TSTP Solution File: SWW473+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWW473+2 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n020.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 : Fri Sep  1 00:18:01 EDT 2023

% Result   : Theorem 30.50s 30.57s
% Output   : CNFRefutation 30.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :  456
% Syntax   : Number of formulae    :  572 (  78 unt; 419 typ;   0 def)
%            Number of atoms       :  274 (  87 equ)
%            Maximal formula atoms :   14 (   1 avg)
%            Number of connectives :  219 (  98   ~;  89   |;  13   &)
%                                         (   8 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   3 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  693 ( 358   >; 335   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :  411 ( 411 usr;  61 con; 0-3 aty)
%            Number of variables   :  218 (  24 sgn; 114   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    is_fun_a_bool: $i > $o ).

tff(decl_23,type,
    cOMBB_bool_bool_a: ( $i * $i ) > $i ).

tff(decl_24,type,
    is_fun_pname_bool: $i > $o ).

tff(decl_25,type,
    cOMBB_647938656_pname: ( $i * $i ) > $i ).

tff(decl_26,type,
    is_fun949378684l_bool: $i > $o ).

tff(decl_27,type,
    cOMBB_2140588453a_bool: ( $i * $i ) > $i ).

tff(decl_28,type,
    is_fun1661590463l_bool: $i > $o ).

tff(decl_29,type,
    cOMBB_307249310e_bool: ( $i * $i ) > $i ).

tff(decl_30,type,
    is_bool: $i > $o ).

tff(decl_31,type,
    cOMBK_bool_a: $i > $i ).

tff(decl_32,type,
    cOMBK_bool_pname: $i > $i ).

tff(decl_33,type,
    cOMBK_324466864a_bool: $i > $i ).

tff(decl_34,type,
    cOMBK_1857069011e_bool: $i > $i ).

tff(decl_35,type,
    cOMBS_a_bool_bool: ( $i * $i ) > $i ).

tff(decl_36,type,
    cOMBS_568398431l_bool: ( $i * $i ) > $i ).

tff(decl_37,type,
    cOMBS_1035972772l_bool: ( $i * $i ) > $i ).

tff(decl_38,type,
    cOMBS_350070575l_bool: ( $i * $i ) > $i ).

tff(decl_39,type,
    finite_finite_a: $i ).

tff(decl_40,type,
    finite_finite_pname: $i ).

tff(decl_41,type,
    x_a: $i ).

tff(decl_42,type,
    undefined_a: $i > $i ).

tff(decl_43,type,
    is_a: $i > $o ).

tff(decl_44,type,
    pname: $i ).

tff(decl_45,type,
    undefined_pname: $i > $i ).

tff(decl_46,type,
    is_pname: $i > $o ).

tff(decl_47,type,
    bool: $i ).

tff(decl_48,type,
    fun: ( $i * $i ) > $i ).

tff(decl_49,type,
    undefined_fun_a_bool: $i > $i ).

tff(decl_50,type,
    undefi17486888e_bool: $i > $i ).

tff(decl_51,type,
    undefi1699038445l_bool: $i > $i ).

tff(decl_52,type,
    undefi64961550l_bool: $i > $i ).

tff(decl_53,type,
    bot_bot_bool: $i ).

tff(decl_54,type,
    bot_bot_fun_a_bool: $i ).

tff(decl_55,type,
    bot_bo844097828e_bool: $i ).

tff(decl_56,type,
    bot_bo1389914601l_bool: $i ).

tff(decl_57,type,
    bot_bo1649642514l_bool: $i ).

tff(decl_58,type,
    collect_a: $i > $i ).

tff(decl_59,type,
    collect_pname: $i > $i ).

tff(decl_60,type,
    collect_fun_a_bool: $i > $i ).

tff(decl_61,type,
    collec1974731493e_bool: $i > $i ).

tff(decl_62,type,
    image_a_a: ( $i * $i ) > $i ).

tff(decl_63,type,
    image_a_pname: ( $i * $i ) > $i ).

