [X0: fun_nat_bool] :
      ( ? [X2: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0))
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK66(X0)),X0)) ),
    introduced(choice_axiom,[]) ).

tff(f3874,plain,
    ! [X0: fun_nat_bool] :
      ( ( ! [X1: nat] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
        | ( bot_bot_fun_nat_bool != X0 ) )
      & ( ( bot_bot_fun_nat_bool = X0 )
        | ? [X2: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X0)) ) ),
    inference(rectify,[],[f3873]) ).

tff(f3873,plain,
    ! [X0: fun_nat_bool] :
      ( ( ! [X1: nat] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
        | ( bot_bot_fun_nat_bool != X0 ) )
      & ( ( bot_bot_fun_nat_bool = X0 )
        | ? [X1: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0)) ) ),
    inference(nnf_transformation,[],[f1510]) ).

tff(f1510,plain,
    ! [X0: fun_nat_bool] :
      ( ! [X1: nat] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X0))
    <=> ( bot_bot_fun_nat_bool = X0 ) ),
    inference(rectify,[],[f533]) ).

tff(f533,axiom,
    ! [X2: fun_nat_bool] :
      ( ! [X27: nat] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X27),X2))
    <=> ( bot_bot_fun_nat_bool = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_532_all__not__in__conv) ).

tff(f8672,plain,
    spl250_228,
    inference(avatar_split_clause,[],[f4851,f8670]) ).

tff(f8670,plain,
    ( spl250_228
  <=> ! [X0: fun_int_bool] :
        ( ( bot_bot_fun_int_bool = X0 )
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK65(X0)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_228])]) ).

tff(f4851,plain,
    ! [X0: fun_int_bool] :
      ( ( bot_bot_fun_int_bool = X0 )
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK65(X0)),X0)) ),
    inference(cnf_transformation,[],[f3872]) ).

tff(f3872,plain,
    ! [X0: fun_int_bool] :
      ( ( ! [X1: int] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
        | ( bot_bot_fun_int_bool != X0 ) )
      & ( ( bot_bot_fun_int_bool = X0 )
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK65(X0)),X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK65])],[f3870,f3871]) ).

tff(f3871,plain,
    ! [X0: fun_int_bool] :
      ( ? [X2: int] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X0))
     => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK65(X0)),X0)) ),
    introduced(choice_axiom,[]) ).

tff(f3870,plain,
    ! [X0: fun_int_bool] :
      ( ( ! [X1: int] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
        | ( bot_bot_fun_int_bool != X0 ) )
      & ( ( bot_bot_fun_int_bool = X0 )
        | ? [X2: int] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X0)) ) ),
    inference(rectify,[],[f3869]) ).

tff(f3869,plain,
    ! [X0: fun_int_bool] :
      ( ( ! [X1: int] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
        | ( bot_bot_fun_int_bool != X0 ) )
      & ( ( bot_bot_fun_int_bool = X0 )
        | ? [X1: int] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0)) ) ),
    inference(nnf_transformation,[],[f1509]) ).

tff(f1509,plain,
    ! [X0: fun_int_bool] :
      ( ! [X1: int] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X0))
    <=> ( bot_bot_fun_int_bool = X0 ) ),
    inference(rectify,[],[f532]) ).

tff(f532,axiom,
    ! [X2: fun_int_bool] :
      ( ! [X27: int] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X27),X2))
    <=> ( bot_bot_fun_int_bool = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_531_all__not__in__conv) ).

tff(f8668,plain,
    spl250_227,
    inference(avatar_split_clause,[],[f4849,f8666]) ).

tff(f8666,plain,
    ( spl250_227
  <=> ! [X0: fun_a_bool] :
        ( ( bot_bot_fun_a_bool = X0 )
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK64(X0)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_227])]) ).

tff(f4849,plain,
    ! [X0: fun_a_bool] :
      ( ( bot_bot_fun_a_bool = X0 )
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK64(X0)),X0)) ),
    inference(cnf_transformation,[],[f3868]) ).

tff(f3868,plain,
    ! [X0: fun_a_bool] :
      ( ( ! [X1: x_a] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
        | ( bot_bot_fun_a_bool != X0 ) )
      & ( ( bot_bot_fun_a_bool = X0 )
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK64(X0)),X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK64])],[f3866,f3867]) ).

tff(f3867,plain,
    ! [X0: fun_a_bool] :
      ( ? [X2: x_a] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK64(X0)),X0)) ),
    introduced(choice_axiom,[]) ).

tff(f3866,plain,
    ! [X0: fun_a_bool] :
      ( ( ! [X1: x_a] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
        | ( bot_bot_fun_a_bool != X0 ) )
      & ( ( bot_bot_fun_a_bool = X0 )
        | ? [X2: x_a] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X0)) ) ),
    inference(rectify,[],[f3865]) ).

tff(f3865,plain,
    ! [X0: fun_a_bool] :
      ( ( ! [X1: x_a] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
        | ( bot_bot_fun_a_bool != X0 ) )
      & ( ( bot_bot_fun_a_bool = X0 )
        | ? [X1: x_a] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0)) ) ),
    inference(nnf_transformation,[],[f1508]) ).

tff(f1508,plain,
    ! [X0: fun_a_bool] :
      ( ! [X1: x_a] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X0))
    <=> ( bot_bot_fun_a_bool = X0 ) ),
    inference(rectify,[],[f534]) ).

tff(f534,axiom,
    ! [X2: fun_a_bool] :
      ( ! [X27: x_a] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X27),X2))
    <=> ( bot_bot_fun_a_bool = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_533_all__not__in__conv) ).

tff(f8664,plain,
    spl250_226,
    inference(avatar_split_clause,[],[f4847,f8662]) ).

tff(f8662,plain,
    ( spl250_226
  <=> ! [X0: fun_pname_bool] :
        ( ( bot_bo844097828e_bool = X0 )
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK63(X0)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_226])]) ).

tff(f4847,plain,
    ! [X0: fun_pname_bool] :
      ( ( bot_bo844097828e_bool = X0 )
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK63(X0)),X0)) ),
    inference(cnf_transformation,[],[f3864]) ).

tff(f3864,plain,
    ! [X0: fun_pname_bool] :
      ( ( ! [X1: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
        | ( bot_bo844097828e_bool != X0 ) )
      & ( ( bot_bo844097828e_bool = X0 )
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK63(X0)),X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK63])],[f3862,f3863]) ).

tff(f3863,plain,
    ! [X0: fun_pname_bool] :
      ( ? [X2: pname] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X0))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK63(X0)),X0)) ),
    introduced(choice_axiom,[]) ).

tff(f3862,plain,
    ! [X0: fun_pname_bool] :
      ( ( ! [X1: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
        | ( bot_bo844097828e_bool != X0 ) )
      & ( ( bot_bo844097828e_bool = X0 )
        | ? [X2: pname] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X0)) ) ),
    inference(rectify,[],[f3861]) ).

tff(f3861,plain,
    ! [X0: fun_pname_bool] :
      ( ( ! [X1: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
        | ( bot_bo844097828e_bool != X0 ) )
      & ( ( bot_bo844097828e_bool = X0 )
        | ? [X1: pname] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0)) ) ),
    inference(nnf_transformation,[],[f1507]) ).

tff(f1507,plain,
    ! [X0: fun_pname_bool] :
      ( ! [X1: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X0))
    <=> ( bot_bo844097828e_bool = X0 ) ),
    inference(rectify,[],[f535]) ).

tff(f535,axiom,
    ! [X2: fun_pname_bool] :
      ( ! [X27: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X27),X2))
    <=> ( bot_bo844097828e_bool = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_534_all__not__in__conv) ).

tff(f8660,plain,
    spl250_225,
    inference(avatar_split_clause,[],[f4784,f8658]) ).

tff(f8658,plain,
    ( spl250_225
  <=> ! [X0: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_225])]) ).

tff(f4784,plain,
    ! [X0: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,X0))) ),
    inference(cnf_transformation,[],[f3816]) ).

tff(f3816,plain,
    ! [X0: fun_nat_bool] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,X0))) )
      & ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,X0)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0)) ) ),
    inference(nnf_transformation,[],[f1477]) ).

tff(f1477,plain,
    ! [X0: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X0))
    <=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,X0))) ),
    inference(rectify,[],[f1115]) ).

tff(f1115,axiom,
    ! [X2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
    <=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1114_transfer__nat__int__set__relations_I1_J) ).

tff(f8656,plain,
    spl250_224,
    inference(avatar_split_clause,[],[f4681,f8654]) ).

tff(f8654,plain,
    ( spl250_224
  <=> ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_224])]) ).

tff(f4681,plain,
    ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X0))),
    inference(cnf_transformation,[],[f1409]) ).

tff(f1409,plain,
    ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),X0))),
    inference(rectify,[],[f991]) ).

tff(f991,axiom,
    ! [X12: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X12),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X12),X12))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_990_le__square) ).

tff(f8652,plain,
    spl250_223,
    inference(avatar_split_clause,[],[f4680,f8650]) ).

tff(f8644,plain,
    ( spl250_222
    | ~ spl250_57
    | ~ spl250_190 ),
    inference(avatar_split_clause,[],[f8481,f8307,f7569,f8641]) ).

tff(f8641,plain,
    ( spl250_222
  <=> ( bot_bot_fun_a_bool = collect_a(bot_bot_fun_a_bool) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_222])]) ).

tff(f8307,plain,
    ( spl250_190
  <=> ! [X0: fun_a_bool] :
        ( ( bot_bot_fun_a_bool = collect_a(X0) )
        | hBOOL(hAPP_a_bool(X0,sK44(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_190])]) ).

tff(f8481,plain,
    ( ( bot_bot_fun_a_bool = collect_a(bot_bot_fun_a_bool) )
    | ~ spl250_57
    | ~ spl250_190 ),
    inference(resolution,[],[f8308,f7570]) ).

tff(f8308,plain,
    ( ! [X0: fun_a_bool] :
        ( hBOOL(hAPP_a_bool(X0,sK44(X0)))
        | ( bot_bot_fun_a_bool = collect_a(X0) ) )
    | ~ spl250_190 ),
    inference(avatar_component_clause,[],[f8307]) ).

tff(f8503,plain,
    ( ~ spl250_130
    | spl250_1
    | ~ spl250_163 ),
    inference(avatar_split_clause,[],[f8471,f8139,f7314,f7965]) ).

tff(f8139,plain,
    ( spl250_163
  <=> ( fFalse = fTrue ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_163])]) ).

tff(f8471,plain,
    ( ~ hBOOL(fTrue)
    | spl250_1
    | ~ spl250_163 ),
    inference(superposition,[],[f7316,f8141]) ).

tff(f8141,plain,
    ( ( fFalse = fTrue )
    | ~ spl250_163 ),
    inference(avatar_component_clause,[],[f8139]) ).

tff(f7316,plain,
    ( ~ hBOOL(fFalse)
    | spl250_1 ),
    inference(avatar_component_clause,[],[f7314]) ).

tff(f8437,plain,
    ( spl250_163
    | ~ spl250_62
    | ~ spl250_85
    | ~ spl250_212 ),
    inference(avatar_split_clause,[],[f8399,f8396,f7733,f7590,f8139]) ).

tff(f7590,plain,
    ( spl250_62
  <=> ! [X0: nat] : hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_62])]) ).

tff(f8399,plain,
    ( ( fFalse = fTrue )
    | ~ spl250_62
    | ~ spl250_85
    | ~ spl250_212 ),
    inference(forward_demodulation,[],[f8397,f7908]) ).

tff(f7908,plain,
    ( ! [X0: nat] : ( fTrue = hAPP_nat_bool(bot_bot_fun_nat_bool,X0) )
    | ~ spl250_62
    | ~ spl250_85 ),
    inference(resolution,[],[f7734,f7591]) ).

tff(f7591,plain,
    ( ! [X0: nat] : hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0))
    | ~ spl250_62 ),
    inference(avatar_component_clause,[],[f7590]) ).

tff(f8435,plain,
    spl250_221,
    inference(avatar_split_clause,[],[f7174,f8433]) ).

tff(f8433,plain,
    ( spl250_221
  <=> ! [X0: nat,X1: nat] :
        ( ( one_one_nat = X1 )
        | ( zero_zero_nat = X1 )
        | ~ sP7(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_221])]) ).

tff(f7174,plain,
    ! [X0: nat,X1: nat] :
      ( ( one_one_nat = X1 )
      | ( zero_zero_nat = X1 )
      | ~ sP7(X0,X1) ),
    inference(forward_demodulation,[],[f5606,f4566]) ).

tff(f5606,plain,
    ! [X0: nat,X1: nat] :
      ( ( zero_zero_nat = X1 )
      | ( hAPP_nat_nat(suc,zero_zero_nat) = X1 )
      | ~ sP7(X0,X1) ),
    inference(cnf_transformation,[],[f4142]) ).

tff(f4142,plain,
    ! [X0: nat,X1: nat] :
      ( ( sP7(X0,X1)
        | ( ( ( hAPP_nat_nat(suc,zero_zero_nat) != X0 )
            | ( zero_zero_nat != X1 ) )
          & ( ( zero_zero_nat != X0 )
            | ( hAPP_nat_nat(suc,zero_zero_nat) != X1 ) ) ) )
      & ( ( ( hAPP_nat_nat(suc,zero_zero_nat) = X0 )
          & ( zero_zero_nat = X1 ) )
        | ( ( zero_zero_nat = X0 )
          & ( hAPP_nat_nat(suc,zero_zero_nat) = X1 ) )
        | ~ sP7(X0,X1) ) ),
    inference(rectify,[],[f4141]) ).

tff(f4141,plain,
    ! [X1: nat,X0: nat] :
      ( ( sP7(X1,X0)
        | ( ( ( hAPP_nat_nat(suc,zero_zero_nat) != X1 )
            | ( zero_zero_nat != X0 ) )
          & ( ( zero_zero_nat != X1 )
            | ( hAPP_nat_nat(suc,zero_zero_nat) != X0 ) ) ) )
      & ( ( ( hAPP_nat_nat(suc,zero_zero_nat) = X1 )
          & ( zero_zero_nat = X0 ) )
        | ( ( zero_zero_nat = X1 )
          & ( hAPP_nat_nat(suc,zero_zero_nat) = X0 ) )
        | ~ sP7(X1,X0) ) ),
    inference(flattening,[],[f4140]) ).

tff(f4140,plain,
    ! [X1: nat,X0: nat] :
      ( ( sP7(X1,X0)
        | ( ( ( hAPP_nat_nat(suc,zero_zero_nat) != X1 )
            | ( zero_zero_nat != X0 ) )
          & ( ( zero_zero_nat != X1 )
            | ( hAPP_nat_nat(suc,zero_zero_nat) != X0 ) ) ) )
      & ( ( ( hAPP_nat_nat(suc,zero_zero_nat) = X1 )
          & ( zero_zero_nat = X0 ) )
        | ( ( zero_zero_nat = X1 )
          & ( hAPP_nat_nat(suc,zero_zero_nat) = X0 ) )
        | ~ sP7(X1,X0) ) ),
    inference(nnf_transformation,[],[f3697]) ).

tff(f8431,plain,
    spl250_220,
    inference(avatar_split_clause,[],[f7173,f8429]) ).

tff(f8429,plain,
    ( spl250_220
  <=> ! [X0: nat,X1: nat] :
        ( ( one_one_nat = X1 )
        | ( one_one_nat = X0 )
        | ~ sP7(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_220])]) ).

tff(f7173,plain,
    ! [X0: nat,X1: nat] :
      ( ( one_one_nat = X1 )
      | ( one_one_nat = X0 )
      | ~ sP7(X0,X1) ),
    inference(forward_demodulation,[],[f7172,f4566]) ).

tff(f7172,plain,
    ! [X0: nat,X1: nat] :
      ( ( one_one_nat = X0 )
      | ( hAPP_nat_nat(suc,zero_zero_nat) = X1 )
      | ~ sP7(X0,X1) ),
    inference(forward_demodulation,[],[f5608,f4566]) ).

tff(f5608,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(suc,zero_zero_nat) = X0 )
      | ( hAPP_nat_nat(suc,zero_zero_nat) = X1 )
      | ~ sP7(X0,X1) ),
    inference(cnf_transformation,[],[f4142]) ).

tff(f8427,plain,
    spl250_219,
    inference(avatar_split_clause,[],[f7171,f8425]) ).

tff(f8425,plain,
    ( spl250_219
  <=> ! [X0: nat,X1: nat] :
        ( ( one_one_nat = X0 )
        | ( zero_zero_nat = X0 )
        | ~ sP7(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_219])]) ).

tff(f7171,plain,
    ! [X0: nat,X1: nat] :
      ( ( one_one_nat = X0 )
      | ( zero_zero_nat = X0 )
      | ~ sP7(X0,X1) ),
    inference(forward_demodulation,[],[f5609,f4566]) ).

tff(f5609,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(suc,zero_zero_nat) = X0 )
      | ( zero_zero_nat = X0 )
      | ~ sP7(X0,X1) ),
    inference(cnf_transformation,[],[f4142]) ).

tff(f8423,plain,
    spl250_218,
    inference(avatar_split_clause,[],[f7166,f8421]) ).

tff(f8421,plain,
    ( spl250_218
  <=> ! [X0: nat,X1: nat] :
        ( ( one_one_nat = X1 )
        | ( zero_zero_nat = X1 )
        | ~ sP6(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_218])]) ).

tff(f7166,plain,
    ! [X0: nat,X1: nat] :
      ( ( one_one_nat = X1 )
      | ( zero_zero_nat = X1 )
      | ~ sP6(X0,X1) ),
    inference(forward_demodulation,[],[f5598,f4566]) ).

tff(f5598,plain,
    ! [X0: nat,X1: nat] :
      ( ( zero_zero_nat = X1 )
      | ( hAPP_nat_nat(suc,zero_zero_nat) = X1 )
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f4138]) ).

tff(f4138,plain,
    ! [X0: nat,X1: nat] :
      ( ( sP6(X0,X1)
        | ( ( ( hAPP_nat_nat(suc,zero_zero_nat) != X0 )
            | ( zero_zero_nat != X1 ) )
          & ( ( zero_zero_nat != X0 )
            | ( hAPP_nat_nat(suc,zero_zero_nat) != X1 ) ) ) )
      & ( ( ( hAPP_nat_nat(suc,zero_zero_nat) = X0 )
          & ( zero_zero_nat = X1 ) )
        | ( ( zero_zero_nat = X0 )
          & ( hAPP_nat_nat(suc,zero_zero_nat) = X1 ) )
        | ~ sP6(X0,X1) ) ),
    inference(rectify,[],[f4137]) ).

tff(f4137,plain,
    ! [X1: nat,X0: nat] :
      ( ( sP6(X1,X0)
        | ( ( ( hAPP_nat_nat(suc,zero_zero_nat) != X1 )
            | ( zero_zero_nat != X0 ) )
          & ( ( zero_zero_nat != X1 )
            | ( hAPP_nat_nat(suc,zero_zero_nat) != X0 ) ) ) )
      & ( ( ( hAPP_nat_nat(suc,zero_zero_nat) = X1 )
          & ( zero_zero_nat = X0 ) )
        | ( ( zero_zero_nat = X1 )
          & ( hAPP_nat_nat(suc,zero_zero_nat) = X0 ) )
        | ~ sP6(X1,X0) ) ),
    inference(flattening,[],[f4136]) ).

tff(f4136,plain,
    ! [X1: nat,X0: nat] :
      ( ( sP6(X1,X0)
        | ( ( ( hAPP_nat_nat(suc,zero_zero_nat) != X1 )
            | ( zero_zero_nat != X0 ) )
          & ( ( zero_zero_nat != X1 )
            | ( hAPP_nat_nat(suc,zero_zero_nat) != X0 ) ) ) )
      & ( ( ( hAPP_nat_nat(suc,zero_zero_nat) = X1 )
          & ( zero_zero_nat = X0 ) )
        | ( ( zero_zero_nat = X1 )
          & ( hAPP_nat_nat(suc,zero_zero_nat) = X0 ) )
        | ~ sP6(X1,X0) ) ),
    inference(nnf_transformation,[],[f3695]) ).

tff(f8419,plain,
    spl250_217,
    inference(avatar_split_clause,[],[f7165,f8417]) ).

tff(f8417,plain,
    ( spl250_217
  <=> ! [X0: nat,X1: nat] :
        ( ( one_one_nat = X1 )
        | ( one_one_nat = X0 )
        | ~ sP6(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_217])]) ).

tff(f7165,plain,
    ! [X0: nat,X1: nat] :
      ( ( one_one_nat = X1 )
      | ( one_one_nat = X0 )
      | ~ sP6(X0,X1) ),
    inference(forward_demodulation,[],[f7164,f4566]) ).

tff(f7164,plain,
    ! [X0: nat,X1: nat] :
      ( ( one_one_nat = X0 )
      | ( hAPP_nat_nat(suc,zero_zero_nat) = X1 )
      | ~ sP6(X0,X1) ),
    inference(forward_demodulation,[],[f5600,f4566]) ).

tff(f5600,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(suc,zero_zero_nat) = X0 )
      | ( hAPP_nat_nat(suc,zero_zero_nat) = X1 )
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f4138]) ).

tff(f8415,plain,
    spl250_216,
    inference(avatar_split_clause,[],[f7163,f8413]) ).

tff(f8413,plain,
    ( spl250_216
  <=> ! [X0: nat,X1: nat] :
        ( ( one_one_nat = X0 )
        | ( zero_zero_nat = X0 )
        | ~ sP6(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_216])]) ).

tff(f7163,plain,
    ! [X0: nat,X1: nat] :
      ( ( one_one_nat = X0 )
      | ( zero_zero_nat = X0 )
      | ~ sP6(X0,X1) ),
    inference(forward_demodulation,[],[f5601,f4566]) ).

tff(f5601,plain,
    ! [X0: nat,X1: nat] :
      ( ( hAPP_nat_nat(suc,zero_zero_nat) = X0 )
      | ( zero_zero_nat = X0 )
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f4138]) ).

tff(f8411,plain,
    spl250_215,
    inference(avatar_split_clause,[],[f6965,f8409]) ).

tff(f8409,plain,
    ( spl250_215
  <=> ! [X0: nat] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),one_one_nat))
        | ( zero_zero_nat = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_215])]) ).

tff(f6965,plain,
    ! [X0: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),one_one_nat))
      | ( zero_zero_nat = X0 ) ),
    inference(forward_demodulation,[],[f4843,f4566]) ).