tff(decl_64,type,
    image_a_fun_a_bool: ( $i * $i ) > $i ).

tff(decl_65,type,
    image_819518260e_bool: ( $i * $i ) > $i ).

tff(decl_66,type,
    image_pname_a: ( $i * $i ) > $i ).

tff(decl_67,type,
    image_pname_pname: ( $i * $i ) > $i ).

tff(decl_68,type,
    image_112932426a_bool: ( $i * $i ) > $i ).

tff(decl_69,type,
    image_47868345e_bool: ( $i * $i ) > $i ).

tff(decl_70,type,
    image_nat_a: ( $i * $i ) > $i ).

tff(decl_71,type,
    image_nat_pname: ( $i * $i ) > $i ).

tff(decl_72,type,
    image_nat_fun_a_bool: ( $i * $i ) > $i ).

tff(decl_73,type,
    image_1655916159e_bool: ( $i * $i ) > $i ).

tff(decl_74,type,
    image_fun_a_bool_a: ( $i * $i ) > $i ).

tff(decl_75,type,
    image_1854862208_pname: ( $i * $i ) > $i ).

tff(decl_76,type,
    image_876012084bool_a: ( $i * $i ) > $i ).

tff(decl_77,type,
    image_1283814551_pname: ( $i * $i ) > $i ).

tff(decl_78,type,
    image_fun_nat_bool_a: ( $i * $i ) > $i ).

tff(decl_79,type,
    image_1921560913_pname: ( $i * $i ) > $i ).

tff(decl_80,type,
    insert_a: ( $i * $i ) > $i ).

tff(decl_81,type,
    insert_pname: ( $i * $i ) > $i ).

tff(decl_82,type,
    insert_fun_a_bool: ( $i * $i ) > $i ).

tff(decl_83,type,
    insert1325755072e_bool: ( $i * $i ) > $i ).

tff(decl_84,type,
    fFalse: $i ).

tff(decl_85,type,
    fTrue: $i ).

tff(decl_86,type,
    hAPP_a_a: ( $i * $i ) > $i ).

tff(decl_87,type,
    hAPP_a_pname: ( $i * $i ) > $i ).

tff(decl_88,type,
    hAPP_a_bool: ( $i * $i ) > $i ).

tff(decl_89,type,
    hAPP_a_fun_a_bool: ( $i * $i ) > $i ).

tff(decl_90,type,
    hAPP_a93125764e_bool: ( $i * $i ) > $i ).

tff(decl_91,type,
    hAPP_a85458249l_bool: ( $i * $i ) > $i ).

tff(decl_92,type,
    hAPP_a217006258l_bool: ( $i * $i ) > $i ).

tff(decl_93,type,
    hAPP_pname_a: ( $i * $i ) > $i ).

tff(decl_94,type,
    hAPP_pname_pname: ( $i * $i ) > $i ).

tff(decl_95,type,
    hAPP_pname_bool: ( $i * $i ) > $i ).

tff(decl_96,type,
    hAPP_p1534023578a_bool: ( $i * $i ) > $i ).

tff(decl_97,type,
    hAPP_p61793385e_bool: ( $i * $i ) > $i ).

tff(decl_98,type,
    hAPP_p1824510254l_bool: ( $i * $i ) > $i ).

tff(decl_99,type,
    hAPP_p338031245l_bool: ( $i * $i ) > $i ).

tff(decl_100,type,
    hAPP_bool_bool: ( $i * $i ) > $i ).

tff(decl_101,type,
    hAPP_nat_a: ( $i * $i ) > $i ).

tff(decl_102,type,
    hAPP_nat_pname: ( $i * $i ) > $i ).

tff(decl_103,type,
    hAPP_nat_bool: ( $i * $i ) > $i ).

tff(decl_104,type,
    hAPP_nat_fun_a_bool: ( $i * $i ) > $i ).

tff(decl_105,type,
    hAPP_n1025906991e_bool: ( $i * $i ) > $i ).

tff(decl_106,type,
    hAPP_n1414589940l_bool: ( $i * $i ) > $i ).

tff(decl_107,type,
    hAPP_n850744903l_bool: ( $i * $i ) > $i ).

tff(decl_108,type,
    hAPP_f1128469712_pname: ( $i * $i ) > $i ).

tff(decl_109,type,
    hAPP_fun_a_bool_bool: ( $i * $i ) > $i ).

tff(decl_110,type,
    hAPP_f2050579477a_bool: ( $i * $i ) > $i ).

tff(decl_111,type,
    hAPP_f1794073134e_bool: ( $i * $i ) > $i ).

tff(decl_112,type,
    hAPP_f1631501043l_bool: ( $i * $i ) > $i ).

tff(decl_113,type,
    hAPP_f1297739591_pname: ( $i * $i ) > $i ).

tff(decl_114,type,
    hAPP_f1664156314l_bool: ( $i * $i ) > $i ).

tff(decl_115,type,
    hAPP_f1051908748a_bool: ( $i * $i ) > $i ).

tff(decl_116,type,
    hAPP_f759274231e_bool: ( $i * $i ) > $i ).

tff(decl_117,type,
    hAPP_f434788991l_bool: ( $i * $i ) > $i ).

tff(decl_118,type,
    hAPP_f1291551745_pname: ( $i * $i ) > $i ).

tff(decl_119,type,
    hAPP_f54304608l_bool: ( $i * $i ) > $i ).

tff(decl_120,type,
    hAPP_f1549043526a_bool: ( $i * $i ) > $i ).

tff(decl_121,type,
    hAPP_f654413245e_bool: ( $i * $i ) > $i ).

tff(decl_122,type,
    hAPP_f621171935l_bool: ( $i * $i ) > $i ).

tff(decl_123,type,
    hAPP_f2117159681l_bool: ( $i * $i ) > $i ).

tff(decl_124,type,
    hAPP_f1935102916l_bool: ( $i * $i ) > $i ).

tff(decl_125,type,
    hAPP_f559147733l_bool: ( $i * $i ) > $i ).

tff(decl_126,type,
    hAPP_f1637334154l_bool: ( $i * $i ) > $i ).

tff(decl_127,type,
    hAPP_f292226953l_bool: ( $i * $i ) > $i ).

tff(decl_128,type,
    hAPP_f389811538l_bool: ( $i * $i ) > $i ).

tff(decl_129,type,
    hAPP_f937997336l_bool: ( $i * $i ) > $i ).

tff(decl_130,type,
    g: $i ).

tff(decl_131,type,
    p: $i > $i ).

tff(decl_132,type,
    u: $i ).

tff(decl_133,type,
    mgt: $i > $i ).

tff(decl_134,type,
    pn: $i ).

tff(decl_135,type,
    wt: $i > $i ).

tff(decl_136,type,
    ord_le1311769555a_bool: $i ).

tff(decl_137,type,
    hBOOL: $i > $o ).

tff(decl_138,type,
    finite2012431853t_bool: $i ).

tff(decl_139,type,
    finite1701474069l_bool: $i ).

tff(decl_140,type,
    ord_le1454342156l_bool: $i ).

tff(decl_141,type,
    cOMBC_595898202l_bool: $i > $i ).

tff(decl_142,type,
    hAPP_f1772781669l_bool: ( $i * $i ) > $i ).

tff(decl_143,type,
    collec1015864663l_bool: $i > $i ).

tff(decl_144,type,
    finite595471783e_bool: $i ).

tff(decl_145,type,
    finite786885583l_bool: $i ).

tff(decl_146,type,
    ord_le675606854l_bool: $i ).

tff(decl_147,type,
    cOMBC_7971162l_bool: $i > $i ).

tff(decl_148,type,
    hAPP_f510955609l_bool: ( $i * $i ) > $i ).

tff(decl_149,type,
    collec1613912337l_bool: $i > $i ).