tff(f4843,plain,
    ! [X0: nat] :
      ( ( zero_zero_nat = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,zero_zero_nat))) ),
    inference(cnf_transformation,[],[f3859]) ).

tff(f3859,plain,
    ! [X0: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,zero_zero_nat)))
        | ( zero_zero_nat != X0 ) )
      & ( ( zero_zero_nat = X0 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,zero_zero_nat))) ) ),
    inference(nnf_transformation,[],[f1505]) ).

tff(f1505,plain,
    ! [X0: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,zero_zero_nat)))
    <=> ( zero_zero_nat = X0 ) ),
    inference(rectify,[],[f948]) ).

tff(f948,axiom,
    ! [X14: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),hAPP_nat_nat(suc,zero_zero_nat)))
    <=> ( zero_zero_nat = X14 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_947_less__Suc0) ).

tff(f8407,plain,
    spl250_214,
    inference(avatar_split_clause,[],[f6931,f8405]) ).

tff(f8403,plain,
    spl250_213,
    inference(avatar_split_clause,[],[f6930,f8401]) ).

tff(f8398,plain,
    ( spl250_212
    | ~ spl250_36
    | ~ spl250_67 ),
    inference(avatar_split_clause,[],[f7730,f7612,f7477,f8396]) ).

tff(f7477,plain,
    ( spl250_36
  <=> ( bot_bot_fun_nat_bool = cOMBK_bool_nat(fFalse) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_36])]) ).

tff(f7730,plain,
    ( ! [X0: nat] : ( fFalse = hAPP_nat_bool(bot_bot_fun_nat_bool,X0) )
    | ~ spl250_36
    | ~ spl250_67 ),
    inference(superposition,[],[f7613,f7479]) ).

tff(f7479,plain,
    ( ( bot_bot_fun_nat_bool = cOMBK_bool_nat(fFalse) )
    | ~ spl250_36 ),
    inference(avatar_component_clause,[],[f7477]) ).

tff(f8394,plain,
    spl250_211,
    inference(avatar_split_clause,[],[f6596,f8392]) ).

tff(f8392,plain,
    ( spl250_211
  <=> ! [X0: nat] :
        ( ( zero_zero_nat = X0 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_211])]) ).

tff(f6596,plain,
    ! [X0: nat] :
      ( ( zero_zero_nat = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
    inference(definition_unfolding,[],[f4733,f4549,f4549]) ).

tff(f4549,plain,
    bot_bot_nat = zero_zero_nat,
    inference(cnf_transformation,[],[f931]) ).

tff(f931,axiom,
    bot_bot_nat = zero_zero_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_930_bot__nat__def) ).

tff(f4733,plain,
    ! [X0: nat] :
      ( ( bot_bot_nat = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),bot_bot_nat)) ),
    inference(cnf_transformation,[],[f2605]) ).

tff(f2605,plain,
    ! [X0: nat] :
      ( ( bot_bot_nat = X0 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),bot_bot_nat)) ),
    inference(ennf_transformation,[],[f1456]) ).

tff(f1456,plain,
    ! [X0: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),bot_bot_nat))
     => ( bot_bot_nat = X0 ) ),
    inference(rectify,[],[f621]) ).

tff(f621,axiom,
    ! [X71: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X71),bot_bot_nat))
     => ( bot_bot_nat = X71 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_le__bot) ).

tff(f8390,plain,
    spl250_210,
    inference(avatar_split_clause,[],[f6010,f8388]) ).

tff(f6010,plain,
    ! [X0: fun_int_bool,X1: int] :
      ( hBOOL(hAPP_int_bool(X0,sK205(X0,X1)))
      | ~ sP12(X0,X1) ),
    inference(cnf_transformation,[],[f4299]) ).

tff(f8386,plain,
    spl250_209,
    inference(avatar_split_clause,[],[f5974,f8384]) ).

tff(f8384,plain,
    ( spl250_209
  <=> ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(X0,sK190(X0,X1)))
        | ~ sP11(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_209])]) ).

tff(f5974,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,sK190(X0,X1)))
      | ~ sP11(X0,X1) ),
    inference(cnf_transformation,[],[f4275]) ).

tff(f8382,plain,
    spl250_208,
    inference(avatar_split_clause,[],[f5971,f8380]) ).

tff(f8380,plain,
    ( spl250_208
  <=> ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK190(X0,X1)))
        | ~ sP11(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_208])]) ).

tff(f5971,plain,
    ! [X0: fun_fu425979586l_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK190(X0,X1)))
      | ~ sP11(X0,X1) ),
    inference(cnf_transformation,[],[f4275]) ).

tff(f8378,plain,
    spl250_207,
    inference(avatar_split_clause,[],[f5940,f8376]) ).

tff(f8376,plain,
    ( spl250_207
  <=> ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(X0,sK181(X0,X1)))
        | ~ sP10(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_207])]) ).

tff(f5940,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,sK181(X0,X1)))
      | ~ sP10(X0,X1) ),
    inference(cnf_transformation,[],[f4257]) ).

tff(f8374,plain,
    spl250_206,
    inference(avatar_split_clause,[],[f5937,f8372]) ).

tff(f8372,plain,
    ( spl250_206
  <=> ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK181(X0,X1)))
        | ~ sP10(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_206])]) ).

tff(f5937,plain,
    ! [X0: fun_fu819804446l_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK181(X0,X1)))
      | ~ sP10(X0,X1) ),
    inference(cnf_transformation,[],[f4257]) ).

tff(f8370,plain,
    spl250_205,
    inference(avatar_split_clause,[],[f5905,f8368]) ).

tff(f8368,plain,
    ( spl250_205
  <=> ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(X0,sK171(X0,X1)))
        | ~ sP9(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_205])]) ).

tff(f5905,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,sK171(X0,X1)))
      | ~ sP9(X0,X1) ),
    inference(cnf_transformation,[],[f4237]) ).

tff(f8366,plain,
    spl250_204,
    inference(avatar_split_clause,[],[f5902,f8364]) ).

tff(f8364,plain,
    ( spl250_204
  <=> ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK171(X0,X1)))
        | ~ sP9(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_204])]) ).

tff(f5902,plain,
    ! [X0: fun_fun_a_bool_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK171(X0,X1)))
      | ~ sP9(X0,X1) ),
    inference(cnf_transformation,[],[f4237]) ).

tff(f8362,plain,
    spl250_203,
    inference(avatar_split_clause,[],[f5867,f8360]) ).

tff(f8360,plain,
    ( spl250_203
  <=> ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(X0,sK161(X0,X1)))
        | ~ sP8(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_203])]) ).

tff(f5867,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,sK161(X0,X1)))
      | ~ sP8(X0,X1) ),
    inference(cnf_transformation,[],[f4217]) ).

tff(f8358,plain,
    spl250_202,
    inference(avatar_split_clause,[],[f5864,f8356]) ).

tff(f8356,plain,
    ( spl250_202
  <=> ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK161(X0,X1)))
        | ~ sP8(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_202])]) ).

tff(f5864,plain,
    ! [X0: fun_fu1430349052l_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK161(X0,X1)))
      | ~ sP8(X0,X1) ),
    inference(cnf_transformation,[],[f4217]) ).

tff(f8353,plain,
    spl250_201,
    inference(avatar_split_clause,[],[f5607,f8351]) ).

tff(f8351,plain,
    ( spl250_201
  <=> ! [X0: nat,X1: nat] :
        ( ( zero_zero_nat = X1 )
        | ( zero_zero_nat = X0 )
        | ~ sP7(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_201])]) ).

tff(f5607,plain,
    ! [X0: nat,X1: nat] :
      ( ( zero_zero_nat = X1 )
      | ( zero_zero_nat = X0 )
      | ~ sP7(X0,X1) ),
    inference(cnf_transformation,[],[f4142]) ).

tff(f8349,plain,
    spl250_200,
    inference(avatar_split_clause,[],[f5599,f8347]) ).

tff(f8347,plain,
    ( spl250_200
  <=> ! [X0: nat,X1: nat] :
        ( ( zero_zero_nat = X1 )
        | ( zero_zero_nat = X0 )
        | ~ sP6(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_200])]) ).

tff(f5599,plain,
    ! [X0: nat,X1: nat] :
      ( ( zero_zero_nat = X1 )
      | ( zero_zero_nat = X0 )
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f4138]) ).

tff(f8345,plain,
    spl250_199,
    inference(avatar_split_clause,[],[f4994,f8343]) ).

tff(f8343,plain,
    ( spl250_199
  <=> ! [X0: nat,X1: nat] :
        ( ( X0 = X1 )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_199])]) ).

tff(f4994,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f1630]) ).

tff(f1630,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1)) ),
    inference(rectify,[],[f1221]) ).

tff(f1221,axiom,
    ! [X15: nat,X16: nat] :
      ( ( X15 = X16 )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X15),X16)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).

tff(f8341,plain,
    spl250_198,
    inference(avatar_split_clause,[],[f4993,f8339]) ).

tff(f8339,plain,
    ( spl250_198
  <=> ! [X0: int,X1: int] :
        ( ( X0 = X1 )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_198])]) ).

tff(f4993,plain,
    ! [X0: int,X1: int] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X0),X1)) ),
    inference(cnf_transformation,[],[f1629]) ).

tff(f1629,plain,
    ! [X0: int,X1: int] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X0),X1)) ),
    inference(rectify,[],[f1219]) ).

tff(f1219,axiom,
    ! [X15: int,X16: int] :
      ( ( X15 = X16 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X15),X16)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Int__Oint_T) ).

tff(f8337,plain,
    spl250_197,
    inference(avatar_split_clause,[],[f4992,f8335]) ).

tff(f8335,plain,
    ( spl250_197
  <=> ! [X0: fun_nat_bool,X1: fun_nat_bool] :
        ( ( X0 = X1 )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_197])]) ).

tff(f4992,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X1)) ),
    inference(cnf_transformation,[],[f1628]) ).

tff(f1628,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X1)) ),
    inference(rectify,[],[f1239]) ).

tff(f1239,axiom,
    ! [X15: fun_nat_bool,X16: fun_nat_bool] :
      ( ( X15 = X16 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X15),X16)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).

tff(f8333,plain,
    spl250_196,
    inference(avatar_split_clause,[],[f4991,f8331]) ).

tff(f8331,plain,
    ( spl250_196
  <=> ! [X0: fun_int_bool,X1: fun_int_bool] :
        ( ( X0 = X1 )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_196])]) ).

tff(f4991,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X0),X1)) ),
    inference(cnf_transformation,[],[f1627]) ).

tff(f1627,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X0),X1)) ),
    inference(rectify,[],[f1237]) ).

tff(f1237,axiom,
    ! [X15: fun_int_bool,X16: fun_int_bool] :
      ( ( X15 = X16 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X15),X16)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T) ).

tff(f8329,plain,
    spl250_195,
    inference(avatar_split_clause,[],[f4990,f8327]) ).

tff(f8327,plain,
    ( spl250_195
  <=> ! [X0: fun_a_bool,X1: fun_a_bool] :
        ( ( X0 = X1 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_195])]) ).

tff(f4990,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),X1)) ),
    inference(cnf_transformation,[],[f1626]) ).

tff(f1626,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),X1)) ),
    inference(rectify,[],[f1231]) ).

tff(f1231,axiom,
    ! [X15: fun_a_bool,X16: fun_a_bool] :
      ( ( X15 = X16 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X15),X16)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).

tff(f8325,plain,
    spl250_194,
    inference(avatar_split_clause,[],[f4989,f8323]) ).

tff(f8323,plain,
    ( spl250_194
  <=> ! [X0: fun_pname_bool,X1: fun_pname_bool] :
        ( ( X0 = X1 )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_194])]) ).

tff(f4989,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X0),X1)) ),
    inference(cnf_transformation,[],[f1625]) ).

tff(f1625,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X0),X1)) ),
    inference(rectify,[],[f1241]) ).

tff(f1241,axiom,
    ! [X15: fun_pname_bool,X16: fun_pname_bool] :
      ( ( X15 = X16 )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X15),X16)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).

tff(f8321,plain,
    spl250_193,
    inference(avatar_split_clause,[],[f4984,f8319]) ).

tff(f8319,plain,
    ( spl250_193
  <=> ! [X0: x_a,X1: x_a] :
        ( ( X0 = X1 )
        | ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_193])]) ).

tff(f4984,plain,
    ! [X0: x_a,X1: x_a] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1)) ),
    inference(cnf_transformation,[],[f1620]) ).

tff(f1620,plain,
    ! [X0: x_a,X1: x_a] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1)) ),
    inference(rectify,[],[f1213]) ).

tff(f1213,axiom,
    ! [X15: x_a,X16: x_a] :
      ( ( X15 = X16 )
      | ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X15),X16)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000t__a_T) ).

tff(f8317,plain,
    spl250_192,
    inference(avatar_split_clause,[],[f4983,f8315]) ).

tff(f8315,plain,
    ( spl250_192
  <=> ! [X0: pname,X1: pname] :
        ( ( X0 = X1 )
        | ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_192])]) ).

tff(f4983,plain,
    ! [X0: pname,X1: pname] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X1)) ),
    inference(cnf_transformation,[],[f1619]) ).

tff(f1619,plain,
    ! [X0: pname,X1: pname] :
      ( ( X0 = X1 )
      | ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X1)) ),
    inference(rectify,[],[f1223]) ).

tff(f1223,axiom,
    ! [X15: pname,X16: pname] :
      ( ( X15 = X16 )
      | ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X15),X16)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Opname_T) ).

tff(f8313,plain,
    spl250_191,
    inference(avatar_split_clause,[],[f4758,f8311]) ).

tff(f8311,plain,
    ( spl250_191
  <=> ! [X0: fun_a_bool] :
        ( ( bot_bot_fun_a_bool = collect_a(X0) )
        | hBOOL(hAPP_a_bool(X0,sK45(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_191])]) ).

tff(f4758,plain,
    ! [X0: fun_a_bool] :
      ( ( bot_bot_fun_a_bool = collect_a(X0) )
      | hBOOL(hAPP_a_bool(X0,sK45(X0))) ),
    inference(cnf_transformation,[],[f3782]) ).

tff(f3782,plain,
    ! [X0: fun_a_bool] :
      ( ( ( bot_bot_fun_a_bool = collect_a(X0) )
        | hBOOL(hAPP_a_bool(X0,sK45(X0))) )
      & ( ! [X2: x_a] : ~ hBOOL(hAPP_a_bool(X0,X2))
        | ( bot_bot_fun_a_bool != collect_a(X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK45])],[f3780,f3781]) ).

tff(f3781,plain,
    ! [X0: fun_a_bool] :
      ( ? [X1: x_a] : hBOOL(hAPP_a_bool(X0,X1))
     => hBOOL(hAPP_a_bool(X0,sK45(X0))) ),
    introduced(choice_axiom,[]) ).

tff(f3780,plain,
    ! [X0: fun_a_bool] :
      ( ( ( bot_bot_fun_a_bool = collect_a(X0) )
        | ? [X1: x_a] : hBOOL(hAPP_a_bool(X0,X1)) )
      & ( ! [X2: x_a] : ~ hBOOL(hAPP_a_bool(X0,X2))
        | ( bot_bot_fun_a_bool != collect_a(X0) ) ) ),
    inference(rectify,[],[f3779]) ).

tff(f3779,plain,
    ! [X0: fun_a_bool] :
      ( ( ( bot_bot_fun_a_bool = collect_a(X0) )
        | ? [X1: x_a] : hBOOL(hAPP_a_bool(X0,X1)) )
      & ( ! [X1: x_a] : ~ hBOOL(hAPP_a_bool(X0,X1))
        | ( bot_bot_fun_a_bool != collect_a(X0) ) ) ),
    inference(nnf_transformation,[],[f1467]) ).

tff(f1467,plain,
    ! [X0: fun_a_bool] :
      ( ( bot_bot_fun_a_bool = collect_a(X0) )
    <=> ! [X1: x_a] : ~ hBOOL(hAPP_a_bool(X0,X1)) ),
    inference(rectify,[],[f511]) ).

tff(f511,axiom,
    ! [X10: fun_a_bool] :
      ( ( collect_a(X10) = bot_bot_fun_a_bool )
    <=> ! [X27: x_a] : ~ hBOOL(hAPP_a_bool(X10,X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_510_Collect__empty__eq) ).

tff(f8309,plain,
    spl250_190,
    inference(avatar_split_clause,[],[f4756,f8307]) ).

tff(f4756,plain,
    ! [X0: fun_a_bool] :
      ( ( bot_bot_fun_a_bool = collect_a(X0) )
      | hBOOL(hAPP_a_bool(X0,sK44(X0))) ),
    inference(cnf_transformation,[],[f3778]) ).

tff(f3778,plain,
    ! [X0: fun_a_bool] :
      ( ( ( bot_bot_fun_a_bool = collect_a(X0) )
        | hBOOL(hAPP_a_bool(X0,sK44(X0))) )
      & ( ! [X2: x_a] : ~ hBOOL(hAPP_a_bool(X0,X2))
        | ( bot_bot_fun_a_bool != collect_a(X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK44])],[f3776,f3777]) ).

tff(f3777,plain,
    ! [X0: fun_a_bool] :
      ( ? [X1: x_a] : hBOOL(hAPP_a_bool(X0,X1))
     => hBOOL(hAPP_a_bool(X0,sK44(X0))) ),
    introduced(choice_axiom,[]) ).

tff(f3776,plain,
    ! [X0: fun_a_bool] :
      ( ( ( bot_bot_fun_a_bool = collect_a(X0) )
        | ? [X1: x_a] : hBOOL(hAPP_a_bool(X0,X1)) )
      & ( ! [X2: x_a] : ~ hBOOL(hAPP_a_bool(X0,X2))
        | ( bot_bot_fun_a_bool != collect_a(X0) ) ) ),
    inference(rectify,[],[f3775]) ).

tff(f3775,plain,
    ! [X0: fun_a_bool] :
      ( ( ( bot_bot_fun_a_bool = collect_a(X0) )
        | ? [X1: x_a] : hBOOL(hAPP_a_bool(X0,X1)) )
      & ( ! [X1: x_a] : ~ hBOOL(hAPP_a_bool(X0,X1))
        | ( bot_bot_fun_a_bool != collect_a(X0) ) ) ),
    inference(nnf_transformation,[],[f1466]) ).

tff(f1466,plain,
    ! [X0: fun_a_bool] :
      ( ( bot_bot_fun_a_bool = collect_a(X0) )
    <=> ! [X1: x_a] : ~ hBOOL(hAPP_a_bool(X0,X1)) ),
    inference(rectify,[],[f524]) ).

tff(f524,axiom,
    ! [X10: fun_a_bool] :
      ( ( collect_a(X10) = bot_bot_fun_a_bool )
    <=> ! [X27: x_a] : ~ hBOOL(hAPP_a_bool(X10,X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_523_empty__Collect__eq) ).

tff(f8305,plain,
    spl250_189,
    inference(avatar_split_clause,[],[f4722,f8303]) ).

tff(f8303,plain,
    ( spl250_189
  <=> ! [X0: fun_nat_bool] :
        ( ( bot_bot_fun_nat_bool = X0 )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),bot_bot_fun_nat_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_189])]) ).

tff(f4722,plain,
    ! [X0: fun_nat_bool] :
      ( ( bot_bot_fun_nat_bool = X0 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),bot_bot_fun_nat_bool)) ),
    inference(cnf_transformation,[],[f2595]) ).

tff(f2595,plain,
    ! [X0: fun_nat_bool] :
      ( ( bot_bot_fun_nat_bool = X0 )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),bot_bot_fun_nat_bool)) ),
    inference(ennf_transformation,[],[f1446]) ).

tff(f1446,plain,
    ! [X0: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),bot_bot_fun_nat_bool))
     => ( bot_bot_fun_nat_bool = X0 ) ),
    inference(rectify,[],[f619]) ).

tff(f619,axiom,
    ! [X5: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),bot_bot_fun_nat_bool))
     => ( bot_bot_fun_nat_bool = X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_618_le__bot) ).

tff(f8301,plain,
    spl250_188,
    inference(avatar_split_clause,[],[f4721,f8299]) ).

tff(f8299,plain,
    ( spl250_188
  <=> ! [X0: fun_int_bool] :
        ( ( bot_bot_fun_int_bool = X0 )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),bot_bot_fun_int_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_188])]) ).

tff(f4721,plain,
    ! [X0: fun_int_bool] :
      ( ( bot_bot_fun_int_bool = X0 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),bot_bot_fun_int_bool)) ),
    inference(cnf_transformation,[],[f2594]) ).

tff(f2594,plain,
    ! [X0: fun_int_bool] :
      ( ( bot_bot_fun_int_bool = X0 )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),bot_bot_fun_int_bool)) ),
    inference(ennf_transformation,[],[f1445]) ).

tff(f1445,plain,
    ! [X0: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),bot_bot_fun_int_bool))
     => ( bot_bot_fun_int_bool = X0 ) ),
    inference(rectify,[],[f620]) ).

tff(f620,axiom,
    ! [X5: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),bot_bot_fun_int_bool))
     => ( bot_bot_fun_int_bool = X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_619_le__bot) ).

tff(f8297,plain,
    spl250_187,
    inference(avatar_split_clause,[],[f4720,f8295]) ).

tff(f8295,plain,
    ( spl250_187
  <=> ! [X0: fun_a_bool] :
        ( ( bot_bot_fun_a_bool = X0 )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),bot_bot_fun_a_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_187])]) ).

tff(f4720,plain,
    ! [X0: fun_a_bool] :
      ( ( bot_bot_fun_a_bool = X0 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),bot_bot_fun_a_bool)) ),
    inference(cnf_transformation,[],[f2593]) ).

tff(f2593,plain,
    ! [X0: fun_a_bool] :
      ( ( bot_bot_fun_a_bool = X0 )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),bot_bot_fun_a_bool)) ),
    inference(ennf_transformation,[],[f1444]) ).

tff(f1444,plain,
    ! [X0: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),bot_bot_fun_a_bool))
     => ( bot_bot_fun_a_bool = X0 ) ),
    inference(rectify,[],[f622]) ).

tff(f622,axiom,
    ! [X5: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),bot_bot_fun_a_bool))
     => ( bot_bot_fun_a_bool = X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_621_le__bot) ).

tff(f8293,plain,
    spl250_186,
    inference(avatar_split_clause,[],[f4709,f8291]) ).

tff(f8291,plain,
    ( spl250_186
  <=> ! [X0: nat] :
        ( ( hAPP_nat_nat(suc,sK30(X0)) = X0 )
        | ( zero_zero_nat = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_186])]) ).

tff(f4709,plain,
    ! [X0: nat] :
      ( ( hAPP_nat_nat(suc,sK30(X0)) = X0 )
      | ( zero_zero_nat = X0 ) ),
    inference(cnf_transformation,[],[f3744]) ).

tff(f3744,plain,
    ! [X0: nat] :
      ( ( hAPP_nat_nat(suc,sK30(X0)) = X0 )
      | ( zero_zero_nat = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f2582,f3743]) ).

tff(f3743,plain,
    ! [X0: nat] :
      ( ? [X1: nat] : ( hAPP_nat_nat(suc,X1) = X0 )
     => ( hAPP_nat_nat(suc,sK30(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f2582,plain,
    ! [X0: nat] :
      ( ? [X1: nat] : ( hAPP_nat_nat(suc,X1) = X0 )
      | ( zero_zero_nat = X0 ) ),
    inference(ennf_transformation,[],[f1433]) ).

tff(f1433,plain,
    ! [X0: nat] :
      ( ( zero_zero_nat != X0 )
     => ? [X1: nat] : ( hAPP_nat_nat(suc,X1) = X0 ) ),
    inference(rectify,[],[f976]) ).

tff(f976,axiom,
    ! [X11: nat] :
      ( ( zero_zero_nat != X11 )
     => ? [X32: nat] : ( hAPP_nat_nat(suc,X32) = X11 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_975_not0__implies__Suc) ).

tff(f8289,plain,
    spl250_185,
    inference(avatar_split_clause,[],[f4708,f8287]) ).

tff(f8287,plain,
    ( spl250_185
  <=> ! [X0: nat] :
        ( ( hAPP_nat_nat(suc,sK29(X0)) = X0 )
        | ( zero_zero_nat = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_185])]) ).

tff(f4708,plain,
    ! [X0: nat] :
      ( ( hAPP_nat_nat(suc,sK29(X0)) = X0 )
      | ( zero_zero_nat = X0 ) ),
    inference(cnf_transformation,[],[f3742]) ).

tff(f3742,plain,
    ! [X0: nat] :
      ( ( hAPP_nat_nat(suc,sK29(X0)) = X0 )
      | ( zero_zero_nat = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f2581,f3741]) ).

tff(f3741,plain,
    ! [X0: nat] :
      ( ? [X1: nat] : ( hAPP_nat_nat(suc,X1) = X0 )
     => ( hAPP_nat_nat(suc,sK29(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f2581,plain,
    ! [X0: nat] :
      ( ? [X1: nat] : ( hAPP_nat_nat(suc,X1) = X0 )
      | ( zero_zero_nat = X0 ) ),
    inference(ennf_transformation,[],[f1432]) ).

tff(f1432,plain,
    ! [X0: nat] :
      ( ( zero_zero_nat != X0 )
     => ~ ! [X1: nat] : ( hAPP_nat_nat(suc,X1) != X0 ) ),
    inference(rectify,[],[f974]) ).

tff(f974,axiom,
    ! [X16: nat] :
      ( ( zero_zero_nat != X16 )
     => ~ ! [X129: nat] : ( hAPP_nat_nat(suc,X129) != X16 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_973_nat_Oexhaust) ).

tff(f8285,plain,
    spl250_184,
    inference(avatar_split_clause,[],[f4707,f8283]) ).

tff(f8283,plain,
    ( spl250_184
  <=> ! [X0: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
        | ( zero_zero_nat = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_184])]) ).

tff(f4707,plain,
    ! [X0: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ( zero_zero_nat = X0 ) ),
    inference(cnf_transformation,[],[f2580]) ).

tff(f2580,plain,
    ! [X0: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
      | ( zero_zero_nat = X0 ) ),
    inference(ennf_transformation,[],[f1431]) ).

tff(f1431,plain,
    ! [X0: nat] :
      ( ( zero_zero_nat != X0 )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
    inference(rectify,[],[f936]) ).

tff(f936,axiom,
    ! [X11: nat] :
      ( ( zero_zero_nat != X11 )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X11)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_935_gr0I) ).

tff(f8281,plain,
    spl250_183,
    inference(avatar_split_clause,[],[f4677,f8279]) ).

tff(f4677,plain,
    ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X0)),one_one_nat) = X0 ),
    inference(cnf_transformation,[],[f1405]) ).

tff(f1405,plain,
    ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X0)),one_one_nat) = X0 ),
    inference(rectify,[],[f747]) ).

tff(f747,axiom,
    ! [X11: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X11)),one_one_nat) = X11 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_746_diff__Suc__1) ).

tff(f8277,plain,
    ( spl250_182
    | ~ spl250_29
    | ~ spl250_135 ),
    inference(avatar_split_clause,[],[f8164,f8025,f7446,f8274]) ).

tff(f8274,plain,
    ( spl250_182
  <=> ( pls = abs_abs_int(pls) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_182])]) ).

tff(f7446,plain,
    ( spl250_29
  <=> ( hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = pls ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_29])]) ).

tff(f8025,plain,
    ( spl250_135
  <=> ! [X0: nat] : ( hAPP_nat_int(semiri1621563631at_int,X0) = abs_abs_int(hAPP_nat_int(semiri1621563631at_int,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_135])]) ).

tff(f8164,plain,
    ( ( pls = abs_abs_int(pls) )
    | ~ spl250_29
    | ~ spl250_135 ),
    inference(superposition,[],[f8026,f7448]) ).

tff(f7448,plain,
    ( ( hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = pls )
    | ~ spl250_29 ),
    inference(avatar_component_clause,[],[f7446]) ).

tff(f8026,plain,
    ( ! [X0: nat] : ( hAPP_nat_int(semiri1621563631at_int,X0) = abs_abs_int(hAPP_nat_int(semiri1621563631at_int,X0)) )
    | ~ spl250_135 ),
    inference(avatar_component_clause,[],[f8025]) ).

tff(f8272,plain,
    ( spl250_181
    | ~ spl250_180 ),
    inference(avatar_split_clause,[],[f8268,f8265,f8270]) ).

tff(f8270,plain,
    ( spl250_181
  <=> ! [X0: nat] : ( hAPP_f22106695ol_nat(the_elem_nat,hAPP_n1699378549t_bool(fequal_nat,X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_181])]) ).

tff(f8265,plain,
    ( spl250_180
  <=> ! [X0: nat] : ( hAPP_f22106695ol_nat(the_elem_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_180])]) ).

tff(f8268,plain,
    ( ! [X0: nat] : ( hAPP_f22106695ol_nat(the_elem_nat,hAPP_n1699378549t_bool(fequal_nat,X0)) = X0 )
    | ~ spl250_180 ),
    inference(forward_demodulation,[],[f8266,f6931]) ).

tff(f8266,plain,
    ( ! [X0: nat] : ( hAPP_f22106695ol_nat(the_elem_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)) = X0 )
    | ~ spl250_180 ),
    inference(avatar_component_clause,[],[f8265]) ).

tff(f8267,plain,
    spl250_180,
    inference(avatar_split_clause,[],[f4675,f8265]) ).

tff(f4675,plain,
    ! [X0: nat] : ( hAPP_f22106695ol_nat(the_elem_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)) = X0 ),
    inference(cnf_transformation,[],[f1403]) ).

tff(f1403,plain,
    ! [X0: nat] : ( hAPP_f22106695ol_nat(the_elem_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),bot_bot_fun_nat_bool)) = X0 ),
    inference(rectify,[],[f698]) ).

tff(f698,axiom,
    ! [X8: nat] : ( hAPP_f22106695ol_nat(the_elem_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),bot_bot_fun_nat_bool)) = X8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_697_the__elem__eq) ).

tff(f8263,plain,
    ( spl250_179
    | ~ spl250_178 ),
    inference(avatar_split_clause,[],[f8259,f8256,f8261]) ).

tff(f8261,plain,
    ( spl250_179
  <=> ! [X0: x_a] : ( hAPP_fun_a_bool_a(the_elem_a,collect_a(hAPP_a_fun_a_bool(fequal_a,X0))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_179])]) ).

tff(f8256,plain,
    ( spl250_178
  <=> ! [X0: x_a] : ( hAPP_fun_a_bool_a(the_elem_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_178])]) ).

tff(f8259,plain,
    ( ! [X0: x_a] : ( hAPP_fun_a_bool_a(the_elem_a,collect_a(hAPP_a_fun_a_bool(fequal_a,X0))) = X0 )
    | ~ spl250_178 ),
    inference(forward_demodulation,[],[f8257,f4680]) ).

tff(f8257,plain,
    ( ! [X0: x_a] : ( hAPP_fun_a_bool_a(the_elem_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)) = X0 )
    | ~ spl250_178 ),
    inference(avatar_component_clause,[],[f8256]) ).

tff(f8258,plain,
    spl250_178,
    inference(avatar_split_clause,[],[f4674,f8256]) ).

tff(f4674,plain,
    ! [X0: x_a] : ( hAPP_fun_a_bool_a(the_elem_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)) = X0 ),
    inference(cnf_transformation,[],[f1402]) ).

tff(f1402,plain,
    ! [X0: x_a] : ( hAPP_fun_a_bool_a(the_elem_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),bot_bot_fun_a_bool)) = X0 ),
    inference(rectify,[],[f697]) ).

tff(f697,axiom,
    ! [X8: x_a] : ( hAPP_fun_a_bool_a(the_elem_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),bot_bot_fun_a_bool)) = X8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_696_the__elem__eq) ).

tff(f8254,plain,
    ( spl250_177
    | ~ spl250_176 ),
    inference(avatar_split_clause,[],[f8250,f8247,f8252]) ).

tff(f8252,plain,
    ( spl250_177
  <=> ! [X0: int] : ( hAPP_f1594865479ol_int(the_elem_int,hAPP_i1948725293t_bool(fequal_int,X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_177])]) ).

tff(f8247,plain,
    ( spl250_176
  <=> ! [X0: int] : ( hAPP_f1594865479ol_int(the_elem_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_176])]) ).

tff(f8250,plain,
    ( ! [X0: int] : ( hAPP_f1594865479ol_int(the_elem_int,hAPP_i1948725293t_bool(fequal_int,X0)) = X0 )
    | ~ spl250_176 ),
    inference(forward_demodulation,[],[f8248,f6930]) ).

tff(f8248,plain,
    ( ! [X0: int] : ( hAPP_f1594865479ol_int(the_elem_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)) = X0 )
    | ~ spl250_176 ),
    inference(avatar_component_clause,[],[f8247]) ).

tff(f8249,plain,
    spl250_176,
    inference(avatar_split_clause,[],[f4673,f8247]) ).

tff(f4673,plain,
    ! [X0: int] : ( hAPP_f1594865479ol_int(the_elem_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)) = X0 ),
    inference(cnf_transformation,[],[f1401]) ).

tff(f1401,plain,
    ! [X0: int] : ( hAPP_f1594865479ol_int(the_elem_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),bot_bot_fun_int_bool)) = X0 ),
    inference(rectify,[],[f699]) ).

tff(f699,axiom,
    ! [X8: int] : ( hAPP_f1594865479ol_int(the_elem_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),bot_bot_fun_int_bool)) = X8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_698_the__elem__eq) ).

tff(f8245,plain,
    spl250_175,
    inference(avatar_split_clause,[],[f4672,f8243]) ).

tff(f8243,plain,
    ( spl250_175
  <=> ! [X0: nat] : ( hAPP_nat_nat(suc,X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),one_one_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_175])]) ).

tff(f8241,plain,
    spl250_174,
    inference(avatar_split_clause,[],[f4671,f8239]) ).

tff(f8239,plain,
    ( spl250_174
  <=> ! [X0: nat] : ( hAPP_nat_nat(suc,X0) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_174])]) ).

tff(f8237,plain,
    ( spl250_173
    | ~ spl250_19
    | ~ spl250_135 ),
    inference(avatar_split_clause,[],[f8163,f8025,f7401,f8234]) ).

tff(f8234,plain,
    ( spl250_173
  <=> ( one_one_int = abs_abs_int(one_one_int) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_173])]) ).

tff(f7401,plain,
    ( spl250_19
  <=> ( one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_19])]) ).

tff(f8163,plain,
    ( ( one_one_int = abs_abs_int(one_one_int) )
    | ~ spl250_19
    | ~ spl250_135 ),
    inference(superposition,[],[f8026,f7403]) ).

tff(f7403,plain,
    ( ( one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat) )
    | ~ spl250_19 ),
    inference(avatar_component_clause,[],[f7401]) ).

tff(f8232,plain,
    spl250_172,
    inference(avatar_split_clause,[],[f4670,f8230]) ).

tff(f8228,plain,
    spl250_171,
    inference(avatar_split_clause,[],[f4669,f8226]) ).

tff(f8226,plain,
    ( spl250_171
  <=> ! [X0: fun_nat_bool] : ( hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_f957591787ol_nat(finite_card_int,image_nat_int(semiri1621563631at_int,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_171])]) ).

tff(f4669,plain,
    ! [X0: fun_nat_bool] : ( hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_f957591787ol_nat(finite_card_int,image_nat_int(semiri1621563631at_int,X0)) ),
    inference(cnf_transformation,[],[f1397]) ).

tff(f1397,plain,
    ! [X0: fun_nat_bool] : ( hAPP_f22106695ol_nat(finite_card_nat,X0) = hAPP_f957591787ol_nat(finite_card_int,image_nat_int(semiri1621563631at_int,X0)) ),
    inference(rectify,[],[f1114]) ).

tff(f1114,axiom,
    ! [X2: fun_nat_bool] : ( hAPP_f22106695ol_nat(finite_card_nat,X2) = hAPP_f957591787ol_nat(finite_card_int,image_nat_int(semiri1621563631at_int,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1113_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) ).

tff(f8198,plain,
    ( spl250_170
    | ~ spl250_156 ),
    inference(avatar_split_clause,[],[f8113,f8110,f8196]) ).

tff(f8196,plain,
    ( spl250_170
  <=> ! [X0: nat] : ~ hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_int,semiri1621563631at_int),X0),pls)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_170])]) ).

tff(f8110,plain,
    ( spl250_156
  <=> ! [X0: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_156])]) ).

tff(f8113,plain,
    ( ! [X0: nat] : ~ hBOOL(hAPP_int_bool(hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(ord_less_int,semiri1621563631at_int),X0),pls))
    | ~ spl250_156 ),
    inference(forward_demodulation,[],[f8111,f5694]) ).

tff(f8111,plain,
    ( ! [X0: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls))
    | ~ spl250_156 ),
    inference(avatar_component_clause,[],[f8110]) ).

tff(f8193,plain,
    ( spl250_169
    | ~ spl250_147 ),
    inference(avatar_split_clause,[],[f8188,f8073,f8191]) ).

tff(f8191,plain,
    ( spl250_169
  <=> ! [X0: int] : sP5(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_169])]) ).

tff(f8073,plain,
    ( spl250_147
  <=> ! [X0: int,X1: int] :
        ( sP5(X0,X1)
        | ( number_number_of_nat(X0) != number_number_of_nat(X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_147])]) ).

tff(f8188,plain,
    ( ! [X0: int] : sP5(X0,X0)
    | ~ spl250_147 ),
    inference(equality_resolution,[],[f8074]) ).

tff(f8074,plain,
    ( ! [X0: int,X1: int] :
        ( ( number_number_of_nat(X0) != number_number_of_nat(X1) )
        | sP5(X0,X1) )
    | ~ spl250_147 ),
    inference(avatar_component_clause,[],[f8073]) ).

tff(f8162,plain,
    spl250_168,
    inference(avatar_split_clause,[],[f6958,f8160]) ).

tff(f8160,plain,
    ( spl250_168
  <=> ! [X0: fun_nat_bool] :
        ( ( bot_bot_fun_nat_bool = X0 )
        | hBOOL(hAPP_nat_bool(X0,sK49(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_168])]) ).

tff(f6958,plain,
    ! [X0: fun_nat_bool] :
      ( ( bot_bot_fun_nat_bool = X0 )
      | hBOOL(hAPP_nat_bool(X0,sK49(X0))) ),
    inference(forward_demodulation,[],[f4766,f4588]) ).

tff(f4766,plain,
    ! [X0: fun_nat_bool] :
      ( ( bot_bot_fun_nat_bool = collect_nat(X0) )
      | hBOOL(hAPP_nat_bool(X0,sK49(X0))) ),
    inference(cnf_transformation,[],[f3798]) ).

tff(f3798,plain,
    ! [X0: fun_nat_bool] :
      ( ( ( bot_bot_fun_nat_bool = collect_nat(X0) )
        | hBOOL(hAPP_nat_bool(X0,sK49(X0))) )
      & ( ! [X2: nat] : ~ hBOOL(hAPP_nat_bool(X0,X2))
        | ( bot_bot_fun_nat_bool != collect_nat(X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK49])],[f3796,f3797]) ).

tff(f3797,plain,
    ! [X0: fun_nat_bool] :
      ( ? [X1: nat] : hBOOL(hAPP_nat_bool(X0,X1))
     => hBOOL(hAPP_nat_bool(X0,sK49(X0))) ),
    introduced(choice_axiom,[]) ).

tff(f3796,plain,
    ! [X0: fun_nat_bool] :
      ( ( ( bot_bot_fun_nat_bool = collect_nat(X0) )
        | ? [X1: nat] : hBOOL(hAPP_nat_bool(X0,X1)) )
      & ( ! [X2: nat] : ~ hBOOL(hAPP_nat_bool(X0,X2))
        | ( bot_bot_fun_nat_bool != collect_nat(X0) ) ) ),
    inference(rectify,[],[f3795]) ).

tff(f3795,plain,
    ! [X0: fun_nat_bool] :
      ( ( ( bot_bot_fun_nat_bool = collect_nat(X0) )
        | ? [X1: nat] : hBOOL(hAPP_nat_bool(X0,X1)) )
      & ( ! [X1: nat] : ~ hBOOL(hAPP_nat_bool(X0,X1))
        | ( bot_bot_fun_nat_bool != collect_nat(X0) ) ) ),
    inference(nnf_transformation,[],[f1471]) ).

tff(f1471,plain,
    ! [X0: fun_nat_bool] :
      ( ( bot_bot_fun_nat_bool = collect_nat(X0) )
    <=> ! [X1: nat] : ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
    inference(rectify,[],[f510]) ).

tff(f510,axiom,
    ! [X10: fun_nat_bool] :
      ( ( collect_nat(X10) = bot_bot_fun_nat_bool )
    <=> ! [X27: nat] : ~ hBOOL(hAPP_nat_bool(X10,X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_509_Collect__empty__eq) ).

tff(f8158,plain,
    spl250_167,
    inference(avatar_split_clause,[],[f6956,f8156]) ).

tff(f6956,plain,
    ! [X0: fun_nat_bool] :
      ( ( bot_bot_fun_nat_bool = X0 )
      | hBOOL(hAPP_nat_bool(X0,sK48(X0))) ),
    inference(forward_demodulation,[],[f4764,f4588]) ).

tff(f4764,plain,
    ! [X0: fun_nat_bool] :
      ( ( bot_bot_fun_nat_bool = collect_nat(X0) )
      | hBOOL(hAPP_nat_bool(X0,sK48(X0))) ),
    inference(cnf_transformation,[],[f3794]) ).

tff(f3794,plain,
    ! [X0: fun_nat_bool] :
      ( ( ( bot_bot_fun_nat_bool = collect_nat(X0) )
        | hBOOL(hAPP_nat_bool(X0,sK48(X0))) )
      & ( ! [X2: nat] : ~ hBOOL(hAPP_nat_bool(X0,X2))
        | ( bot_bot_fun_nat_bool != collect_nat(X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK48])],[f3792,f3793]) ).

tff(f3793,plain,
    ! [X0: fun_nat_bool] :
      ( ? [X1: nat] : hBOOL(hAPP_nat_bool(X0,X1))
     => hBOOL(hAPP_nat_bool(X0,sK48(X0))) ),
    introduced(choice_axiom,[]) ).

tff(f3792,plain,
    ! [X0: fun_nat_bool] :
      ( ( ( bot_bot_fun_nat_bool = collect_nat(X0) )
        | ? [X1: nat] : hBOOL(hAPP_nat_bool(X0,X1)) )
      & ( ! [X2: nat] : ~ hBOOL(hAPP_nat_bool(X0,X2))
        | ( bot_bot_fun_nat_bool != collect_nat(X0) ) ) ),
    inference(rectify,[],[f3791]) ).

tff(f3791,plain,
    ! [X0: fun_nat_bool] :
      ( ( ( bot_bot_fun_nat_bool = collect_nat(X0) )
        | ? [X1: nat] : hBOOL(hAPP_nat_bool(X0,X1)) )
      & ( ! [X1: nat] : ~ hBOOL(hAPP_nat_bool(X0,X1))
        | ( bot_bot_fun_nat_bool != collect_nat(X0) ) ) ),
    inference(nnf_transformation,[],[f1470]) ).

tff(f1470,plain,
    ! [X0: fun_nat_bool] :
      ( ( bot_bot_fun_nat_bool = collect_nat(X0) )
    <=> ! [X1: nat] : ~ hBOOL(hAPP_nat_bool(X0,X1)) ),
    inference(rectify,[],[f523]) ).

tff(f523,axiom,
    ! [X10: fun_nat_bool] :
      ( ( collect_nat(X10) = bot_bot_fun_nat_bool )
    <=> ! [X27: nat] : ~ hBOOL(hAPP_nat_bool(X10,X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_522_empty__Collect__eq) ).

tff(f8154,plain,
    spl250_166,
    inference(avatar_split_clause,[],[f6954,f8152]) ).

tff(f8152,plain,
    ( spl250_166
  <=> ! [X0: fun_int_bool] :
        ( ( bot_bot_fun_int_bool = X0 )
        | hBOOL(hAPP_int_bool(X0,sK47(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_166])]) ).

tff(f6954,plain,
    ! [X0: fun_int_bool] :
      ( ( bot_bot_fun_int_bool = X0 )
      | hBOOL(hAPP_int_bool(X0,sK47(X0))) ),
    inference(forward_demodulation,[],[f4762,f4586]) ).

tff(f4762,plain,
    ! [X0: fun_int_bool] :
      ( ( bot_bot_fun_int_bool = collect_int(X0) )
      | hBOOL(hAPP_int_bool(X0,sK47(X0))) ),
    inference(cnf_transformation,[],[f3790]) ).