tff(decl_150,type,
    finite347923420a_bool: $i ).

tff(decl_151,type,
    finite1381704300l_bool: $i ).

tff(decl_152,type,
    ord_le1375614389l_bool: $i ).

tff(decl_153,type,
    cOMBC_331553030l_bool: $i > $i ).

tff(decl_154,type,
    hAPP_f1434722111l_bool: ( $i * $i ) > $i ).

tff(decl_155,type,
    collec707592106l_bool: $i > $i ).

tff(decl_156,type,
    cOMBC_1732670874l_bool: $i > $i ).

tff(decl_157,type,
    ord_le313189616e_bool: $i ).

tff(decl_158,type,
    cOMBC_1284144636l_bool: $i > $i ).

tff(decl_159,type,
    finite_finite_nat: $i ).

tff(decl_160,type,
    ord_le1568362934t_bool: $i ).

tff(decl_161,type,
    cOMBC_1693257480l_bool: $i > $i ).

tff(decl_162,type,
    hAPP_f103356543l_bool: ( $i * $i ) > $i ).

tff(decl_163,type,
    collect_fun_nat_bool: $i > $i ).

tff(decl_164,type,
    image_2129980159t_bool: ( $i * $i ) > $i ).

tff(decl_165,type,
    image_26036933t_bool: ( $i * $i ) > $i ).

tff(decl_166,type,
    image_a_nat: ( $i * $i ) > $i ).

tff(decl_167,type,
    image_496248727ol_nat: ( $i * $i ) > $i ).

tff(decl_168,type,
    image_1551609309ol_nat: ( $i * $i ) > $i ).

tff(decl_169,type,
    image_fun_a_bool_nat: ( $i * $i ) > $i ).

tff(decl_170,type,
    insert_fun_nat_bool: ( $i * $i ) > $i ).

tff(decl_171,type,
    insert_nat: ( $i * $i ) > $i ).

tff(decl_172,type,
    ord_less_eq_nat: $i ).

tff(decl_173,type,
    finite_card_pname: $i ).

tff(decl_174,type,
    hAPP_f921600141ol_nat: ( $i * $i ) > $i ).

tff(decl_175,type,
    hAPP_n1699378549t_bool: ( $i * $i ) > $i ).

tff(decl_176,type,
    finite_card_a: $i ).

tff(decl_177,type,
    hAPP_fun_a_bool_nat: ( $i * $i ) > $i ).

tff(decl_178,type,
    finite346522414t_bool: $i ).

tff(decl_179,type,
    hAPP_f696928925ol_nat: ( $i * $i ) > $i ).

tff(decl_180,type,
    finite1340463720e_bool: $i ).

tff(decl_181,type,
    hAPP_f55526627ol_nat: ( $i * $i ) > $i ).

tff(decl_182,type,
    finite1306199131a_bool: $i ).

tff(decl_183,type,
    hAPP_f2009550088ol_nat: ( $i * $i ) > $i ).

tff(decl_184,type,
    finite_card_nat: $i ).

tff(decl_185,type,
    image_pname_nat: ( $i * $i ) > $i ).

tff(decl_186,type,
    hAPP_f22106695ol_nat: ( $i * $i ) > $i ).

tff(decl_187,type,
    member_fun_nat_bool: $i ).

tff(decl_188,type,
    hAPP_f1951378235l_bool: ( $i * $i ) > $i ).

tff(decl_189,type,
    suc: $i ).

tff(decl_190,type,
    hAPP_nat_nat: ( $i * $i ) > $i ).

tff(decl_191,type,
    member799430823e_bool: $i ).

tff(decl_192,type,
    hAPP_f556039215l_bool: ( $i * $i ) > $i ).

tff(decl_193,type,
    member_fun_a_bool: $i ).

tff(decl_194,type,
    hAPP_f285962445l_bool: ( $i * $i ) > $i ).

tff(decl_195,type,
    member_nat: $i ).