tff(f3790,plain,
    ! [X0: fun_int_bool] :
      ( ( ( bot_bot_fun_int_bool = collect_int(X0) )
        | hBOOL(hAPP_int_bool(X0,sK47(X0))) )
      & ( ! [X2: int] : ~ hBOOL(hAPP_int_bool(X0,X2))
        | ( bot_bot_fun_int_bool != collect_int(X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK47])],[f3788,f3789]) ).

tff(f3789,plain,
    ! [X0: fun_int_bool] :
      ( ? [X1: int] : hBOOL(hAPP_int_bool(X0,X1))
     => hBOOL(hAPP_int_bool(X0,sK47(X0))) ),
    introduced(choice_axiom,[]) ).

tff(f3788,plain,
    ! [X0: fun_int_bool] :
      ( ( ( bot_bot_fun_int_bool = collect_int(X0) )
        | ? [X1: int] : hBOOL(hAPP_int_bool(X0,X1)) )
      & ( ! [X2: int] : ~ hBOOL(hAPP_int_bool(X0,X2))
        | ( bot_bot_fun_int_bool != collect_int(X0) ) ) ),
    inference(rectify,[],[f3787]) ).

tff(f3787,plain,
    ! [X0: fun_int_bool] :
      ( ( ( bot_bot_fun_int_bool = collect_int(X0) )
        | ? [X1: int] : hBOOL(hAPP_int_bool(X0,X1)) )
      & ( ! [X1: int] : ~ hBOOL(hAPP_int_bool(X0,X1))
        | ( bot_bot_fun_int_bool != collect_int(X0) ) ) ),
    inference(nnf_transformation,[],[f1469]) ).

tff(f1469,plain,
    ! [X0: fun_int_bool] :
      ( ( bot_bot_fun_int_bool = collect_int(X0) )
    <=> ! [X1: int] : ~ hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(rectify,[],[f509]) ).

tff(f509,axiom,
    ! [X10: fun_int_bool] :
      ( ( collect_int(X10) = bot_bot_fun_int_bool )
    <=> ! [X27: int] : ~ hBOOL(hAPP_int_bool(X10,X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_508_Collect__empty__eq) ).

tff(f8150,plain,
    spl250_165,
    inference(avatar_split_clause,[],[f6952,f8148]) ).

tff(f6952,plain,
    ! [X0: fun_int_bool] :
      ( ( bot_bot_fun_int_bool = X0 )
      | hBOOL(hAPP_int_bool(X0,sK46(X0))) ),
    inference(forward_demodulation,[],[f4760,f4586]) ).

tff(f4760,plain,
    ! [X0: fun_int_bool] :
      ( ( bot_bot_fun_int_bool = collect_int(X0) )
      | hBOOL(hAPP_int_bool(X0,sK46(X0))) ),
    inference(cnf_transformation,[],[f3786]) ).

tff(f3786,plain,
    ! [X0: fun_int_bool] :
      ( ( ( bot_bot_fun_int_bool = collect_int(X0) )
        | hBOOL(hAPP_int_bool(X0,sK46(X0))) )
      & ( ! [X2: int] : ~ hBOOL(hAPP_int_bool(X0,X2))
        | ( bot_bot_fun_int_bool != collect_int(X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK46])],[f3784,f3785]) ).

tff(f3785,plain,
    ! [X0: fun_int_bool] :
      ( ? [X1: int] : hBOOL(hAPP_int_bool(X0,X1))
     => hBOOL(hAPP_int_bool(X0,sK46(X0))) ),
    introduced(choice_axiom,[]) ).

tff(f3784,plain,
    ! [X0: fun_int_bool] :
      ( ( ( bot_bot_fun_int_bool = collect_int(X0) )
        | ? [X1: int] : hBOOL(hAPP_int_bool(X0,X1)) )
      & ( ! [X2: int] : ~ hBOOL(hAPP_int_bool(X0,X2))
        | ( bot_bot_fun_int_bool != collect_int(X0) ) ) ),
    inference(rectify,[],[f3783]) ).

tff(f3783,plain,
    ! [X0: fun_int_bool] :
      ( ( ( bot_bot_fun_int_bool = collect_int(X0) )
        | ? [X1: int] : hBOOL(hAPP_int_bool(X0,X1)) )
      & ( ! [X1: int] : ~ hBOOL(hAPP_int_bool(X0,X1))
        | ( bot_bot_fun_int_bool != collect_int(X0) ) ) ),
    inference(nnf_transformation,[],[f1468]) ).

tff(f1468,plain,
    ! [X0: fun_int_bool] :
      ( ( bot_bot_fun_int_bool = collect_int(X0) )
    <=> ! [X1: int] : ~ hBOOL(hAPP_int_bool(X0,X1)) ),
    inference(rectify,[],[f522]) ).

tff(f522,axiom,
    ! [X10: fun_int_bool] :
      ( ( collect_int(X10) = bot_bot_fun_int_bool )
    <=> ! [X27: int] : ~ hBOOL(hAPP_int_bool(X10,X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_521_empty__Collect__eq) ).

tff(f8146,plain,
    spl250_164,
    inference(avatar_split_clause,[],[f6950,f8144]) ).

tff(f8144,plain,
    ( spl250_164
  <=> ! [X0: int] :
        ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
        | ( zero_zero_nat = number_number_of_nat(X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_164])]) ).

tff(f6950,plain,
    ! [X0: int] :
      ( ~ hBOOL(hAPP_int_bool(nat_neg,X0))
      | ( zero_zero_nat = number_number_of_nat(X0) ) ),
    inference(forward_demodulation,[],[f4718,f4587]) ).

tff(f4718,plain,
    ! [X0: int] :
      ( ( zero_zero_nat = number_number_of_nat(X0) )
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
    inference(cnf_transformation,[],[f2591]) ).

tff(f2591,plain,
    ! [X0: int] :
      ( ( zero_zero_nat = number_number_of_nat(X0) )
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
    inference(ennf_transformation,[],[f1442]) ).

tff(f1442,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
     => ( zero_zero_nat = number_number_of_nat(X0) ) ),
    inference(rectify,[],[f1154]) ).

tff(f1154,axiom,
    ! [X130: int] :
      ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X130)))
     => ( zero_zero_nat = number_number_of_nat(X130) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1153_neg__imp__number__of__eq__0) ).

tff(f8142,plain,
    ( spl250_163
    | ~ spl250_60
    | ~ spl250_85
    | ~ spl250_152 ),
    inference(avatar_split_clause,[],[f8096,f8093,f7733,f7581,f8139]) ).

tff(f7581,plain,
    ( spl250_60
  <=> ! [X0: int] : hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_60])]) ).

tff(f8096,plain,
    ( ( fFalse = fTrue )
    | ~ spl250_60
    | ~ spl250_85
    | ~ spl250_152 ),
    inference(forward_demodulation,[],[f8094,f7903]) ).

tff(f7903,plain,
    ( ! [X0: int] : ( fTrue = hAPP_int_bool(bot_bot_fun_int_bool,X0) )
    | ~ spl250_60
    | ~ spl250_85 ),
    inference(resolution,[],[f7734,f7582]) ).

tff(f7582,plain,
    ( ! [X0: int] : hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X0))
    | ~ spl250_60 ),
    inference(avatar_component_clause,[],[f7581]) ).

tff(f8137,plain,
    spl250_162,
    inference(avatar_split_clause,[],[f6935,f8135]) ).

tff(f8135,plain,
    ( spl250_162
  <=> ! [X0: nat] : ( hAPP_n1699378549t_bool(fequal_nat,X0) = hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_162])]) ).

tff(f8133,plain,
    spl250_161,
    inference(avatar_split_clause,[],[f6933,f8131]) ).

tff(f8131,plain,
    ( spl250_161
  <=> ! [X0: int] : ( hAPP_i1948725293t_bool(fequal_int,X0) = hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_161])]) ).

tff(f8129,plain,
    spl250_160,
    inference(avatar_split_clause,[],[f6929,f8127]) ).

tff(f8127,plain,
    ( spl250_160
  <=> ! [X0: nat] : ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_160])]) ).

tff(f6929,plain,
    ! [X0: nat] : ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X0)) = X0 ),
    inference(forward_demodulation,[],[f4676,f4588]) ).

tff(f4676,plain,
    ! [X0: nat] : ( hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X0))) = X0 ),
    inference(cnf_transformation,[],[f1404]) ).

tff(f1404,plain,
    ! [X0: nat] : ( hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X0))) = X0 ),
    inference(rectify,[],[f897]) ).

tff(f897,axiom,
    ! [X14: nat] : ( hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X14))) = X14 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_896_card__Collect__less__nat) ).

tff(f8125,plain,
    spl250_159,
    inference(avatar_split_clause,[],[f6870,f8123]) ).

tff(f8123,plain,
    ( spl250_159
  <=> ! [X2: x_a,X1: fun_a_bool] : hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_159])]) ).

tff(f6870,plain,
    ! [X2: x_a,X1: fun_a_bool] : hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1),X2)),
    inference(equality_resolution,[],[f6292]) ).

tff(f6292,plain,
    ! [X2: x_a,X0: x_a,X1: fun_a_bool] :
      ( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1),X2))
      | ( X0 != X2 ) ),
    inference(cnf_transformation,[],[f4404]) ).

tff(f8121,plain,
    spl250_158,
    inference(avatar_split_clause,[],[f6602,f8119]) ).

tff(f6602,plain,
    ! [X0: nat] :
      ( ( zero_zero_nat = X0 )
      | ( pls != hAPP_nat_int(semiri1621563631at_int,X0) ) ),
    inference(definition_unfolding,[],[f4805,f4550]) ).

tff(f4805,plain,
    ! [X0: nat] :
      ( ( zero_zero_nat = X0 )
      | ( zero_zero_int != hAPP_nat_int(semiri1621563631at_int,X0) ) ),
    inference(cnf_transformation,[],[f3837]) ).

tff(f3837,plain,
    ! [X0: nat] :
      ( ( ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,X0) )
        | ( zero_zero_nat != X0 ) )
      & ( ( zero_zero_nat = X0 )
        | ( zero_zero_int != hAPP_nat_int(semiri1621563631at_int,X0) ) ) ),
    inference(nnf_transformation,[],[f1486]) ).

tff(f1486,plain,
    ! [X0: nat] :
      ( ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,X0) )
    <=> ( zero_zero_nat = X0 ) ),
    inference(rectify,[],[f1101]) ).

tff(f1101,axiom,
    ! [X14: nat] :
      ( ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,X14) )
    <=> ( zero_zero_nat = X14 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1100_int__eq__0__conv) ).

tff(f8117,plain,
    spl250_157,
    inference(avatar_split_clause,[],[f6580,f8115]) ).

tff(f6580,plain,
    ! [X0: nat] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,X0))),
    inference(definition_unfolding,[],[f4665,f4550]) ).

tff(f4665,plain,
    ! [X0: nat] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X0))),
    inference(cnf_transformation,[],[f1393]) ).

tff(f1393,plain,
    ! [X0: nat] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X0))),
    inference(rectify,[],[f1119]) ).

tff(f1119,axiom,
    ! [X95: nat] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X95))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1118_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).

tff(f8112,plain,
    spl250_156,
    inference(avatar_split_clause,[],[f6579,f8110]) ).

tff(f6579,plain,
    ! [X0: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls)),
    inference(definition_unfolding,[],[f4659,f4550]) ).

tff(f4659,plain,
    ! [X0: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int)),
    inference(cnf_transformation,[],[f1387]) ).

tff(f1387,plain,
    ! [X0: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int)),
    inference(rectify,[],[f1098]) ).

tff(f1098,axiom,
    ! [X19: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X19)),zero_zero_int)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1097_int__less__0__conv) ).

tff(f8108,plain,
    spl250_155,
    inference(avatar_split_clause,[],[f6261,f8106]) ).

tff(f8106,plain,
    ( spl250_155
  <=> ! [X2: int,X0: bool,X1: bool] :
        ( sP16(X0,X2,X1)
        | ~ hBOOL(X0)
        | ~ hBOOL(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_155])]) ).

tff(f6261,plain,
    ! [X2: int,X0: bool,X1: bool] :
      ( sP16(X0,X2,X1)
      | ~ hBOOL(X0)
      | ~ hBOOL(X1) ),
    inference(cnf_transformation,[],[f4370]) ).

tff(f8104,plain,
    spl250_154,
    inference(avatar_split_clause,[],[f6260,f8102]) ).

tff(f8102,plain,
    ( spl250_154
  <=> ! [X2: int,X0: bool,X1: bool] :
        ( sP16(X0,X2,X1)
        | hBOOL(X0)
        | hBOOL(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_154])]) ).

tff(f6260,plain,
    ! [X2: int,X0: bool,X1: bool] :
      ( sP16(X0,X2,X1)
      | hBOOL(X0)
      | hBOOL(X1) ),
    inference(cnf_transformation,[],[f4370]) ).

tff(f8100,plain,
    spl250_153,
    inference(avatar_split_clause,[],[f6254,f8098]) ).

tff(f8098,plain,
    ( spl250_153
  <=> ! [X2: int,X0: bool,X1: bool] :
        ( sP15(X0,X2,X1)
        | ~ hBOOL(X0)
        | ~ hBOOL(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_153])]) ).

tff(f6254,plain,
    ! [X2: int,X0: bool,X1: bool] :
      ( sP15(X0,X2,X1)
      | ~ hBOOL(X0)
      | ~ hBOOL(X1) ),
    inference(cnf_transformation,[],[f4365]) ).

tff(f8095,plain,
    ( spl250_152
    | ~ spl250_61
    | ~ spl250_66 ),
    inference(avatar_split_clause,[],[f7728,f7608,f7585,f8093]) ).

tff(f7585,plain,
    ( spl250_61
  <=> ( bot_bot_fun_int_bool = cOMBK_bool_int(fFalse) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_61])]) ).

tff(f7728,plain,
    ( ! [X0: int] : ( fFalse = hAPP_int_bool(bot_bot_fun_int_bool,X0) )
    | ~ spl250_61
    | ~ spl250_66 ),
    inference(superposition,[],[f7609,f7587]) ).

tff(f7587,plain,
    ( ( bot_bot_fun_int_bool = cOMBK_bool_int(fFalse) )
    | ~ spl250_61 ),
    inference(avatar_component_clause,[],[f7585]) ).

tff(f8091,plain,
    spl250_151,
    inference(avatar_split_clause,[],[f6253,f8089]) ).

tff(f8089,plain,
    ( spl250_151
  <=> ! [X2: int,X0: bool,X1: bool] :
        ( sP15(X0,X2,X1)
        | hBOOL(X0)
        | hBOOL(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_151])]) ).

tff(f6253,plain,
    ! [X2: int,X0: bool,X1: bool] :
      ( sP15(X0,X2,X1)
      | hBOOL(X0)
      | hBOOL(X1) ),
    inference(cnf_transformation,[],[f4365]) ).

tff(f8087,plain,
    spl250_150,
    inference(avatar_split_clause,[],[f5482,f8085]) ).

tff(f8085,plain,
    ( spl250_150
  <=> ! [X0: fun_nat_int,X1: fun_nat_bool] :
        ( ( bot_bot_fun_nat_bool = X1 )
        | ( bot_bot_fun_int_bool != image_nat_int(X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_150])]) ).

tff(f5482,plain,
    ! [X0: fun_nat_int,X1: fun_nat_bool] :
      ( ( bot_bot_fun_nat_bool = X1 )
      | ( bot_bot_fun_int_bool != image_nat_int(X0,X1) ) ),
    inference(cnf_transformation,[],[f4049]) ).

tff(f4049,plain,
    ! [X0: fun_nat_int,X1: fun_nat_bool] :
      ( ( ( bot_bot_fun_int_bool = image_nat_int(X0,X1) )
        | ( bot_bot_fun_nat_bool != X1 ) )
      & ( ( bot_bot_fun_nat_bool = X1 )
        | ( bot_bot_fun_int_bool != image_nat_int(X0,X1) ) ) ),
    inference(nnf_transformation,[],[f1974]) ).

tff(f1974,plain,
    ! [X0: fun_nat_int,X1: fun_nat_bool] :
      ( ( bot_bot_fun_int_bool = image_nat_int(X0,X1) )
    <=> ( bot_bot_fun_nat_bool = X1 ) ),
    inference(rectify,[],[f613]) ).

tff(f613,axiom,
    ! [X6: fun_nat_int,X2: fun_nat_bool] :
      ( ( image_nat_int(X6,X2) = bot_bot_fun_int_bool )
    <=> ( bot_bot_fun_nat_bool = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_image__is__empty) ).

tff(f8083,plain,
    spl250_149,
    inference(avatar_split_clause,[],[f5478,f8081]) ).

tff(f8081,plain,
    ( spl250_149
  <=> ! [X0: fun_pname_a,X1: fun_pname_bool] :
        ( ( bot_bo844097828e_bool = X1 )
        | ( bot_bot_fun_a_bool != image_pname_a(X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_149])]) ).

tff(f5478,plain,
    ! [X0: fun_pname_a,X1: fun_pname_bool] :
      ( ( bot_bo844097828e_bool = X1 )
      | ( bot_bot_fun_a_bool != image_pname_a(X0,X1) ) ),
    inference(cnf_transformation,[],[f4047]) ).

tff(f4047,plain,
    ! [X0: fun_pname_a,X1: fun_pname_bool] :
      ( ( ( bot_bot_fun_a_bool = image_pname_a(X0,X1) )
        | ( bot_bo844097828e_bool != X1 ) )
      & ( ( bot_bo844097828e_bool = X1 )
        | ( bot_bot_fun_a_bool != image_pname_a(X0,X1) ) ) ),
    inference(nnf_transformation,[],[f1972]) ).

tff(f1972,plain,
    ! [X0: fun_pname_a,X1: fun_pname_bool] :
      ( ( bot_bot_fun_a_bool = image_pname_a(X0,X1) )
    <=> ( bot_bo844097828e_bool = X1 ) ),
    inference(rectify,[],[f614]) ).

tff(f614,axiom,
    ! [X6: fun_pname_a,X2: fun_pname_bool] :
      ( ( image_pname_a(X6,X2) = bot_bot_fun_a_bool )
    <=> ( bot_bo844097828e_bool = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_image__is__empty) ).

tff(f8079,plain,
    spl250_148,
    inference(avatar_split_clause,[],[f5477,f8077]) ).

tff(f8077,plain,
    ( spl250_148
  <=> ! [X0: int,X1: int] :
        ( ( number_number_of_nat(X0) = number_number_of_nat(X1) )
        | ~ sP5(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_148])]) ).

tff(f5477,plain,
    ! [X0: int,X1: int] :
      ( ( number_number_of_nat(X0) = number_number_of_nat(X1) )
      | ~ sP5(X0,X1) ),
    inference(cnf_transformation,[],[f4046]) ).

tff(f4046,plain,
    ! [X0: int,X1: int] :
      ( ( ( number_number_of_nat(X0) = number_number_of_nat(X1) )
        | ~ sP5(X0,X1) )
      & ( sP5(X0,X1)
        | ( number_number_of_nat(X0) != number_number_of_nat(X1) ) ) ),
    inference(nnf_transformation,[],[f3694]) ).

tff(f3694,plain,
    ! [X0: int,X1: int] :
      ( ( number_number_of_nat(X0) = number_number_of_nat(X1) )
    <=> sP5(X0,X1) ),
    inference(definition_folding,[],[f3066,f3693,f3692]) ).

tff(f3066,plain,
    ! [X0: int,X1: int] :
      ( ( number_number_of_nat(X0) = number_number_of_nat(X1) )
    <=> ( ( ( ( ( X0 = X1 )
              | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) )
            & ( ( zero_zero_int = number_number_of_int(X0) )
              | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ) )
          | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) )
        & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int))
          | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ) ) ),
    inference(ennf_transformation,[],[f1971]) ).

tff(f1971,plain,
    ! [X0: int,X1: int] :
      ( ( number_number_of_nat(X0) = number_number_of_nat(X1) )
    <=> ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
         => ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1)))
             => ( X0 = X1 ) )
            & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1)))
             => ( zero_zero_int = number_number_of_int(X0) ) ) ) )
        & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0)))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int)) ) ) ),
    inference(rectify,[],[f1155]) ).

tff(f1155,axiom,
    ! [X151: int,X152: int] :
      ( ( number_number_of_nat(X151) = number_number_of_nat(X152) )
    <=> ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X151)))
         => ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X152)))
             => ( X151 = X152 ) )
            & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X152)))
             => ( zero_zero_int = number_number_of_int(X151) ) ) ) )
        & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X151)))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X152)),zero_zero_int)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1154_eq__nat__number__of) ).

tff(f8075,plain,
    spl250_147,
    inference(avatar_split_clause,[],[f5476,f8073]) ).

tff(f5476,plain,
    ! [X0: int,X1: int] :
      ( sP5(X0,X1)
      | ( number_number_of_nat(X0) != number_number_of_nat(X1) ) ),
    inference(cnf_transformation,[],[f4046]) ).

tff(f8071,plain,
    spl250_146,
    inference(avatar_split_clause,[],[f4988,f8069]) ).

tff(f8069,plain,
    ( spl250_146
  <=> ! [X0: bool,X1: bool] :
        ( hBOOL(X1)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_146])]) ).

tff(f4988,plain,
    ! [X0: bool,X1: bool] :
      ( hBOOL(X1)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
    inference(cnf_transformation,[],[f1624]) ).

tff(f1624,plain,
    ! [X0: bool,X1: bool] :
      ( hBOOL(X1)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
    inference(rectify,[],[f1204]) ).

tff(f1204,axiom,
    ! [X156: bool,X157: bool] :
      ( hBOOL(X157)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X156),X157)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).

tff(f8067,plain,
    spl250_145,
    inference(avatar_split_clause,[],[f4987,f8065]) ).

tff(f8065,plain,
    ( spl250_145
  <=> ! [X0: bool,X1: bool] :
        ( hBOOL(X0)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_145])]) ).

tff(f4987,plain,
    ! [X0: bool,X1: bool] :
      ( hBOOL(X0)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
    inference(cnf_transformation,[],[f1623]) ).

tff(f1623,plain,
    ! [X0: bool,X1: bool] :
      ( hBOOL(X0)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X0),X1)) ),
    inference(rectify,[],[f1203]) ).

tff(f1203,axiom,
    ! [X156: bool,X157: bool] :
      ( hBOOL(X156)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X156),X157)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).

tff(f8063,plain,
    spl250_144,
    inference(avatar_split_clause,[],[f4974,f8061]) ).