tff(decl_196,type,
    hAPP_n215258509l_bool: ( $i * $i ) > $i ).

tff(decl_197,type,
    member_pname: $i ).

tff(decl_198,type,
    member_a: $i ).

tff(decl_199,type,
    fconj: $i ).

tff(decl_200,type,
    cOMBB_1972296269bool_a: ( $i * $i ) > $i ).

tff(decl_201,type,
    cOMBB_444170502t_bool: ( $i * $i ) > $i ).

tff(decl_202,type,
    cOMBS_1187019125l_bool: ( $i * $i ) > $i ).

tff(decl_203,type,
    cOMBB_2095475776e_bool: ( $i * $i ) > $i ).

tff(decl_204,type,
    cOMBB_338059395a_bool: ( $i * $i ) > $i ).

tff(decl_205,type,
    cOMBB_675860798_pname: ( $i * $i ) > $i ).

tff(decl_206,type,
    collect_nat: $i > $i ).

tff(decl_207,type,
    cOMBB_1015721476ol_nat: ( $i * $i ) > $i ).

tff(decl_208,type,
    cOMBS_nat_bool_bool: ( $i * $i ) > $i ).

tff(decl_209,type,
    minus_minus_nat: $i > $i ).

tff(decl_210,type,
    cOMBC_nat_nat_bool: $i > $i ).

tff(decl_211,type,
    fdisj: $i ).

tff(decl_212,type,
    image_nat_nat: ( $i * $i ) > $i ).

tff(decl_213,type,
    image_a_fun_nat_bool: ( $i * $i ) > $i ).

tff(decl_214,type,
    ord_less_eq_bool: $i ).

tff(decl_215,type,
    hAPP_b589554111l_bool: ( $i * $i ) > $i ).

tff(decl_216,type,
    cOMBC_226598744l_bool: $i > $i ).

tff(decl_217,type,
    hAPP_f800510211t_bool: ( $i * $i ) > $i ).

tff(decl_218,type,
    fequal_pname: $i ).

tff(decl_219,type,
    cOMBB_1212655066ol_nat: ( $i * $i ) > $i ).

tff(decl_220,type,
    cOMBC_nat_pname_bool: $i > $i ).

tff(decl_221,type,
    hAPP_p1499970991t_bool: ( $i * $i ) > $i ).

tff(decl_222,type,
    cOMBC_1355376034l_bool: $i > $i ).

tff(decl_223,type,
    cOMBB_610033911bool_a: ( $i * $i ) > $i ).

tff(decl_224,type,
    cOMBC_a_pname_bool: $i > $i ).

tff(decl_225,type,
    cOMBC_1058051404l_bool: $i > $i ).

tff(decl_226,type,
    cOMBB_542850580_pname: ( $i * $i ) > $i ).

tff(decl_227,type,
    cOMBC_1149511130e_bool: $i > $i ).

tff(decl_228,type,
    cOMBC_1245412066l_bool: $i > $i ).

tff(decl_229,type,
    hAPP_f1246832597l_bool: ( $i * $i ) > $i ).

tff(decl_230,type,
    cOMBB_141086128t_bool: ( $i * $i ) > $i ).

tff(decl_231,type,
    cOMBC_615407716e_bool: $i > $i ).

tff(decl_232,type,
    hAPP_p130839763l_bool: ( $i * $i ) > $i ).

tff(decl_233,type,
    cOMBC_1988546018l_bool: $i > $i ).

tff(decl_234,type,
    cOMBB_598082538e_bool: ( $i * $i ) > $i ).

tff(decl_235,type,
    cOMBC_1004116266e_bool: $i > $i ).

tff(decl_236,type,
    cOMBC_1880041174l_bool: $i > $i ).

tff(decl_237,type,
    cOMBB_1693087065a_bool: ( $i * $i ) > $i ).

tff(decl_238,type,
    cOMBC_1738168533e_bool: $i > $i ).

tff(decl_239,type,
    fequal_nat: $i ).