tff(f8061,plain,
    ( spl250_144
  <=> ! [X0: bool,X1: bool] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X0))
        | hBOOL(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_144])]) ).

tff(f4974,plain,
    ! [X0: bool,X1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X0))
      | hBOOL(X1) ),
    inference(cnf_transformation,[],[f1610]) ).

tff(f1610,plain,
    ! [X0: bool,X1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X0))
      | hBOOL(X1) ),
    inference(rectify,[],[f1210]) ).

tff(f1210,axiom,
    ! [X157: bool,X156: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X156),X157))
      | hBOOL(X156) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).

tff(f8059,plain,
    spl250_143,
    inference(avatar_split_clause,[],[f4973,f8057]) ).

tff(f8057,plain,
    ( spl250_143
  <=> ! [X0: bool,X1: bool] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X0))
        | ~ hBOOL(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_143])]) ).

tff(f4973,plain,
    ! [X0: bool,X1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X0))
      | ~ hBOOL(X1) ),
    inference(cnf_transformation,[],[f1609]) ).

tff(f1609,plain,
    ! [X0: bool,X1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X0))
      | ~ hBOOL(X1) ),
    inference(rectify,[],[f1205]) ).

tff(f1205,axiom,
    ! [X157: bool,X156: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X156),X157))
      | ~ hBOOL(X156) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).

tff(f8055,plain,
    spl250_142,
    inference(avatar_split_clause,[],[f4972,f8053]) ).

tff(f8053,plain,
    ( spl250_142
  <=> ! [X0: bool,X1: bool] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1))
        | ~ hBOOL(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_142])]) ).

tff(f4972,plain,
    ! [X0: bool,X1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1))
      | ~ hBOOL(X1) ),
    inference(cnf_transformation,[],[f1608]) ).

tff(f1608,plain,
    ! [X0: bool,X1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X0),X1))
      | ~ hBOOL(X1) ),
    inference(rectify,[],[f1206]) ).

tff(f1206,axiom,
    ! [X156: bool,X157: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X156),X157))
      | ~ hBOOL(X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).

tff(f8051,plain,
    spl250_141,
    inference(avatar_split_clause,[],[f4971,f8049]) ).

tff(f8049,plain,
    ( spl250_141
  <=> ! [X0: bool,X1: bool] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1))
        | ~ hBOOL(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_141])]) ).

tff(f4971,plain,
    ! [X0: bool,X1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1))
      | ~ hBOOL(X1) ),
    inference(cnf_transformation,[],[f1607]) ).

tff(f1607,plain,
    ! [X0: bool,X1: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X0),X1))
      | ~ hBOOL(X1) ),
    inference(rectify,[],[f1211]) ).

tff(f1211,axiom,
    ! [X156: bool,X157: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X156),X157))
      | ~ hBOOL(X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).

tff(f8047,plain,
    spl250_140,
    inference(avatar_split_clause,[],[f4882,f8045]) ).

tff(f8045,plain,
    ( spl250_140
  <=> ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fFalse),X0),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_140])]) ).

tff(f4882,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fFalse),X0),X1) = X1 ),
    inference(cnf_transformation,[],[f1530]) ).

tff(f1530,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fFalse),X0),X1) = X1 ),
    inference(rectify,[],[f1216]) ).

tff(f1216,axiom,
    ! [X15: nat,X16: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fFalse),X15),X16) = X16 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_000tc__Nat__Onat_T) ).

tff(f8043,plain,
    spl250_139,
    inference(avatar_split_clause,[],[f4881,f8041]) ).

tff(f8041,plain,
    ( spl250_139
  <=> ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fTrue),X0),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_139])]) ).

tff(f4881,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fTrue),X0),X1) = X0 ),
    inference(cnf_transformation,[],[f1529]) ).

tff(f1529,plain,
    ! [X0: nat,X1: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fTrue),X0),X1) = X0 ),
    inference(rectify,[],[f1215]) ).

tff(f1215,axiom,
    ! [X15: nat,X16: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fTrue),X15),X16) = X15 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_000tc__Nat__Onat_T) ).

tff(f8039,plain,
    spl250_138,
    inference(avatar_split_clause,[],[f4755,f8037]) ).

tff(f8037,plain,
    ( spl250_138
  <=> ! [X2: x_a,X0: fun_a_bool] :
        ( ~ hBOOL(hAPP_a_bool(X0,X2))
        | ( bot_bot_fun_a_bool != collect_a(X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_138])]) ).

tff(f4755,plain,
    ! [X2: x_a,X0: fun_a_bool] :
      ( ~ hBOOL(hAPP_a_bool(X0,X2))
      | ( bot_bot_fun_a_bool != collect_a(X0) ) ),
    inference(cnf_transformation,[],[f3778]) ).

tff(f8035,plain,
    spl250_137,
    inference(avatar_split_clause,[],[f4668,f8033]) ).

tff(f4668,plain,
    ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X0))),
    inference(cnf_transformation,[],[f1396]) ).

tff(f1396,plain,
    ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),hAPP_nat_nat(suc,X0))),
    inference(rectify,[],[f856]) ).

tff(f856,axiom,
    ! [X11: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X11),hAPP_nat_nat(suc,X11))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_855_lessI) ).

tff(f8031,plain,
    spl250_136,
    inference(avatar_split_clause,[],[f4667,f8029]) ).

tff(f4667,plain,
    ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,X0))),
    inference(cnf_transformation,[],[f1395]) ).

tff(f1395,plain,
    ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,X0))),
    inference(rectify,[],[f924]) ).

tff(f924,axiom,
    ! [X11: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,X11))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_923_zero__less__Suc) ).

tff(f8027,plain,
    spl250_135,
    inference(avatar_split_clause,[],[f4662,f8025]) ).

tff(f4662,plain,
    ! [X0: nat] : ( hAPP_nat_int(semiri1621563631at_int,X0) = abs_abs_int(hAPP_nat_int(semiri1621563631at_int,X0)) ),
    inference(cnf_transformation,[],[f1390]) ).

tff(f1390,plain,
    ! [X0: nat] : ( hAPP_nat_int(semiri1621563631at_int,X0) = abs_abs_int(hAPP_nat_int(semiri1621563631at_int,X0)) ),
    inference(rectify,[],[f1153]) ).

tff(f1153,axiom,
    ! [X12: nat] : ( hAPP_nat_int(semiri1621563631at_int,X12) = abs_abs_int(hAPP_nat_int(semiri1621563631at_int,X12)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1152_abs__int__eq) ).

tff(f8022,plain,
    spl250_134,
    inference(avatar_split_clause,[],[f4660,f8020]) ).

tff(f8020,plain,
    ( spl250_134
  <=> ! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_134])]) ).

tff(f4660,plain,
    ! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X0)),
    inference(cnf_transformation,[],[f1388]) ).

tff(f1388,plain,
    ! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X0)),X0)),
    inference(rectify,[],[f171]) ).

tff(f171,axiom,
    ! [X11: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X11)),X11)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_Suc__n__not__le__n) ).

tff(f8015,plain,
    ( spl250_133
    | spl250_9
    | ~ spl250_128 ),
    inference(avatar_split_clause,[],[f7996,f7954,f7354,f8012]) ).

tff(f8012,plain,
    ( spl250_133
  <=> sP4(one_one_int,one_one_int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_133])]) ).

tff(f7954,plain,
    ( spl250_128
  <=> ! [X1: int] :
        ( hBOOL(hAPP_int_bool(nat_neg,X1))
        | sP4(X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_128])]) ).

tff(f7996,plain,
    ( sP4(one_one_int,one_one_int)
    | spl250_9
    | ~ spl250_128 ),
    inference(resolution,[],[f7955,f7356]) ).

tff(f7955,plain,
    ( ! [X1: int] :
        ( hBOOL(hAPP_int_bool(nat_neg,X1))
        | sP4(X1,X1) )
    | ~ spl250_128 ),
    inference(avatar_component_clause,[],[f7954]) ).

tff(f8010,plain,
    spl250_132,
    inference(avatar_split_clause,[],[f4544,f8007]) ).

tff(f4544,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
    inference(cnf_transformation,[],[f1304]) ).

tff(f1304,axiom,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).

tff(f8005,plain,
    ~ spl250_131,
    inference(avatar_split_clause,[],[f4543,f8002]) ).

tff(f4543,plain,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)),
    inference(cnf_transformation,[],[f1308]) ).

tff(f1308,axiom,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).

tff(f7968,plain,
    ( spl250_130
    | ~ spl250_8
    | ~ spl250_129 ),
    inference(avatar_split_clause,[],[f7963,f7958,f7349,f7965]) ).

tff(f7349,plain,
    ( spl250_8
  <=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_8])]) ).

tff(f7963,plain,
    ( hBOOL(fTrue)
    | ~ spl250_8
    | ~ spl250_129 ),
    inference(superposition,[],[f7351,f7960]) ).

tff(f7351,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u))
    | ~ spl250_8 ),
    inference(avatar_component_clause,[],[f7349]) ).

tff(f7961,plain,
    ( spl250_129
    | ~ spl250_8
    | ~ spl250_85 ),
    inference(avatar_split_clause,[],[f7916,f7733,f7349,f7958]) ).

tff(f7916,plain,
    ( ( fTrue = hAPP_f1664156314l_bool(finite_finite_pname,u) )
    | ~ spl250_8
    | ~ spl250_85 ),
    inference(resolution,[],[f7734,f7351]) ).

tff(f7956,plain,
    spl250_128,
    inference(avatar_split_clause,[],[f7118,f7954]) ).

tff(f7118,plain,
    ! [X1: int] :
      ( hBOOL(hAPP_int_bool(nat_neg,X1))
      | sP4(X1,X1) ),
    inference(forward_demodulation,[],[f6796,f4587]) ).

tff(f6796,plain,
    ! [X1: int] :
      ( sP4(X1,X1)
      | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ),
    inference(equality_resolution,[],[f5474]) ).

tff(f5474,plain,
    ! [X0: int,X1: int] :
      ( sP4(X0,X1)
      | ( X0 != X1 )
      | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X0))) ),
    inference(cnf_transformation,[],[f4045]) ).

tff(f7952,plain,
    spl250_127,
    inference(avatar_split_clause,[],[f6957,f7950]) ).

tff(f7950,plain,
    ( spl250_127
  <=> ! [X2: nat,X0: fun_nat_bool] :
        ( ( bot_bot_fun_nat_bool != X0 )
        | ~ hBOOL(hAPP_nat_bool(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_127])]) ).

tff(f6957,plain,
    ! [X2: nat,X0: fun_nat_bool] :
      ( ( bot_bot_fun_nat_bool != X0 )
      | ~ hBOOL(hAPP_nat_bool(X0,X2)) ),
    inference(forward_demodulation,[],[f4763,f4588]) ).

tff(f4763,plain,
    ! [X2: nat,X0: fun_nat_bool] :
      ( ~ hBOOL(hAPP_nat_bool(X0,X2))
      | ( bot_bot_fun_nat_bool != collect_nat(X0) ) ),
    inference(cnf_transformation,[],[f3794]) ).

tff(f7948,plain,
    spl250_126,
    inference(avatar_split_clause,[],[f6953,f7946]) ).

tff(f7946,plain,
    ( spl250_126
  <=> ! [X2: int,X0: fun_int_bool] :
        ( ( bot_bot_fun_int_bool != X0 )
        | ~ hBOOL(hAPP_int_bool(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_126])]) ).

tff(f6953,plain,
    ! [X2: int,X0: fun_int_bool] :
      ( ( bot_bot_fun_int_bool != X0 )
      | ~ hBOOL(hAPP_int_bool(X0,X2)) ),
    inference(forward_demodulation,[],[f4759,f4586]) ).

tff(f4759,plain,
    ! [X2: int,X0: fun_int_bool] :
      ( ~ hBOOL(hAPP_int_bool(X0,X2))
      | ( bot_bot_fun_int_bool != collect_int(X0) ) ),
    inference(cnf_transformation,[],[f3786]) ).

tff(f7944,plain,
    spl250_125,
    inference(avatar_split_clause,[],[f6928,f7942]) ).

tff(f7942,plain,
    ( spl250_125
  <=> ! [X0: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_125])]) ).

tff(f6928,plain,
    ! [X0: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0))),
    inference(forward_demodulation,[],[f4664,f4588]) ).

tff(f4664,plain,
    ! [X0: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)))),
    inference(cnf_transformation,[],[f1392]) ).

tff(f1392,plain,
    ! [X0: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X0)))),
    inference(rectify,[],[f121]) ).

tff(f121,axiom,
    ! [X13: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X13)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_finite__Collect__le__nat) ).

tff(f7940,plain,
    spl250_124,
    inference(avatar_split_clause,[],[f6927,f7938]) ).

tff(f7938,plain,
    ( spl250_124
  <=> ! [X0: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_124])]) ).

tff(f6927,plain,
    ! [X0: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X0))),
    inference(forward_demodulation,[],[f4663,f4588]) ).

tff(f4663,plain,
    ! [X0: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X0)))),
    inference(cnf_transformation,[],[f1391]) ).

tff(f1391,plain,
    ! [X0: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X0)))),
    inference(rectify,[],[f858]) ).

tff(f858,axiom,
    ! [X13: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X13)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_857_finite__Collect__less__nat) ).

tff(f7936,plain,
    spl250_123,
    inference(avatar_split_clause,[],[f6717,f7933]) ).

tff(f7933,plain,
    ( spl250_123
  <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(pls)),one_one_int)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_123])]) ).

tff(f6717,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(pls)),one_one_int)),
    inference(equality_resolution,[],[f6613]) ).

tff(f6613,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int))
      | ( pls != X0 ) ),
    inference(definition_unfolding,[],[f4834,f4550]) ).

tff(f4834,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int))
      | ( zero_zero_int != X0 ) ),
    inference(cnf_transformation,[],[f3854]) ).

tff(f7931,plain,
    spl250_122,
    inference(avatar_split_clause,[],[f5255,f7929]) ).

tff(f7929,plain,
    ( spl250_122
  <=> ! [X0: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_f54304608l_bool(X0,sK113(X0)))
        | ~ sP3(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_122])]) ).

tff(f5255,plain,
    ! [X0: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f54304608l_bool(X0,sK113(X0)))
      | ~ sP3(X0) ),
    inference(cnf_transformation,[],[f3968]) ).

tff(f7899,plain,
    spl250_121,
    inference(avatar_split_clause,[],[f5252,f7897]) ).

tff(f7897,plain,
    ( spl250_121
  <=> ! [X0: fun_fu425979586l_bool] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK113(X0)))
        | ~ sP3(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_121])]) ).

tff(f5252,plain,
    ! [X0: fun_fu425979586l_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK113(X0)))
      | ~ sP3(X0) ),
    inference(cnf_transformation,[],[f3968]) ).

tff(f7895,plain,
    spl250_120,
    inference(avatar_split_clause,[],[f5212,f7893]) ).

tff(f7893,plain,
    ( spl250_120
  <=> ! [X0: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_f448129468l_bool(X0,sK106(X0)))
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_120])]) ).

tff(f5212,plain,
    ! [X0: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f448129468l_bool(X0,sK106(X0)))
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f3957]) ).

tff(f7891,plain,
    spl250_119,
    inference(avatar_split_clause,[],[f5209,f7889]) ).

tff(f7889,plain,
    ( spl250_119
  <=> ! [X0: fun_fu819804446l_bool] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK106(X0)))
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_119])]) ).

tff(f5209,plain,
    ! [X0: fun_fu819804446l_bool] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK106(X0)))
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f3957]) ).

tff(f7887,plain,
    spl250_118,
    inference(avatar_split_clause,[],[f5173,f7885]) ).

tff(f7885,plain,
    ( spl250_118
  <=> ! [X0: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(X0,sK99(X0)))
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_118])]) ).

tff(f5173,plain,
    ! [X0: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(X0,sK99(X0)))
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f3947]) ).

tff(f7883,plain,
    spl250_117,
    inference(avatar_split_clause,[],[f5170,f7881]) ).

tff(f7881,plain,
    ( spl250_117
  <=> ! [X0: fun_fun_a_bool_bool] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK99(X0)))
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_117])]) ).

tff(f5170,plain,
    ! [X0: fun_fun_a_bool_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK99(X0)))
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f3947]) ).

tff(f7879,plain,
    spl250_116,
    inference(avatar_split_clause,[],[f5132,f7877]) ).

tff(f7877,plain,
    ( spl250_116
  <=> ! [X0: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(X0,sK92(X0)))
        | ~ sP0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_116])]) ).

tff(f5132,plain,
    ! [X0: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(X0,sK92(X0)))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f3936]) ).

tff(f7875,plain,
    spl250_115,
    inference(avatar_split_clause,[],[f5129,f7873]) ).

tff(f7873,plain,
    ( spl250_115
  <=> ! [X0: fun_fu1430349052l_bool] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK92(X0)))
        | ~ sP0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_115])]) ).

tff(f5129,plain,
    ! [X0: fun_fu1430349052l_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK92(X0)))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f3936]) ).

tff(f7871,plain,
    spl250_114,
    inference(avatar_split_clause,[],[f4879,f7869]) ).

tff(f4879,plain,
    ! [X0: x_a,X1: fun_a_bool] : ( bot_bot_fun_a_bool != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) ),
    inference(cnf_transformation,[],[f1527]) ).

tff(f1527,plain,
    ! [X0: x_a,X1: fun_a_bool] : ( bot_bot_fun_a_bool != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X0),X1) ),
    inference(rectify,[],[f604]) ).

tff(f604,axiom,
    ! [X5: x_a,X2: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5),X2) != bot_bot_fun_a_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_603_insert__not__empty) ).

tff(f7867,plain,
    spl250_113,
    inference(avatar_split_clause,[],[f4877,f7865]) ).

tff(f4877,plain,
    ! [X0: nat,X1: fun_nat_bool] : ( bot_bot_fun_nat_bool != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) ),
    inference(cnf_transformation,[],[f1525]) ).

tff(f1525,plain,
    ! [X0: nat,X1: fun_nat_bool] : ( bot_bot_fun_nat_bool != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X0),X1) ),
    inference(rectify,[],[f608]) ).

tff(f608,axiom,
    ! [X5: nat,X2: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5),X2) != bot_bot_fun_nat_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_607_empty__not__insert) ).

tff(f7863,plain,
    spl250_112,
    inference(avatar_split_clause,[],[f4875,f7861]) ).

tff(f4875,plain,
    ! [X0: int,X1: fun_int_bool] : ( bot_bot_fun_int_bool != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) ),
    inference(cnf_transformation,[],[f1523]) ).

tff(f1523,plain,
    ! [X0: int,X1: fun_int_bool] : ( bot_bot_fun_int_bool != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X0),X1) ),
    inference(rectify,[],[f606]) ).

tff(f606,axiom,
    ! [X5: int,X2: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5),X2) != bot_bot_fun_int_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_605_insert__not__empty) ).

tff(f7859,plain,
    spl250_111,
    inference(avatar_split_clause,[],[f4658,f7857]) ).

tff(f4658,plain,
    ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),zero_zero_nat) = X0 ),
    inference(cnf_transformation,[],[f1386]) ).

tff(f1386,plain,
    ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X0),zero_zero_nat) = X0 ),
    inference(rectify,[],[f934]) ).

tff(f934,axiom,
    ! [X12: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X12),zero_zero_nat) = X12 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_933_Nat_Oadd__0__right) ).

tff(f7855,plain,
    spl250_110,
    inference(avatar_split_clause,[],[f4657,f7853]) ).

tff(f4657,plain,
    ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),zero_zero_nat) = X0 ),
    inference(cnf_transformation,[],[f1385]) ).

tff(f1385,plain,
    ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),zero_zero_nat) = X0 ),
    inference(rectify,[],[f929]) ).

tff(f929,axiom,
    ! [X12: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X12),zero_zero_nat) = X12 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_928_minus__nat_Odiff__0) ).

tff(f7851,plain,
    spl250_109,
    inference(avatar_split_clause,[],[f4656,f7849]) ).

tff(f7849,plain,
    ( spl250_109
  <=> ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),one_one_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_109])]) ).

tff(f4656,plain,
    ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),one_one_nat) = X0 ),
    inference(cnf_transformation,[],[f1384]) ).

tff(f1384,plain,
    ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),one_one_nat) = X0 ),
    inference(rectify,[],[f995]) ).

tff(f995,axiom,
    ! [X11: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X11),one_one_nat) = X11 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_994_nat__mult__1__right) ).

tff(f7847,plain,
    spl250_108,
    inference(avatar_split_clause,[],[f4655,f7845]) ).

tff(f4655,plain,
    ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),X0) = X0 ),
    inference(cnf_transformation,[],[f1383]) ).

tff(f1383,plain,
    ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),X0) = X0 ),
    inference(rectify,[],[f935]) ).

tff(f935,axiom,
    ! [X11: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),X11) = X11 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_934_plus__nat_Oadd__0) ).

tff(f7843,plain,
    spl250_107,
    inference(avatar_split_clause,[],[f4654,f7841]) ).

tff(f7841,plain,
    ( spl250_107
  <=> ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_107])]) ).

tff(f4654,plain,
    ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),X0) = X0 ),
    inference(cnf_transformation,[],[f1382]) ).

tff(f1382,plain,
    ! [X0: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),X0) = X0 ),
    inference(rectify,[],[f997]) ).

tff(f997,axiom,
    ! [X11: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),X11) = X11 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_996_nat__mult__1) ).

tff(f7839,plain,
    spl250_106,
    inference(avatar_split_clause,[],[f4652,f7837]) ).

tff(f4652,plain,
    ! [X0: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),pls) = X0 ),
    inference(cnf_transformation,[],[f1380]) ).

tff(f1380,plain,
    ! [X0: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),pls) = X0 ),
    inference(rectify,[],[f1187]) ).

tff(f1187,axiom,
    ! [X19: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X19),pls) = X19 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1186_add__Pls__right) ).

tff(f7835,plain,
    spl250_105,
    inference(avatar_split_clause,[],[f4651,f7833]) ).

tff(f7833,plain,
    ( spl250_105
  <=> ! [X0: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),one_one_int) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_105])]) ).

tff(f4651,plain,
    ! [X0: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),one_one_int) = X0 ),
    inference(cnf_transformation,[],[f1379]) ).

tff(f1379,plain,
    ! [X0: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X0),one_one_int) = X0 ),
    inference(rectify,[],[f1021]) ).

tff(f1021,axiom,
    ! [X95: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X95),one_one_int) = X95 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1020_zmult__1__right) ).

tff(f7831,plain,
    spl250_104,
    inference(avatar_split_clause,[],[f4650,f7829]) ).

tff(f7829,plain,
    ( spl250_104
  <=> ! [X0: int] : ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),pls) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_104])]) ).

tff(f4650,plain,
    ! [X0: int] : ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),pls) = X0 ),
    inference(cnf_transformation,[],[f1378]) ).

tff(f1378,plain,
    ! [X0: int] : ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X0),pls) = X0 ),
    inference(rectify,[],[f1185]) ).

tff(f1185,axiom,
    ! [X19: int] : ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X19),pls) = X19 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1184_diff__bin__simps_I1_J) ).

tff(f7827,plain,
    spl250_103,
    inference(avatar_split_clause,[],[f4648,f7825]) ).

tff(f4648,plain,
    ! [X0: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),X0) = X0 ),
    inference(cnf_transformation,[],[f1376]) ).

tff(f1376,plain,
    ! [X0: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),X0) = X0 ),
    inference(rectify,[],[f1186]) ).

tff(f1186,axiom,
    ! [X19: int] : ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),X19) = X19 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1185_add__Pls) ).

tff(f7823,plain,
    spl250_102,
    inference(avatar_split_clause,[],[f4647,f7821]) ).

tff(f7821,plain,
    ( spl250_102
  <=> ! [X0: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_102])]) ).

tff(f4647,plain,
    ! [X0: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),X0) = X0 ),
    inference(cnf_transformation,[],[f1375]) ).

tff(f1375,plain,
    ! [X0: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),X0) = X0 ),
    inference(rectify,[],[f1020]) ).

tff(f1020,axiom,
    ! [X95: int] : ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),X95) = X95 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1019_zmult__1) ).

tff(f7819,plain,
    ( spl250_101
    | ~ spl250_84 ),
    inference(avatar_split_clause,[],[f7757,f7683,f7816]) ).

tff(f7816,plain,
    ( spl250_101
  <=> sP4(pls,pls) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_101])]) ).

tff(f7683,plain,
    ( spl250_84
  <=> ! [X1: int] :
        ( ( pls != X1 )
        | sP4(X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_84])]) ).

tff(f7757,plain,
    ( sP4(pls,pls)
    | ~ spl250_84 ),
    inference(equality_resolution,[],[f7684]) ).

tff(f7684,plain,
    ( ! [X1: int] :
        ( ( pls != X1 )
        | sP4(X1,X1) )
    | ~ spl250_84 ),
    inference(avatar_component_clause,[],[f7683]) ).

tff(f7814,plain,
    spl250_100,
    inference(avatar_split_clause,[],[f4646,f7812]) ).

tff(f7812,plain,
    ( spl250_100
  <=> ! [X0: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),bot_bot_fun_a_bool) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_100])]) ).

tff(f4646,plain,
    ! [X0: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),bot_bot_fun_a_bool) = X0 ),
    inference(cnf_transformation,[],[f1374]) ).

tff(f1374,plain,
    ! [X0: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),bot_bot_fun_a_bool) = X0 ),
    inference(rectify,[],[f517]) ).

tff(f517,axiom,
    ! [X2: fun_a_bool] : ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),bot_bot_fun_a_bool) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_516_Diff__empty) ).

tff(f7810,plain,
    spl250_99,
    inference(avatar_split_clause,[],[f4645,f7808]) ).

tff(f7808,plain,
    ( spl250_99
  <=> ! [X0: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),bot_bot_fun_nat_bool) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_99])]) ).

tff(f4645,plain,
    ! [X0: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),bot_bot_fun_nat_bool) = X0 ),
    inference(cnf_transformation,[],[f1373]) ).

tff(f1373,plain,
    ! [X0: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),bot_bot_fun_nat_bool) = X0 ),
    inference(rectify,[],[f515]) ).

tff(f515,axiom,
    ! [X2: fun_nat_bool] : ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),bot_bot_fun_nat_bool) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_514_Diff__empty) ).

tff(f7806,plain,
    spl250_98,
    inference(avatar_split_clause,[],[f4644,f7804]) ).

tff(f7804,plain,
    ( spl250_98
  <=> ! [X0: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),bot_bot_fun_int_bool) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_98])]) ).

tff(f4644,plain,
    ! [X0: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),bot_bot_fun_int_bool) = X0 ),
    inference(cnf_transformation,[],[f1372]) ).

tff(f1372,plain,
    ! [X0: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),bot_bot_fun_int_bool) = X0 ),
    inference(rectify,[],[f516]) ).

tff(f516,axiom,
    ! [X2: fun_int_bool] : ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),bot_bot_fun_int_bool) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_515_Diff__empty) ).

tff(f7802,plain,
    spl250_97,
    inference(avatar_split_clause,[],[f4643,f7800]) ).

tff(f4643,plain,
    ! [X0: nat] : ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X0) ),
    inference(cnf_transformation,[],[f1371]) ).

tff(f1371,plain,
    ! [X0: nat] : ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X0),X0) ),
    inference(rectify,[],[f928]) ).

tff(f928,axiom,
    ! [X12: nat] : ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X12),X12) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_927_diff__self__eq__0) ).

tff(f7798,plain,
    spl250_96,
    inference(avatar_split_clause,[],[f4642,f7796]) ).

tff(f7796,plain,
    ( spl250_96
  <=> ! [X0: nat] : ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),zero_zero_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_96])]) ).

tff(f4642,plain,
    ! [X0: nat] : ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),zero_zero_nat) ),
    inference(cnf_transformation,[],[f1370]) ).

tff(f1370,plain,
    ! [X0: nat] : ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X0),zero_zero_nat) ),
    inference(rectify,[],[f980]) ).

tff(f980,axiom,
    ! [X12: nat] : ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X12),zero_zero_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_979_mult__0__right) ).

tff(f7794,plain,
    spl250_95,
    inference(avatar_split_clause,[],[f4641,f7792]) ).

tff(f7792,plain,
    ( spl250_95
  <=> ! [X0: nat] : ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_95])]) ).

tff(f4641,plain,
    ! [X0: nat] : ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),X0) ),
    inference(cnf_transformation,[],[f1369]) ).

tff(f1369,plain,
    ! [X0: nat] : ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),X0) ),
    inference(rectify,[],[f930]) ).

tff(f930,axiom,
    ! [X11: nat] : ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_929_diff__0__eq__0) ).

tff(f7790,plain,
    spl250_94,
    inference(avatar_split_clause,[],[f4640,f7788]) ).

tff(f7788,plain,
    ( spl250_94
  <=> ! [X0: nat] : ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_94])]) ).

tff(f4640,plain,
    ! [X0: nat] : ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),X0) ),
    inference(cnf_transformation,[],[f1368]) ).

tff(f1368,plain,
    ! [X0: nat] : ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),X0) ),
    inference(rectify,[],[f979]) ).

tff(f979,axiom,
    ! [X11: nat] : ( zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_978_mult__0) ).

tff(f7786,plain,
    spl250_93,
    inference(avatar_split_clause,[],[f4639,f7784]) ).

tff(f7784,plain,
    ( spl250_93
  <=> ! [X0: fun_a_bool] : ( bot_bot_fun_a_bool = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_93])]) ).

tff(f4639,plain,
    ! [X0: fun_a_bool] : ( bot_bot_fun_a_bool = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X0) ),
    inference(cnf_transformation,[],[f1367]) ).

tff(f1367,plain,
    ! [X0: fun_a_bool] : ( bot_bot_fun_a_bool = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X0),X0) ),
    inference(rectify,[],[f514]) ).

tff(f514,axiom,
    ! [X2: fun_a_bool] : ( bot_bot_fun_a_bool = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_513_Diff__cancel) ).

tff(f7782,plain,
    spl250_92,
    inference(avatar_split_clause,[],[f4638,f7780]) ).

tff(f7780,plain,
    ( spl250_92
  <=> ! [X0: fun_a_bool] : ( bot_bot_fun_a_bool = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,bot_bot_fun_a_bool),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_92])]) ).

tff(f4638,plain,
    ! [X0: fun_a_bool] : ( bot_bot_fun_a_bool = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,bot_bot_fun_a_bool),X0) ),
    inference(cnf_transformation,[],[f1366]) ).

tff(f1366,plain,
    ! [X0: fun_a_bool] : ( bot_bot_fun_a_bool = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,bot_bot_fun_a_bool),X0) ),
    inference(rectify,[],[f527]) ).

tff(f527,axiom,
    ! [X2: fun_a_bool] : ( bot_bot_fun_a_bool = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,bot_bot_fun_a_bool),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_526_empty__Diff) ).

tff(f7778,plain,
    spl250_91,
    inference(avatar_split_clause,[],[f4637,f7776]) ).

tff(f7776,plain,
    ( spl250_91
  <=> ! [X0: fun_int_bool] : ( bot_bot_fun_int_bool = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_91])]) ).

tff(f4637,plain,
    ! [X0: fun_int_bool] : ( bot_bot_fun_int_bool = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X0) ),
    inference(cnf_transformation,[],[f1365]) ).

tff(f1365,plain,
    ! [X0: fun_int_bool] : ( bot_bot_fun_int_bool = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X0),X0) ),
    inference(rectify,[],[f513]) ).

tff(f513,axiom,
    ! [X2: fun_int_bool] : ( bot_bot_fun_int_bool = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_512_Diff__cancel) ).

tff(f7773,plain,
    spl250_90,
    inference(avatar_split_clause,[],[f4636,f7771]) ).

tff(f7771,plain,
    ( spl250_90
  <=> ! [X0: fun_int_bool] : ( bot_bot_fun_int_bool = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,bot_bot_fun_int_bool),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_90])]) ).

tff(f4636,plain,
    ! [X0: fun_int_bool] : ( bot_bot_fun_int_bool = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,bot_bot_fun_int_bool),X0) ),
    inference(cnf_transformation,[],[f1364]) ).

tff(f1364,plain,
    ! [X0: fun_int_bool] : ( bot_bot_fun_int_bool = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,bot_bot_fun_int_bool),X0) ),
    inference(rectify,[],[f526]) ).

tff(f526,axiom,
    ! [X2: fun_int_bool] : ( bot_bot_fun_int_bool = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,bot_bot_fun_int_bool),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_525_empty__Diff) ).

tff(f7769,plain,
    spl250_89,
    inference(avatar_split_clause,[],[f4635,f7767]) ).

tff(f7767,plain,
    ( spl250_89
  <=> ! [X0: fun_nat_bool] : ( bot_bot_fun_nat_bool = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_89])]) ).

tff(f4635,plain,
    ! [X0: fun_nat_bool] : ( bot_bot_fun_nat_bool = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X0) ),
    inference(cnf_transformation,[],[f1363]) ).

tff(f1363,plain,
    ! [X0: fun_nat_bool] : ( bot_bot_fun_nat_bool = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X0),X0) ),
    inference(rectify,[],[f512]) ).

tff(f512,axiom,
    ! [X2: fun_nat_bool] : ( bot_bot_fun_nat_bool = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_511_Diff__cancel) ).

tff(f7765,plain,
    spl250_88,
    inference(avatar_split_clause,[],[f4634,f7763]) ).

tff(f7763,plain,
    ( spl250_88
  <=> ! [X0: fun_nat_bool] : ( bot_bot_fun_nat_bool = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,bot_bot_fun_nat_bool),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_88])]) ).

tff(f4634,plain,
    ! [X0: fun_nat_bool] : ( bot_bot_fun_nat_bool = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,bot_bot_fun_nat_bool),X0) ),
    inference(cnf_transformation,[],[f1362]) ).

tff(f1362,plain,
    ! [X0: fun_nat_bool] : ( bot_bot_fun_nat_bool = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,bot_bot_fun_nat_bool),X0) ),
    inference(rectify,[],[f525]) ).

tff(f525,axiom,
    ! [X2: fun_nat_bool] : ( bot_bot_fun_nat_bool = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,bot_bot_fun_nat_bool),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_524_empty__Diff) ).

tff(f7761,plain,
    spl250_87,
    inference(avatar_split_clause,[],[f4633,f7759]) ).

tff(f7759,plain,
    ( spl250_87
  <=> ! [X0: int] : ( pls = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,pls),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_87])]) ).

tff(f4633,plain,
    ! [X0: int] : ( pls = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,pls),X0) ),
    inference(cnf_transformation,[],[f1361]) ).

tff(f1361,plain,
    ! [X0: int] : ( pls = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,pls),X0) ),
    inference(rectify,[],[f1188]) ).

tff(f1188,axiom,
    ! [X132: int] : ( pls = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,pls),X132) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1187_mult__Pls) ).

tff(f7749,plain,
    ( spl250_86
    | spl250_1
    | ~ spl250_55
    | ~ spl250_58 ),
    inference(avatar_split_clause,[],[f7695,f7572,f7561,f7314,f7746]) ).

tff(f7746,plain,
    ( spl250_86
  <=> ( bot_bot_bool = fTrue ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_86])]) ).

tff(f7695,plain,
    ( hBOOL(fFalse)
    | ( bot_bot_bool = fTrue )
    | ~ spl250_55
    | ~ spl250_58 ),
    inference(superposition,[],[f7574,f7562]) ).

tff(f7574,plain,
    ( hBOOL(bot_bot_bool)
    | ~ spl250_58 ),
    inference(avatar_component_clause,[],[f7572]) ).

tff(f7735,plain,
    ( spl250_85
    | spl250_1
    | ~ spl250_55 ),
    inference(avatar_split_clause,[],[f7689,f7561,f7314,f7733]) ).

tff(f7689,plain,
    ( ! [X0: bool] :
        ( ~ hBOOL(X0)
        | ( fTrue = X0 ) )
    | spl250_1
    | ~ spl250_55 ),
    inference(superposition,[],[f7316,f7562]) ).

tff(f7685,plain,
    spl250_84,
    inference(avatar_split_clause,[],[f7117,f7683]) ).

tff(f7117,plain,
    ! [X1: int] :
      ( ( pls != X1 )
      | sP4(X1,X1) ),
    inference(forward_demodulation,[],[f6795,f4587]) ).

tff(f6795,plain,
    ! [X1: int] :
      ( sP4(X1,X1)
      | ( pls != number_number_of_int(X1) ) ),
    inference(equality_resolution,[],[f6645]) ).

tff(f6645,plain,
    ! [X0: int,X1: int] :
      ( sP4(X0,X1)
      | ( X0 != X1 )
      | ( pls != number_number_of_int(X1) ) ),
    inference(definition_unfolding,[],[f5475,f4550]) ).

tff(f5475,plain,
    ! [X0: int,X1: int] :
      ( sP4(X0,X1)
      | ( X0 != X1 )
      | ( zero_zero_int != number_number_of_int(X1) ) ),
    inference(cnf_transformation,[],[f4045]) ).

tff(f7681,plain,
    spl250_83,
    inference(avatar_split_clause,[],[f6801,f7679]) ).

tff(f7679,plain,
    ( spl250_83
  <=> ! [X1: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_83])]) ).

tff(f6801,plain,
    ! [X1: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1)),
    inference(equality_resolution,[],[f5513]) ).

tff(f5513,plain,
    ! [X0: int,X1: int] :
      ( ( X0 != X1 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
    inference(cnf_transformation,[],[f4074]) ).

tff(f7677,plain,
    spl250_82,
    inference(avatar_split_clause,[],[f6739,f7675]) ).

tff(f6739,plain,
    ! [X1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X1)),
    inference(equality_resolution,[],[f4982]) ).

tff(f4982,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1))
      | ( X0 != X1 ) ),
    inference(cnf_transformation,[],[f1618]) ).

tff(f1618,plain,
    ! [X0: nat,X1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X0),X1))
      | ( X0 != X1 ) ),
    inference(rectify,[],[f1222]) ).

tff(f1222,axiom,
    ! [X15: nat,X16: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X15),X16))
      | ( X15 != X16 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).

tff(f7673,plain,
    spl250_81,
    inference(avatar_split_clause,[],[f6738,f7671]) ).

tff(f7671,plain,
    ( spl250_81
  <=> ! [X1: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X1),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_81])]) ).

tff(f6738,plain,
    ! [X1: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X1),X1)),
    inference(equality_resolution,[],[f4981]) ).

tff(f4981,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X0),X1))
      | ( X0 != X1 ) ),
    inference(cnf_transformation,[],[f1617]) ).

tff(f1617,plain,
    ! [X0: int,X1: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X0),X1))
      | ( X0 != X1 ) ),
    inference(rectify,[],[f1220]) ).

tff(f1220,axiom,
    ! [X15: int,X16: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X15),X16))
      | ( X15 != X16 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Int__Oint_T) ).

tff(f7669,plain,
    spl250_80,
    inference(avatar_split_clause,[],[f6737,f7667]) ).

tff(f7667,plain,
    ( spl250_80
  <=> ! [X1: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_80])]) ).

tff(f6737,plain,
    ! [X1: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X1)),
    inference(equality_resolution,[],[f4980]) ).

tff(f4980,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X1))
      | ( X0 != X1 ) ),
    inference(cnf_transformation,[],[f1616]) ).

tff(f1616,plain,
    ! [X0: fun_nat_bool,X1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X0),X1))
      | ( X0 != X1 ) ),
    inference(rectify,[],[f1240]) ).

tff(f1240,axiom,
    ! [X15: fun_nat_bool,X16: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X15),X16))
      | ( X15 != X16 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).

tff(f7665,plain,
    spl250_79,
    inference(avatar_split_clause,[],[f6736,f7663]) ).

tff(f7663,plain,
    ( spl250_79
  <=> ! [X1: fun_int_bool] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X1),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_79])]) ).

tff(f6736,plain,
    ! [X1: fun_int_bool] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X1),X1)),
    inference(equality_resolution,[],[f4979]) ).

tff(f4979,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X0),X1))
      | ( X0 != X1 ) ),
    inference(cnf_transformation,[],[f1615]) ).

tff(f1615,plain,
    ! [X0: fun_int_bool,X1: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X0),X1))
      | ( X0 != X1 ) ),
    inference(rectify,[],[f1238]) ).

tff(f1238,axiom,
    ! [X15: fun_int_bool,X16: fun_int_bool] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X15),X16))
      | ( X15 != X16 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T) ).

tff(f7661,plain,
    spl250_78,
    inference(avatar_split_clause,[],[f6735,f7659]) ).

tff(f7659,plain,
    ( spl250_78
  <=> ! [X1: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_78])]) ).

tff(f6735,plain,
    ! [X1: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1),X1)),
    inference(equality_resolution,[],[f4978]) ).

tff(f4978,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),X1))
      | ( X0 != X1 ) ),
    inference(cnf_transformation,[],[f1614]) ).

tff(f1614,plain,
    ! [X0: fun_a_bool,X1: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X0),X1))
      | ( X0 != X1 ) ),
    inference(rectify,[],[f1232]) ).

tff(f1232,axiom,
    ! [X15: fun_a_bool,X16: fun_a_bool] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X15),X16))
      | ( X15 != X16 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).

tff(f7657,plain,
    spl250_77,
    inference(avatar_split_clause,[],[f6734,f7655]) ).

tff(f7655,plain,
    ( spl250_77
  <=> ! [X1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_77])]) ).

tff(f6734,plain,
    ! [X1: fun_pname_bool] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1),X1)),
    inference(equality_resolution,[],[f4977]) ).

tff(f4977,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X0),X1))
      | ( X0 != X1 ) ),
    inference(cnf_transformation,[],[f1613]) ).

tff(f1613,plain,
    ! [X0: fun_pname_bool,X1: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X0),X1))
      | ( X0 != X1 ) ),
    inference(rectify,[],[f1242]) ).

tff(f1242,axiom,
    ! [X15: fun_pname_bool,X16: fun_pname_bool] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X15),X16))
      | ( X15 != X16 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).

tff(f7653,plain,
    spl250_76,
    inference(avatar_split_clause,[],[f6733,f7651]) ).

tff(f7651,plain,
    ( spl250_76
  <=> ! [X1: x_a] : hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_76])]) ).

tff(f6733,plain,
    ! [X1: x_a] : hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X1)),
    inference(equality_resolution,[],[f4976]) ).

tff(f4976,plain,
    ! [X0: x_a,X1: x_a] :
      ( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1))
      | ( X0 != X1 ) ),
    inference(cnf_transformation,[],[f1612]) ).

tff(f1612,plain,
    ! [X0: x_a,X1: x_a] :
      ( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X0),X1))
      | ( X0 != X1 ) ),
    inference(rectify,[],[f1214]) ).

tff(f1214,axiom,
    ! [X15: x_a,X16: x_a] :
      ( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X15),X16))
      | ( X15 != X16 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000t__a_T) ).

tff(f7649,plain,
    spl250_75,
    inference(avatar_split_clause,[],[f6732,f7647]) ).

tff(f7647,plain,
    ( spl250_75
  <=> ! [X1: pname] : hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_75])]) ).

tff(f6732,plain,
    ! [X1: pname] : hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1),X1)),
    inference(equality_resolution,[],[f4975]) ).

tff(f4975,plain,
    ! [X0: pname,X1: pname] :
      ( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X1))
      | ( X0 != X1 ) ),
    inference(cnf_transformation,[],[f1611]) ).

tff(f1611,plain,
    ! [X0: pname,X1: pname] :
      ( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X0),X1))
      | ( X0 != X1 ) ),
    inference(rectify,[],[f1224]) ).

tff(f1224,axiom,
    ! [X15: pname,X16: pname] :
      ( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X15),X16))
      | ( X15 != X16 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Opname_T) ).

tff(f7645,plain,
    spl250_74,
    inference(avatar_split_clause,[],[f6576,f7643]) ).

tff(f6576,plain,
    ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0)),
    inference(definition_unfolding,[],[f4620,f4549]) ).

tff(f4620,plain,
    ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),X0)),
    inference(cnf_transformation,[],[f1348]) ).

tff(f1348,plain,
    ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),X0)),
    inference(rectify,[],[f629]) ).

tff(f629,axiom,
    ! [X72: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),X72)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_628_bot__least) ).

tff(f7641,plain,
    spl250_73,
    inference(avatar_split_clause,[],[f6568,f7638]) ).

tff(f6568,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),one_one_int)),
    inference(definition_unfolding,[],[f4577,f4550]) ).

tff(f4577,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
    inference(cnf_transformation,[],[f1087]) ).

tff(f1087,axiom,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1086_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).

tff(f7636,plain,
    spl250_72,
    inference(avatar_split_clause,[],[f6567,f7633]) ).