tff(decl_240,type,
    cOMBB_800536526ol_nat: ( $i * $i ) > $i ).

tff(decl_241,type,
    cOMBB_1321347587bool_a: ( $i * $i ) > $i ).

tff(decl_242,type,
    cOMBC_a_nat_bool: $i > $i ).

tff(decl_243,type,
    hAPP_a_nat: ( $i * $i ) > $i ).

tff(decl_244,type,
    cOMBB_523834888_pname: ( $i * $i ) > $i ).

tff(decl_245,type,
    cOMBC_pname_nat_bool: $i > $i ).

tff(decl_246,type,
    hAPP_pname_nat: ( $i * $i ) > $i ).

tff(decl_247,type,
    cOMBB_1250273980t_bool: ( $i * $i ) > $i ).

tff(decl_248,type,
    cOMBC_385542954t_bool: $i > $i ).

tff(decl_249,type,
    cOMBB_1896684278e_bool: ( $i * $i ) > $i ).

tff(decl_250,type,
    cOMBC_1666426608t_bool: $i > $i ).

tff(decl_251,type,
    cOMBB_164527437a_bool: ( $i * $i ) > $i ).

tff(decl_252,type,
    cOMBC_619334683t_bool: $i > $i ).

tff(decl_253,type,
    fequal_a: $i ).

tff(decl_254,type,
    cOMBB_1885489796ol_nat: ( $i * $i ) > $i ).

tff(decl_255,type,
    cOMBC_nat_a_bool: $i > $i ).

tff(decl_256,type,
    hAPP_a_fun_nat_bool: ( $i * $i ) > $i ).

tff(decl_257,type,
    fequal_fun_nat_bool: $i ).

tff(decl_258,type,
    cOMBB_2026977092ol_nat: ( $i * $i ) > $i ).

tff(decl_259,type,
    fequal533582459e_bool: $i ).

tff(decl_260,type,
    cOMBB_2117322052ol_nat: ( $i * $i ) > $i ).

tff(decl_261,type,
    cOMBC_386238098l_bool: $i > $i ).

tff(decl_262,type,
    hAPP_f1066163005t_bool: ( $i * $i ) > $i ).

tff(decl_263,type,
    fequal_fun_a_bool: $i ).

tff(decl_264,type,
    cOMBB_1823939024ol_nat: ( $i * $i ) > $i ).

tff(decl_265,type,
    cOMBC_1928494297l_bool: $i > $i ).

tff(decl_266,type,
    hAPP_f282463732t_bool: ( $i * $i ) > $i ).

tff(decl_267,type,
    cOMBB_928955006_pname: ( $i * $i ) > $i ).

tff(decl_268,type,
    cOMBC_267053842l_bool: $i > $i ).

tff(decl_269,type,
    cOMBB_408569982_pname: ( $i * $i ) > $i ).

tff(decl_270,type,
    cOMBB_392435466_pname: ( $i * $i ) > $i ).

tff(decl_271,type,
    cOMBC_445755039l_bool: $i > $i ).

tff(decl_272,type,
    cOMBB_a_fun_a_bool_a: ( $i * $i ) > $i ).

tff(decl_273,type,
    cOMBC_a_a_bool: $i > $i ).

tff(decl_274,type,
    cOMBB_743407885bool_a: ( $i * $i ) > $i ).

tff(decl_275,type,
    cOMBC_777206479l_bool: $i > $i ).

tff(decl_276,type,
    cOMBB_1137537805bool_a: ( $i * $i ) > $i ).

tff(decl_277,type,
    cOMBC_1834145417l_bool: $i > $i ).

tff(decl_278,type,
    cOMBB_472261505bool_a: ( $i * $i ) > $i ).

tff(decl_279,type,
    cOMBB_1897541054_pname: ( $i * $i ) > $i ).

tff(decl_280,type,
    cOMBC_pname_a_bool: $i > $i ).

tff(decl_281,type,
    fimplies: $i ).

tff(decl_282,type,
    fNot: $i ).