tff(f6567,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),one_one_int)),
    inference(definition_unfolding,[],[f4575,f4550]) ).

tff(f4575,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
    inference(cnf_transformation,[],[f1036]) ).

tff(f1036,axiom,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1035_int__0__less__1) ).

tff(f7631,plain,
    spl250_71,
    inference(avatar_split_clause,[],[f5253,f7629]) ).

tff(f7629,plain,
    ( spl250_71
  <=> ! [X0: fun_fu425979586l_bool] :
        ( ( bot_bot_fun_nat_bool != sK113(X0) )
        | ~ sP3(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_71])]) ).

tff(f5253,plain,
    ! [X0: fun_fu425979586l_bool] :
      ( ( bot_bot_fun_nat_bool != sK113(X0) )
      | ~ sP3(X0) ),
    inference(cnf_transformation,[],[f3968]) ).

tff(f7627,plain,
    spl250_70,
    inference(avatar_split_clause,[],[f5210,f7625]) ).

tff(f7625,plain,
    ( spl250_70
  <=> ! [X0: fun_fu819804446l_bool] :
        ( ( bot_bot_fun_int_bool != sK106(X0) )
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_70])]) ).

tff(f5210,plain,
    ! [X0: fun_fu819804446l_bool] :
      ( ( bot_bot_fun_int_bool != sK106(X0) )
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f3957]) ).

tff(f7623,plain,
    spl250_69,
    inference(avatar_split_clause,[],[f5171,f7621]) ).

tff(f7621,plain,
    ( spl250_69
  <=> ! [X0: fun_fun_a_bool_bool] :
        ( ( bot_bot_fun_a_bool != sK99(X0) )
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_69])]) ).

tff(f5171,plain,
    ! [X0: fun_fun_a_bool_bool] :
      ( ( bot_bot_fun_a_bool != sK99(X0) )
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f3947]) ).

tff(f7619,plain,
    spl250_68,
    inference(avatar_split_clause,[],[f5130,f7617]) ).

tff(f7617,plain,
    ( spl250_68
  <=> ! [X0: fun_fu1430349052l_bool] :
        ( ( bot_bo844097828e_bool != sK92(X0) )
        | ~ sP0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_68])]) ).

tff(f5130,plain,
    ! [X0: fun_fu1430349052l_bool] :
      ( ( bot_bo844097828e_bool != sK92(X0) )
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f3936]) ).

tff(f7614,plain,
    spl250_67,
    inference(avatar_split_clause,[],[f4874,f7612]) ).

tff(f4874,plain,
    ! [X0: bool,X1: nat] : ( hAPP_nat_bool(cOMBK_bool_nat(X0),X1) = X0 ),
    inference(cnf_transformation,[],[f1522]) ).

tff(f1522,plain,
    ! [X0: bool,X1: nat] : ( hAPP_nat_bool(cOMBK_bool_nat(X0),X1) = X0 ),
    inference(rectify,[],[f1230]) ).

tff(f1230,axiom,
    ! [X156: bool,X157: nat] : ( hAPP_nat_bool(cOMBK_bool_nat(X156),X157) = X156 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U) ).

tff(f7610,plain,
    spl250_66,
    inference(avatar_split_clause,[],[f4873,f7608]) ).

tff(f4873,plain,
    ! [X0: bool,X1: int] : ( hAPP_int_bool(cOMBK_bool_int(X0),X1) = X0 ),
    inference(cnf_transformation,[],[f1521]) ).

tff(f1521,plain,
    ! [X0: bool,X1: int] : ( hAPP_int_bool(cOMBK_bool_int(X0),X1) = X0 ),
    inference(rectify,[],[f1229]) ).

tff(f1229,axiom,
    ! [X156: bool,X157: int] : ( hAPP_int_bool(cOMBK_bool_int(X156),X157) = X156 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Int__Oint_U) ).

tff(f7606,plain,
    spl250_65,
    inference(avatar_split_clause,[],[f4872,f7604]) ).

tff(f7604,plain,
    ( spl250_65
  <=> ! [X0: int,X1: nat] : ( hAPP_nat_int(cOMBK_int_nat(X0),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_65])]) ).

tff(f4872,plain,
    ! [X0: int,X1: nat] : ( hAPP_nat_int(cOMBK_int_nat(X0),X1) = X0 ),
    inference(cnf_transformation,[],[f1520]) ).

tff(f1520,plain,
    ! [X0: int,X1: nat] : ( hAPP_nat_int(cOMBK_int_nat(X0),X1) = X0 ),
    inference(rectify,[],[f1228]) ).

tff(f1228,axiom,
    ! [X156: int,X157: nat] : ( hAPP_nat_int(cOMBK_int_nat(X156),X157) = X156 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Int__Oint_000tc__Nat__Onat_U) ).

tff(f7602,plain,
    spl250_64,
    inference(avatar_split_clause,[],[f4871,f7600]) ).

tff(f7600,plain,
    ( spl250_64
  <=> ! [X0: bool,X1: x_a] : ( hAPP_a_bool(cOMBK_bool_a(X0),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_64])]) ).

tff(f4871,plain,
    ! [X0: bool,X1: x_a] : ( hAPP_a_bool(cOMBK_bool_a(X0),X1) = X0 ),
    inference(cnf_transformation,[],[f1519]) ).

tff(f1519,plain,
    ! [X0: bool,X1: x_a] : ( hAPP_a_bool(cOMBK_bool_a(X0),X1) = X0 ),
    inference(rectify,[],[f1225]) ).

tff(f1225,axiom,
    ! [X156: bool,X157: x_a] : ( hAPP_a_bool(cOMBK_bool_a(X156),X157) = X156 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000t__a_U) ).

tff(f7598,plain,
    spl250_63,
    inference(avatar_split_clause,[],[f4870,f7596]) ).

tff(f7596,plain,
    ( spl250_63
  <=> ! [X0: x_a,X1: pname] : ( hAPP_pname_a(cOMBK_a_pname(X0),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_63])]) ).

tff(f4870,plain,
    ! [X0: x_a,X1: pname] : ( hAPP_pname_a(cOMBK_a_pname(X0),X1) = X0 ),
    inference(cnf_transformation,[],[f1518]) ).

tff(f1518,plain,
    ! [X0: x_a,X1: pname] : ( hAPP_pname_a(cOMBK_a_pname(X0),X1) = X0 ),
    inference(rectify,[],[f1226]) ).

tff(f1226,axiom,
    ! [X156: x_a,X157: pname] : ( hAPP_pname_a(cOMBK_a_pname(X156),X157) = X156 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000t__a_000tc__Com__Opname_U) ).

tff(f7594,plain,
    ( ~ spl250_57
    | ~ spl250_59 ),
    inference(avatar_contradiction_clause,[],[f7593]) ).

tff(f7593,plain,
    ( $false
    | ~ spl250_57
    | ~ spl250_59 ),
    inference(resolution,[],[f7570,f7578]) ).

tff(f7578,plain,
    ( ! [X0: x_a] : hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X0))
    | ~ spl250_59 ),
    inference(avatar_component_clause,[],[f7577]) ).

tff(f7577,plain,
    ( spl250_59
  <=> ! [X0: x_a] : hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_59])]) ).

tff(f7592,plain,
    ( ~ spl250_58
    | spl250_62 ),
    inference(avatar_split_clause,[],[f4802,f7590,f7572]) ).

tff(f4802,plain,
    ! [X0: nat] :
      ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0))
      | ~ hBOOL(bot_bot_bool) ),
    inference(cnf_transformation,[],[f3835]) ).

tff(f3835,plain,
    ! [X0: nat] :
      ( ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0)) ) ),
    inference(nnf_transformation,[],[f1484]) ).

tff(f1484,plain,
    ! [X0: nat] :
      ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X0))
    <=> hBOOL(bot_bot_bool) ),
    inference(rectify,[],[f536]) ).

tff(f536,axiom,
    ! [X8: nat] :
      ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X8))
    <=> hBOOL(bot_bot_bool) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_535_bot__apply) ).

tff(f7588,plain,
    ( spl250_61
    | ~ spl250_15
    | ~ spl250_22 ),
    inference(avatar_split_clause,[],[f7481,f7416,f7384,f7585]) ).

tff(f7384,plain,
    ( spl250_15
  <=> ! [X0: fun_int_bool] : ( collect_int(X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_15])]) ).

tff(f7416,plain,
    ( spl250_22
  <=> ( bot_bot_fun_int_bool = collect_int(cOMBK_bool_int(fFalse)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_22])]) ).

tff(f7481,plain,
    ( ( bot_bot_fun_int_bool = cOMBK_bool_int(fFalse) )
    | ~ spl250_15
    | ~ spl250_22 ),
    inference(superposition,[],[f7418,f7385]) ).

tff(f7385,plain,
    ( ! [X0: fun_int_bool] : ( collect_int(X0) = X0 )
    | ~ spl250_15 ),
    inference(avatar_component_clause,[],[f7384]) ).

tff(f7418,plain,
    ( ( bot_bot_fun_int_bool = collect_int(cOMBK_bool_int(fFalse)) )
    | ~ spl250_22 ),
    inference(avatar_component_clause,[],[f7416]) ).

tff(f7583,plain,
    ( ~ spl250_58
    | spl250_60 ),
    inference(avatar_split_clause,[],[f4798,f7581,f7572]) ).

tff(f4798,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X0))
      | ~ hBOOL(bot_bot_bool) ),
    inference(cnf_transformation,[],[f3833]) ).

tff(f3833,plain,
    ! [X0: int] :
      ( ( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X0))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X0)) ) ),
    inference(nnf_transformation,[],[f1482]) ).

tff(f1482,plain,
    ! [X0: int] :
      ( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X0))
    <=> hBOOL(bot_bot_bool) ),
    inference(rectify,[],[f543]) ).

tff(f543,axiom,
    ! [X27: int] :
      ( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X27))
    <=> hBOOL(bot_bot_bool) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_542_bot__fun__def) ).

tff(f7579,plain,
    ( ~ spl250_58
    | spl250_59 ),
    inference(avatar_split_clause,[],[f4768,f7577,f7572]) ).

tff(f4768,plain,
    ! [X0: x_a] :
      ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X0))
      | ~ hBOOL(bot_bot_bool) ),
    inference(cnf_transformation,[],[f3799]) ).

tff(f3799,plain,
    ! [X0: x_a] :
      ( ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X0))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X0)) ) ),
    inference(nnf_transformation,[],[f1472]) ).

tff(f1472,plain,
    ! [X0: x_a] :
      ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X0))
    <=> hBOOL(bot_bot_bool) ),
    inference(rectify,[],[f538]) ).

tff(f538,axiom,
    ! [X8: x_a] :
      ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X8))
    <=> hBOOL(bot_bot_bool) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_537_bot__apply) ).

tff(f7575,plain,
    ( spl250_57
    | spl250_58 ),
    inference(avatar_split_clause,[],[f4767,f7572,f7569]) ).

tff(f4767,plain,
    ! [X0: x_a] :
      ( hBOOL(bot_bot_bool)
      | ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X0)) ),
    inference(cnf_transformation,[],[f3799]) ).

tff(f7567,plain,
    spl250_56,
    inference(avatar_split_clause,[],[f4706,f7565]) ).

tff(f7565,plain,
    ( spl250_56
  <=> ! [X0: bool] :
        ( ~ hBOOL(X0)
        | ~ hBOOL(hAPP_bool_bool(fNot,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_56])]) ).

tff(f4706,plain,
    ! [X0: bool] :
      ( ~ hBOOL(X0)
      | ~ hBOOL(hAPP_bool_bool(fNot,X0)) ),
    inference(cnf_transformation,[],[f1430]) ).

tff(f1430,plain,
    ! [X0: bool] :
      ( ~ hBOOL(X0)
      | ~ hBOOL(hAPP_bool_bool(fNot,X0)) ),
    inference(rectify,[],[f1200]) ).

tff(f1200,axiom,
    ! [X156: bool] :
      ( ~ hBOOL(X156)
      | ~ hBOOL(hAPP_bool_bool(fNot,X156)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).

tff(f7563,plain,
    spl250_55,
    inference(avatar_split_clause,[],[f4704,f7561]) ).

tff(f4704,plain,
    ! [X0: bool] :
      ( ( fFalse = X0 )
      | ( fTrue = X0 ) ),
    inference(cnf_transformation,[],[f1428]) ).

tff(f1428,plain,
    ! [X0: bool] :
      ( ( fFalse = X0 )
      | ( fTrue = X0 ) ),
    inference(rectify,[],[f1217]) ).

tff(f1217,axiom,
    ! [X156: bool] :
      ( ( fFalse = X156 )
      | ( fTrue = X156 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_000tc__Nat__Onat_T) ).

tff(f7559,plain,
    spl250_54,
    inference(avatar_split_clause,[],[f4703,f7557]) ).

tff(f7557,plain,
    ( spl250_54
  <=> ! [X0: bool] :
        ( hBOOL(hAPP_bool_bool(fNot,X0))
        | hBOOL(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_54])]) ).

tff(f4703,plain,
    ! [X0: bool] :
      ( hBOOL(hAPP_bool_bool(fNot,X0))
      | hBOOL(X0) ),
    inference(cnf_transformation,[],[f1427]) ).

tff(f1427,plain,
    ! [X0: bool] :
      ( hBOOL(hAPP_bool_bool(fNot,X0))
      | hBOOL(X0) ),
    inference(rectify,[],[f1201]) ).

tff(f1201,axiom,
    ! [X156: bool] :
      ( hBOOL(hAPP_bool_bool(fNot,X156))
      | hBOOL(X156) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).

tff(f7555,plain,
    spl250_53,
    inference(avatar_split_clause,[],[f4631,f7553]) ).

tff(f4631,plain,
    ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0)),
    inference(cnf_transformation,[],[f1359]) ).

tff(f1359,plain,
    ! [X0: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0)),
    inference(rectify,[],[f131]) ).

tff(f131,axiom,
    ! [X11: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X11),X11)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_le__refl) ).

tff(f7550,plain,
    spl250_52,
    inference(avatar_split_clause,[],[f4629,f7548]) ).

tff(f4629,plain,
    ! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X0)),
    inference(cnf_transformation,[],[f1357]) ).

tff(f1357,plain,
    ! [X0: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X0)),
    inference(rectify,[],[f304]) ).

tff(f304,axiom,
    ! [X33: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X33),X33)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_order__refl) ).

tff(f7546,plain,
    spl250_51,
    inference(avatar_split_clause,[],[f4627,f7544]) ).

tff(f7544,plain,
    ( spl250_51
  <=> ! [X0: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_51])]) ).

tff(f4627,plain,
    ! [X0: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X0)),
    inference(cnf_transformation,[],[f1355]) ).

tff(f1355,plain,
    ! [X0: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X0),X0)),
    inference(rectify,[],[f403]) ).

tff(f403,axiom,
    ! [X2: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_402_subset__refl) ).

tff(f7542,plain,
    spl250_50,
    inference(avatar_split_clause,[],[f4625,f7540]) ).

tff(f7540,plain,
    ( spl250_50
  <=> ! [X0: fun_int_bool] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_50])]) ).

tff(f4625,plain,
    ! [X0: fun_int_bool] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X0)),
    inference(cnf_transformation,[],[f1353]) ).

tff(f1353,plain,
    ! [X0: fun_int_bool] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X0),X0)),
    inference(rectify,[],[f302]) ).

tff(f302,axiom,
    ! [X8: fun_int_bool] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X8),X8)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_order__refl) ).

tff(f7538,plain,
    spl250_49,
    inference(avatar_split_clause,[],[f4623,f7536]) ).

tff(f4623,plain,
    ! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X0)),
    inference(cnf_transformation,[],[f1351]) ).

tff(f1351,plain,
    ! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X0),X0)),
    inference(rectify,[],[f404]) ).

tff(f404,axiom,
    ! [X2: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_403_subset__refl) ).

tff(f7534,plain,
    spl250_48,
    inference(avatar_split_clause,[],[f4618,f7532]) ).

tff(f4618,plain,
    ! [X0: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X0)),
    inference(cnf_transformation,[],[f1346]) ).

tff(f1346,plain,
    ! [X0: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X0)),
    inference(rectify,[],[f627]) ).

tff(f627,axiom,
    ! [X5: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_626_bot__least) ).

tff(f7530,plain,
    spl250_47,
    inference(avatar_split_clause,[],[f4616,f7528]) ).

tff(f4616,plain,
    ! [X0: fun_int_bool] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),X0)),
    inference(cnf_transformation,[],[f1344]) ).

tff(f1344,plain,
    ! [X0: fun_int_bool] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),X0)),
    inference(rectify,[],[f503]) ).

tff(f503,axiom,
    ! [X2: fun_int_bool] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_502_empty__subsetI) ).

tff(f7526,plain,
    spl250_46,
    inference(avatar_split_clause,[],[f4614,f7524]) ).

tff(f4614,plain,
    ! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),X0)),
    inference(cnf_transformation,[],[f1342]) ).

tff(f1342,plain,
    ! [X0: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),X0)),
    inference(rectify,[],[f630]) ).

tff(f630,axiom,
    ! [X5: fun_a_bool] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),X5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_bot__least) ).

tff(f7522,plain,
    spl250_45,
    inference(avatar_split_clause,[],[f4612,f7520]) ).

tff(f7520,plain,
    ( spl250_45
  <=> ! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_45])]) ).

tff(f4612,plain,
    ! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X0)),
    inference(cnf_transformation,[],[f1340]) ).

tff(f1340,plain,
    ! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X0)),
    inference(rectify,[],[f862]) ).

tff(f862,axiom,
    ! [X11: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X11),X11)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_861_less__irrefl__nat) ).

tff(f7518,plain,
    spl250_44,
    inference(avatar_split_clause,[],[f4609,f7516]) ).

tff(f4609,plain,
    ! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat)),
    inference(cnf_transformation,[],[f1337]) ).

tff(f1337,plain,
    ! [X0: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat)),
    inference(rectify,[],[f922]) ).

tff(f922,axiom,
    ! [X11: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X11),zero_zero_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_921_less__zeroE) ).

tff(f7514,plain,
    spl250_43,
    inference(avatar_split_clause,[],[f4608,f7512]) ).

tff(f4608,plain,
    ! [X0: nat] : ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_nat_int(semiri1621563631at_int,X0))),
    inference(cnf_transformation,[],[f1336]) ).

tff(f1336,plain,
    ! [X0: nat] : ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_nat_int(semiri1621563631at_int,X0))),
    inference(rectify,[],[f1152]) ).

tff(f1152,axiom,
    ! [X11: nat] : ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_nat_int(semiri1621563631at_int,X11))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1151_not__neg__int) ).

tff(f7510,plain,
    spl250_42,
    inference(avatar_split_clause,[],[f4606,f7508]) ).

tff(f4606,plain,
    ! [X0: nat] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),bot_bot_fun_nat_bool)),
    inference(cnf_transformation,[],[f1334]) ).

tff(f1334,plain,
    ! [X0: nat] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X0),bot_bot_fun_nat_bool)),
    inference(rectify,[],[f492]) ).

tff(f492,axiom,
    ! [X5: nat] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5),bot_bot_fun_nat_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_491_emptyE) ).

tff(f7506,plain,
    spl250_41,
    inference(avatar_split_clause,[],[f4604,f7504]) ).

tff(f4604,plain,
    ! [X0: int] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),bot_bot_fun_int_bool)),
    inference(cnf_transformation,[],[f1332]) ).

tff(f1332,plain,
    ! [X0: int] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X0),bot_bot_fun_int_bool)),
    inference(rectify,[],[f518]) ).

tff(f518,axiom,
    ! [X29: int] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X29),bot_bot_fun_int_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_517_empty__iff) ).

tff(f7502,plain,
    spl250_40,
    inference(avatar_split_clause,[],[f4602,f7500]) ).

tff(f4602,plain,
    ! [X0: x_a] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),bot_bot_fun_a_bool)),
    inference(cnf_transformation,[],[f1330]) ).

tff(f1330,plain,
    ! [X0: x_a] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X0),bot_bot_fun_a_bool)),
    inference(rectify,[],[f520]) ).

tff(f520,axiom,
    ! [X29: x_a] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X29),bot_bot_fun_a_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_519_empty__iff) ).

tff(f7498,plain,
    spl250_39,
    inference(avatar_split_clause,[],[f4600,f7496]) ).

tff(f4600,plain,
    ! [X0: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),bot_bo844097828e_bool)),
    inference(cnf_transformation,[],[f1328]) ).

tff(f1328,plain,
    ! [X0: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X0),bot_bo844097828e_bool)),
    inference(rectify,[],[f494]) ).

tff(f494,axiom,
    ! [X5: pname] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5),bot_bo844097828e_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_493_emptyE) ).

tff(f7494,plain,
    spl250_38,
    inference(avatar_split_clause,[],[f4542,f7491]) ).

tff(f4542,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
    inference(cnf_transformation,[],[f1307]) ).

tff(f1307,axiom,
    hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).

tff(f7489,plain,
    ( ~ spl250_37
    | ~ spl250_20
    | ~ spl250_24 ),
    inference(avatar_split_clause,[],[f7483,f7426,f7406,f7486]) ).

tff(f7486,plain,
    ( spl250_37
  <=> ( one_one_nat = zero_zero_nat ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_37])]) ).

tff(f7426,plain,
    ( spl250_24
  <=> ! [X0: nat] : ( zero_zero_nat != hAPP_nat_nat(suc,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_24])]) ).

tff(f7483,plain,
    ( ( one_one_nat != zero_zero_nat )
    | ~ spl250_20
    | ~ spl250_24 ),
    inference(superposition,[],[f7427,f7408]) ).

tff(f7427,plain,
    ( ! [X0: nat] : ( zero_zero_nat != hAPP_nat_nat(suc,X0) )
    | ~ spl250_24 ),
    inference(avatar_component_clause,[],[f7426]) ).

tff(f7480,plain,
    ( spl250_36
    | ~ spl250_17
    | ~ spl250_21 ),
    inference(avatar_split_clause,[],[f7474,f7411,f7392,f7477]) ).

tff(f7392,plain,
    ( spl250_17
  <=> ! [X0: fun_nat_bool] : ( collect_nat(X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_17])]) ).

tff(f7411,plain,
    ( spl250_21
  <=> ( bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_21])]) ).

tff(f7474,plain,
    ( ( bot_bot_fun_nat_bool = cOMBK_bool_nat(fFalse) )
    | ~ spl250_17
    | ~ spl250_21 ),
    inference(superposition,[],[f7413,f7393]) ).

tff(f7393,plain,
    ( ! [X0: fun_nat_bool] : ( collect_nat(X0) = X0 )
    | ~ spl250_17 ),
    inference(avatar_component_clause,[],[f7392]) ).

tff(f7413,plain,
    ( ( bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse)) )
    | ~ spl250_21 ),
    inference(avatar_component_clause,[],[f7411]) ).

tff(f7473,plain,
    spl250_35,
    inference(avatar_split_clause,[],[f6911,f7471]) ).

tff(f7471,plain,
    ( spl250_35
  <=> ! [X2: x_a,X3: x_a] : sP28(X3,X2,X2,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_35])]) ).

tff(f6911,plain,
    ! [X2: x_a,X3: x_a] : sP28(X3,X2,X2,X3),
    inference(equality_resolution,[],[f6910]) ).

tff(f6910,plain,
    ! [X2: x_a,X3: x_a,X0: x_a] :
      ( sP28(X0,X2,X2,X3)
      | ( X0 != X3 ) ),
    inference(equality_resolution,[],[f6536]) ).

tff(f6536,plain,
    ! [X2: x_a,X3: x_a,X0: x_a,X1: x_a] :
      ( sP28(X0,X1,X2,X3)
      | ( X1 != X2 )
      | ( X0 != X3 ) ),
    inference(cnf_transformation,[],[f4532]) ).

tff(f7469,plain,
    spl250_34,
    inference(avatar_split_clause,[],[f6909,f7467]) ).

tff(f7467,plain,
    ( spl250_34
  <=> ! [X1: x_a,X3: x_a] : sP28(X1,X1,X3,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_34])]) ).

tff(f6909,plain,
    ! [X3: x_a,X1: x_a] : sP28(X1,X1,X3,X3),
    inference(equality_resolution,[],[f6908]) ).

tff(f6908,plain,
    ! [X2: x_a,X3: x_a,X1: x_a] :
      ( sP28(X1,X1,X2,X3)
      | ( X2 != X3 ) ),
    inference(equality_resolution,[],[f6537]) ).

tff(f6537,plain,
    ! [X2: x_a,X3: x_a,X0: x_a,X1: x_a] :
      ( sP28(X0,X1,X2,X3)
      | ( X0 != X1 )
      | ( X2 != X3 ) ),
    inference(cnf_transformation,[],[f4532]) ).

tff(f7465,plain,
    spl250_33,
    inference(avatar_split_clause,[],[f6907,f7463]) ).

tff(f7463,plain,
    ( spl250_33
  <=> ! [X2: nat,X3: nat] : sP27(X3,X2,X2,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_33])]) ).

tff(f6907,plain,
    ! [X2: nat,X3: nat] : sP27(X3,X2,X2,X3),
    inference(equality_resolution,[],[f6906]) ).

tff(f6906,plain,
    ! [X2: nat,X3: nat,X0: nat] :
      ( sP27(X0,X2,X2,X3)
      | ( X0 != X3 ) ),
    inference(equality_resolution,[],[f6528]) ).

tff(f6528,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( sP27(X0,X1,X2,X3)
      | ( X1 != X2 )
      | ( X0 != X3 ) ),
    inference(cnf_transformation,[],[f4528]) ).

tff(f7461,plain,
    spl250_32,
    inference(avatar_split_clause,[],[f6905,f7459]) ).

tff(f7459,plain,
    ( spl250_32
  <=> ! [X1: nat,X3: nat] : sP27(X1,X1,X3,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_32])]) ).

tff(f6905,plain,
    ! [X3: nat,X1: nat] : sP27(X1,X1,X3,X3),
    inference(equality_resolution,[],[f6904]) ).

tff(f6904,plain,
    ! [X2: nat,X3: nat,X1: nat] :
      ( sP27(X1,X1,X2,X3)
      | ( X2 != X3 ) ),
    inference(equality_resolution,[],[f6529]) ).

tff(f6529,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( sP27(X0,X1,X2,X3)
      | ( X0 != X1 )
      | ( X2 != X3 ) ),
    inference(cnf_transformation,[],[f4528]) ).

tff(f7457,plain,
    spl250_31,
    inference(avatar_split_clause,[],[f6903,f7455]) ).

tff(f7455,plain,
    ( spl250_31
  <=> ! [X2: int,X3: int] : sP26(X3,X2,X2,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_31])]) ).

tff(f6903,plain,
    ! [X2: int,X3: int] : sP26(X3,X2,X2,X3),
    inference(equality_resolution,[],[f6902]) ).

tff(f6902,plain,
    ! [X2: int,X3: int,X0: int] :
      ( sP26(X0,X2,X2,X3)
      | ( X0 != X3 ) ),
    inference(equality_resolution,[],[f6520]) ).

tff(f6520,plain,
    ! [X2: int,X3: int,X0: int,X1: int] :
      ( sP26(X0,X1,X2,X3)
      | ( X1 != X2 )
      | ( X0 != X3 ) ),
    inference(cnf_transformation,[],[f4524]) ).

tff(f7453,plain,
    spl250_30,
    inference(avatar_split_clause,[],[f6901,f7451]) ).

tff(f7451,plain,
    ( spl250_30
  <=> ! [X1: int,X3: int] : sP26(X1,X1,X3,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_30])]) ).

tff(f6901,plain,
    ! [X3: int,X1: int] : sP26(X1,X1,X3,X3),
    inference(equality_resolution,[],[f6900]) ).

tff(f6900,plain,
    ! [X2: int,X3: int,X1: int] :
      ( sP26(X1,X1,X2,X3)
      | ( X2 != X3 ) ),
    inference(equality_resolution,[],[f6521]) ).

tff(f6521,plain,
    ! [X2: int,X3: int,X0: int,X1: int] :
      ( sP26(X0,X1,X2,X3)
      | ( X0 != X1 )
      | ( X2 != X3 ) ),
    inference(cnf_transformation,[],[f4524]) ).

tff(f7449,plain,
    spl250_29,
    inference(avatar_split_clause,[],[f6564,f7446]) ).

tff(f6564,plain,
    hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = pls,
    inference(definition_unfolding,[],[f4567,f4550]) ).

tff(f4567,plain,
    zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
    inference(cnf_transformation,[],[f1117]) ).

tff(f1117,axiom,
    zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1116_transfer__int__nat__numerals_I1_J) ).

tff(f7444,plain,
    spl250_28,
    inference(avatar_split_clause,[],[f4599,f7442]) ).

tff(f7442,plain,
    ( spl250_28
  <=> ! [X0: nat] : ( hAPP_nat_nat(cOMBI_nat,X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_28])]) ).

tff(f4599,plain,
    ! [X0: nat] : ( hAPP_nat_nat(cOMBI_nat,X0) = X0 ),
    inference(cnf_transformation,[],[f1327]) ).

tff(f1327,plain,
    ! [X0: nat] : ( hAPP_nat_nat(cOMBI_nat,X0) = X0 ),
    inference(rectify,[],[f1218]) ).

tff(f1218,axiom,
    ! [X156: nat] : ( hAPP_nat_nat(cOMBI_nat,X156) = X156 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_COMBI_000tc__Nat__Onat_U) ).

tff(f7440,plain,
    spl250_27,
    inference(avatar_split_clause,[],[f4598,f7438]) ).

tff(f7438,plain,
    ( spl250_27
  <=> ! [X0: fun_pname_a] : ( bot_bot_fun_a_bool = image_pname_a(X0,bot_bo844097828e_bool) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_27])]) ).

tff(f4598,plain,
    ! [X0: fun_pname_a] : ( bot_bot_fun_a_bool = image_pname_a(X0,bot_bo844097828e_bool) ),
    inference(cnf_transformation,[],[f1326]) ).

tff(f1326,plain,
    ! [X0: fun_pname_a] : ( bot_bot_fun_a_bool = image_pname_a(X0,bot_bo844097828e_bool) ),
    inference(rectify,[],[f616]) ).

tff(f616,axiom,
    ! [X6: fun_pname_a] : ( bot_bot_fun_a_bool = image_pname_a(X6,bot_bo844097828e_bool) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_615_image__empty) ).

tff(f7436,plain,
    spl250_26,
    inference(avatar_split_clause,[],[f4597,f7434]) ).

tff(f7434,plain,
    ( spl250_26
  <=> ! [X0: fun_nat_int] : ( bot_bot_fun_int_bool = image_nat_int(X0,bot_bot_fun_nat_bool) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_26])]) ).

tff(f4597,plain,
    ! [X0: fun_nat_int] : ( bot_bot_fun_int_bool = image_nat_int(X0,bot_bot_fun_nat_bool) ),
    inference(cnf_transformation,[],[f1325]) ).

tff(f1325,plain,
    ! [X0: fun_nat_int] : ( bot_bot_fun_int_bool = image_nat_int(X0,bot_bot_fun_nat_bool) ),
    inference(rectify,[],[f615]) ).

tff(f615,axiom,
    ! [X6: fun_nat_int] : ( bot_bot_fun_int_bool = image_nat_int(X6,bot_bot_fun_nat_bool) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_614_image__empty) ).

tff(f7432,plain,
    spl250_25,
    inference(avatar_split_clause,[],[f4591,f7430]) ).

tff(f4591,plain,
    ! [X0: nat] : ( hAPP_nat_nat(suc,X0) != X0 ),
    inference(cnf_transformation,[],[f1319]) ).

tff(f1319,plain,
    ! [X0: nat] : ( hAPP_nat_nat(suc,X0) != X0 ),
    inference(rectify,[],[f126]) ).

tff(f126,axiom,
    ! [X11: nat] : ( hAPP_nat_nat(suc,X11) != X11 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_n__not__Suc__n) ).

tff(f7428,plain,
    spl250_24,
    inference(avatar_split_clause,[],[f4589,f7426]) ).

tff(f4589,plain,
    ! [X0: nat] : ( zero_zero_nat != hAPP_nat_nat(suc,X0) ),
    inference(cnf_transformation,[],[f1317]) ).

tff(f1317,plain,
    ! [X0: nat] : ( zero_zero_nat != hAPP_nat_nat(suc,X0) ),
    inference(rectify,[],[f943]) ).

tff(f943,axiom,
    ! [X125: nat] : ( zero_zero_nat != hAPP_nat_nat(suc,X125) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_942_nat_Osimps_I3_J) ).

tff(f7424,plain,
    spl250_23,
    inference(avatar_split_clause,[],[f4572,f7421]) ).

tff(f7421,plain,
    ( spl250_23
  <=> ( bot_bot_fun_a_bool = collect_a(cOMBK_bool_a(fFalse)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_23])]) ).

tff(f4572,plain,
    bot_bot_fun_a_bool = collect_a(cOMBK_bool_a(fFalse)),
    inference(cnf_transformation,[],[f541]) ).

tff(f541,axiom,
    bot_bot_fun_a_bool = collect_a(cOMBK_bool_a(fFalse)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_540_empty__def) ).

tff(f7419,plain,
    spl250_22,
    inference(avatar_split_clause,[],[f4570,f7416]) ).

tff(f4570,plain,
    bot_bot_fun_int_bool = collect_int(cOMBK_bool_int(fFalse)),
    inference(cnf_transformation,[],[f539]) ).

tff(f539,axiom,
    bot_bot_fun_int_bool = collect_int(cOMBK_bool_int(fFalse)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_538_empty__def) ).

tff(f7414,plain,
    spl250_21,
    inference(avatar_split_clause,[],[f4569,f7411]) ).

tff(f4569,plain,
    bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse)),
    inference(cnf_transformation,[],[f540]) ).

tff(f540,axiom,
    bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_539_empty__def) ).

tff(f7409,plain,
    spl250_20,
    inference(avatar_split_clause,[],[f4566,f7406]) ).

tff(f7404,plain,
    spl250_19,
    inference(avatar_split_clause,[],[f4562,f7401]) ).

tff(f4562,plain,
    one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
    inference(cnf_transformation,[],[f1099]) ).

tff(f1099,axiom,
    one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1098_int__1) ).

tff(f7399,plain,
    ~ spl250_18,
    inference(avatar_split_clause,[],[f6559,f7396]) ).

tff(f6559,plain,
    ~ hBOOL(hAPP_int_bool(nat_neg,pls)),
    inference(definition_unfolding,[],[f4552,f4550]) ).

tff(f4552,plain,
    ~ hBOOL(hAPP_int_bool(nat_neg,zero_zero_int)),
    inference(cnf_transformation,[],[f1150]) ).

tff(f1150,axiom,
    ~ hBOOL(hAPP_int_bool(nat_neg,zero_zero_int)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1149_not__neg__0) ).

tff(f7394,plain,
    spl250_17,
    inference(avatar_split_clause,[],[f4588,f7392]) ).

tff(f7390,plain,
    spl250_16,
    inference(avatar_split_clause,[],[f4587,f7388]) ).

tff(f7388,plain,
    ( spl250_16
  <=> ! [X0: int] : ( number_number_of_int(X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_16])]) ).

tff(f7386,plain,
    spl250_15,
    inference(avatar_split_clause,[],[f4586,f7384]) ).

tff(f7382,plain,
    spl250_14,
    inference(avatar_split_clause,[],[f4559,f7379]) ).

tff(f4559,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)),
    inference(cnf_transformation,[],[f499]) ).

tff(f499,axiom,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_498_finite_OemptyI) ).

tff(f7377,plain,
    spl250_13,
    inference(avatar_split_clause,[],[f4558,f7374]) ).

tff(f4558,plain,
    hBOOL(hAPP_f448129468l_bool(finite_finite_int,bot_bot_fun_int_bool)),
    inference(cnf_transformation,[],[f498]) ).

tff(f498,axiom,
    hBOOL(hAPP_f448129468l_bool(finite_finite_int,bot_bot_fun_int_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_finite_OemptyI) ).

tff(f7372,plain,
    spl250_12,
    inference(avatar_split_clause,[],[f4557,f7369]) ).

tff(f4557,plain,
    hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,bot_bot_fun_a_bool)),
    inference(cnf_transformation,[],[f501]) ).

tff(f501,axiom,
    hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,bot_bot_fun_a_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_500_finite_OemptyI) ).

tff(f7367,plain,
    spl250_11,
    inference(avatar_split_clause,[],[f4556,f7364]) ).

tff(f4556,plain,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)),
    inference(cnf_transformation,[],[f500]) ).

tff(f500,axiom,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_499_finite_OemptyI) ).

tff(f7362,plain,
    spl250_10,
    inference(avatar_split_clause,[],[f4554,f7359]) ).

tff(f7359,plain,
    ( spl250_10
  <=> ( zero_zero_nat = number_number_of_nat(pls) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_10])]) ).

tff(f4554,plain,
    zero_zero_nat = number_number_of_nat(pls),
    inference(cnf_transformation,[],[f1179]) ).

tff(f1179,axiom,
    zero_zero_nat = number_number_of_nat(pls),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1178_nat__number__of__Pls) ).

tff(f7357,plain,
    ~ spl250_9,
    inference(avatar_split_clause,[],[f4551,f7354]) ).

tff(f4551,plain,
    ~ hBOOL(hAPP_int_bool(nat_neg,one_one_int)),
    inference(cnf_transformation,[],[f1149]) ).

tff(f1149,axiom,
    ~ hBOOL(hAPP_int_bool(nat_neg,one_one_int)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1148_not__neg__1) ).

tff(f7352,plain,
    spl250_8,
    inference(avatar_split_clause,[],[f4541,f7349]) ).

tff(f4541,plain,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
    inference(cnf_transformation,[],[f1303]) ).

tff(f1303,axiom,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(f7347,plain,
    ~ spl250_7,
    inference(avatar_split_clause,[],[f4540,f7344]) ).

tff(f4540,plain,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
    inference(cnf_transformation,[],[f1311]) ).

tff(f1311,plain,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
    inference(flattening,[],[f1310]) ).

tff(f1310,negated_conjecture,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
    inference(negated_conjecture,[],[f1309]) ).

tff(f1309,conjecture,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).

tff(f7342,plain,
    spl250_6,
    inference(avatar_split_clause,[],[f7170,f7339]) ).

tff(f7339,plain,
    ( spl250_6
  <=> sP7(zero_zero_nat,one_one_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_6])]) ).

tff(f7170,plain,
    sP7(zero_zero_nat,one_one_nat),
    inference(forward_demodulation,[],[f6832,f4566]) ).

tff(f6832,plain,
    sP7(zero_zero_nat,hAPP_nat_nat(suc,zero_zero_nat)),
    inference(equality_resolution,[],[f6831]) ).

tff(f6831,plain,
    ! [X1: nat] :
      ( sP7(zero_zero_nat,X1)
      | ( hAPP_nat_nat(suc,zero_zero_nat) != X1 ) ),
    inference(equality_resolution,[],[f5610]) ).

tff(f5610,plain,
    ! [X0: nat,X1: nat] :
      ( sP7(X0,X1)
      | ( zero_zero_nat != X0 )
      | ( hAPP_nat_nat(suc,zero_zero_nat) != X1 ) ),
    inference(cnf_transformation,[],[f4142]) ).

tff(f7337,plain,
    spl250_5,
    inference(avatar_split_clause,[],[f7169,f7334]) ).

tff(f7334,plain,
    ( spl250_5
  <=> sP7(one_one_nat,zero_zero_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_5])]) ).

tff(f7169,plain,
    sP7(one_one_nat,zero_zero_nat),
    inference(forward_demodulation,[],[f6830,f4566]) ).

tff(f6830,plain,
    sP7(hAPP_nat_nat(suc,zero_zero_nat),zero_zero_nat),
    inference(equality_resolution,[],[f6829]) ).

tff(f6829,plain,
    ! [X1: nat] :
      ( sP7(hAPP_nat_nat(suc,zero_zero_nat),X1)
      | ( zero_zero_nat != X1 ) ),
    inference(equality_resolution,[],[f5611]) ).

tff(f5611,plain,
    ! [X0: nat,X1: nat] :
      ( sP7(X0,X1)
      | ( hAPP_nat_nat(suc,zero_zero_nat) != X0 )
      | ( zero_zero_nat != X1 ) ),
    inference(cnf_transformation,[],[f4142]) ).

tff(f7332,plain,
    spl250_4,
    inference(avatar_split_clause,[],[f7162,f7329]) ).

tff(f7329,plain,
    ( spl250_4
  <=> sP6(zero_zero_nat,one_one_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_4])]) ).

tff(f7162,plain,
    sP6(zero_zero_nat,one_one_nat),
    inference(forward_demodulation,[],[f6828,f4566]) ).

tff(f6828,plain,
    sP6(zero_zero_nat,hAPP_nat_nat(suc,zero_zero_nat)),
    inference(equality_resolution,[],[f6827]) ).

tff(f6827,plain,
    ! [X1: nat] :
      ( sP6(zero_zero_nat,X1)
      | ( hAPP_nat_nat(suc,zero_zero_nat) != X1 ) ),
    inference(equality_resolution,[],[f5602]) ).

tff(f5602,plain,
    ! [X0: nat,X1: nat] :
      ( sP6(X0,X1)
      | ( zero_zero_nat != X0 )
      | ( hAPP_nat_nat(suc,zero_zero_nat) != X1 ) ),
    inference(cnf_transformation,[],[f4138]) ).

tff(f7327,plain,
    spl250_3,
    inference(avatar_split_clause,[],[f7161,f7324]) ).

tff(f7324,plain,
    ( spl250_3
  <=> sP6(one_one_nat,zero_zero_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_3])]) ).

tff(f7161,plain,
    sP6(one_one_nat,zero_zero_nat),
    inference(forward_demodulation,[],[f6826,f4566]) ).

tff(f6826,plain,
    sP6(hAPP_nat_nat(suc,zero_zero_nat),zero_zero_nat),
    inference(equality_resolution,[],[f6825]) ).

tff(f6825,plain,
    ! [X1: nat] :
      ( sP6(hAPP_nat_nat(suc,zero_zero_nat),X1)
      | ( zero_zero_nat != X1 ) ),
    inference(equality_resolution,[],[f5603]) ).

tff(f5603,plain,
    ! [X0: nat,X1: nat] :
      ( sP6(X0,X1)
      | ( hAPP_nat_nat(suc,zero_zero_nat) != X0 )
      | ( zero_zero_nat != X1 ) ),
    inference(cnf_transformation,[],[f4138]) ).

tff(f7322,plain,
    ~ spl250_2,
    inference(avatar_split_clause,[],[f6558,f7319]) ).

tff(f7319,plain,
    ( spl250_2
  <=> ( one_one_int = pls ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl250_2])]) ).

tff(f6558,plain,
    one_one_int != pls,
    inference(definition_unfolding,[],[f4548,f4550]) ).

tff(f4548,plain,
    one_one_int != zero_zero_int,
    inference(cnf_transformation,[],[f1073]) ).

tff(f1073,axiom,
    one_one_int != zero_zero_int,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1072_int__0__neq__1) ).

tff(f7317,plain,
    ~ spl250_1,
    inference(avatar_split_clause,[],[f4547,f7314]) ).

tff(f4547,plain,
    ~ hBOOL(fFalse),
    inference(cnf_transformation,[],[f1208]) ).

tff(f1208,axiom,
    ~ hBOOL(fFalse),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SWW473_3 : TPTP v8.2.0. Released v5.3.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36  % Computer : n028.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Sat May 18 19:49:38 EDT 2024
% 0.16/0.36  % CPUTime    : 
% 0.16/0.36  % (6016)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.48  % (6019)WARNING: value z3 for option sas not known
% 0.22/0.48  % (6023)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)
% 0.22/0.48  % (6017)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.48  % (6018)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.48  % (6019)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)
% 0.22/0.48  % (6020)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.48  % (6021)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)
% 0.22/0.48  % (6022)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)
% 6.10/1.34  % (6021)First to succeed.
% 6.46/1.42  % (6021)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-6016"
% 6.46/1.43  % (6021)Refutation found. Thanks to Tanya!
% 6.46/1.43  % SZS status Theorem for theBenchmark
% 6.46/1.43  % SZS output start Proof for theBenchmark
% See solution above
% 6.99/1.47  % (6021)------------------------------
% 6.99/1.47  % (6021)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 6.99/1.47  % (6021)Termination reason: Refutation
% 6.99/1.47  
% 6.99/1.47  % (6021)Memory used [KB]: 20312
% 6.99/1.47  % (6021)Time elapsed: 0.941 s
% 6.99/1.47  % (6021)Instructions burned: 2577 (million)
% 6.99/1.47  % (6016)Success in time 1.088 s
%------------------------------------------------------------------------------