tff(decl_283,type,
    cOMBB_238756964t_bool: ( $i * $i ) > $i ).

tff(decl_284,type,
    cOMBB_bool_bool_nat: ( $i * $i ) > $i ).

tff(decl_285,type,
    mgt_call: $i ).

tff(decl_286,type,
    bot_bot_fun_nat_bool: $i ).

tff(decl_287,type,
    bot_bo1701429464l_bool: $i ).

tff(decl_288,type,
    cOMBK_1994329625t_bool: $i > $i ).

tff(decl_289,type,
    cOMBK_bool_nat: $i > $i ).

tff(decl_290,type,
    bot_bot_nat: $i ).

tff(decl_291,type,
    cOMBK_a_pname: $i > $i ).

tff(decl_292,type,
    body: $i > $i ).

tff(decl_293,type,
    the_com: $i > $i ).

tff(decl_294,type,
    one_one_nat: $i ).

tff(decl_295,type,
    nat_case_bool: ( $i * $i ) > $i ).

tff(decl_296,type,
    plus_plus_nat: $i > $i ).

tff(decl_297,type,
    ord_less_nat: $i ).

tff(decl_298,type,
    zero_zero_nat: $i ).

tff(decl_299,type,
    hAPP_a_fun_bool_bool: ( $i * $i ) > $i ).

tff(decl_300,type,
    hAPP_n1006566506l_bool: ( $i * $i ) > $i ).

tff(decl_301,type,
    hAPP_p393069232l_bool: ( $i * $i ) > $i ).

tff(decl_302,type,
    hAPP_a1392362872l_bool: ( $i * $i ) > $i ).

tff(decl_303,type,
    hAPP_f198738859l_bool: ( $i * $i ) > $i ).

tff(decl_304,type,
    hAPP_f1748468828l_bool: ( $i * $i ) > $i ).

tff(decl_305,type,
    hAPP_f1476298914l_bool: ( $i * $i ) > $i ).

tff(decl_306,type,
    na: $i ).

tff(decl_307,type,
    esk1_3: ( $i * $i * $i ) > $i ).

tff(decl_308,type,
    esk2_3: ( $i * $i * $i ) > $i ).

tff(decl_309,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_310,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_311,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_312,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_313,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_314,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_315,type,
    esk9_3: ( $i * $i * $i ) > $i ).

tff(decl_316,type,
    esk10_3: ( $i * $i * $i ) > $i ).

tff(decl_317,type,
    esk11_3: ( $i * $i * $i ) > $i ).

tff(decl_318,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_319,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_320,type,
    esk14_3: ( $i * $i * $i ) > $i ).

tff(decl_321,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_322,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_323,type,
    esk17_3: ( $i * $i * $i ) > $i ).

tff(decl_324,type,
    esk18_3: ( $i * $i * $i ) > $i ).

tff(decl_325,type,
    esk19_3: ( $i * $i * $i ) > $i ).

tff(decl_326,type,
    esk20_3: ( $i * $i * $i ) > $i ).

tff(decl_327,type,
    esk21_3: ( $i * $i * $i ) > $i ).

tff(decl_328,type,
    esk22_3: ( $i * $i * $i ) > $i ).

tff(decl_329,type,
    esk23_3: ( $i * $i * $i ) > $i ).

tff(decl_330,type,
    esk24_3: ( $i * $i * $i ) > $i ).

tff(decl_331,type,
    esk25_3: ( $i * $i * $i ) > $i ).

tff(decl_332,type,
    esk26_3: ( $i * $i * $i ) > $i ).

tff(decl_333,type,
    esk27_3: ( $i * $i * $i ) > $i ).

tff(decl_334,type,
    esk28_3: ( $i * $i * $i ) > $i ).

tff(decl_335,type,
    esk29_3: ( $i * $i * $i ) > $i ).

tff(decl_336,type,
    esk30_3: ( $i * $i * $i ) > $i ).

tff(decl_337,type,
    esk31_3: ( $i * $i * $i ) > $i ).

tff(decl_338,type,
    esk32_3: ( $i * $i * $i ) > $i ).

tff(decl_339,type,
    esk33_2: ( $i * $i ) > $i ).

tff(decl_340,type,
    esk34_2: ( $i * $i ) > $i ).

tff(decl_341,type,
    esk35_2: ( $i * $i ) > $i ).

tff(decl_342,type,
    esk36_2: ( $i * $i ) > $i ).

tff(decl_343,type,
    esk37_2: ( $i * $i ) > $i ).

tff(decl_344,type,
    esk38_2: ( $i * $i ) > $i ).

tff(decl_345,type,
    esk39_2: ( $i * $i ) > $i ).

tff(decl_346,type,
    esk40_2: ( $i * $i ) > $i ).

tff(decl_347,type,
    esk41_2: ( $i * $i ) > $i ).

tff(decl_348,type,
    esk42_2: ( $i * $i ) > $i ).

tff(decl_349,type,
    esk43_2: ( $i * $i ) > $i ).

tff(decl_350,type,
    esk44_2: ( $i * $i ) > $i ).

tff(decl_351,type,
    esk45_2: ( $i * $i ) > $i ).

tff(decl_352,type,
    esk46_2: ( $i * $i ) > $i ).

tff(decl_353,type,
    esk47_2: ( $i * $i ) > $i ).

tff(decl_354,type,
    esk48_2: ( $i * $i ) > $i ).

tff(decl_355,type,
    esk49_2: ( $i * $i ) > $i ).

tff(decl_356,type,
    esk50_2: ( $i * $i ) > $i ).

tff(decl_357,type,
    esk51_2: ( $i * $i ) > $i ).

tff(decl_358,type,
    esk52_2: ( $i * $i ) > $i ).

tff(decl_359,type,
    esk53_2: ( $i * $i ) > $i ).

tff(decl_360,type,
    esk54_2: ( $i * $i ) > $i ).

tff(decl_361,type,
    esk55_2: ( $i * $i ) > $i ).

tff(decl_362,type,
    esk56_2: ( $i * $i ) > $i ).

tff(decl_363,type,
    esk57_3: ( $i * $i * $i ) > $i ).

tff(decl_364,type,
    esk58_2: ( $i * $i ) > $i ).

tff(decl_365,type,
    esk59_3: ( $i * $i * $i ) > $i ).

tff(decl_366,type,
    esk60_3: ( $i * $i * $i ) > $i ).

tff(decl_367,type,
    esk61_3: ( $i * $i * $i ) > $i ).

tff(decl_368,type,
    esk62_3: ( $i * $i * $i ) > $i ).

tff(decl_369,type,
    esk63_3: ( $i * $i * $i ) > $i ).

tff(decl_370,type,
    esk64_3: ( $i * $i * $i ) > $i ).

tff(decl_371,type,
    esk65_3: ( $i * $i * $i ) > $i ).

tff(decl_372,type,
    esk66_3: ( $i * $i * $i ) > $i ).

tff(decl_373,type,
    esk67_3: ( $i * $i * $i ) > $i ).

tff(decl_374,type,
    esk68_3: ( $i * $i * $i ) > $i ).

tff(decl_375,type,
    esk69_2: ( $i * $i ) > $i ).

tff(decl_376,type,
    esk70_2: ( $i * $i ) > $i ).

tff(decl_377,type,
    esk71_2: ( $i * $i ) > $i ).

tff(decl_378,type,
    esk72_3: ( $i * $i * $i ) > $i ).

tff(decl_379,type,
    esk73_3: ( $i * $i * $i ) > $i ).

tff(decl_380,type,
    esk74_3: ( $i * $i * $i ) > $i ).

tff(decl_381,type,
    esk75_3: ( $i * $i * $i ) > $i ).

tff(decl_382,type,
    esk76_3: ( $i * $i * $i ) > $i ).

tff(decl_383,type,
    esk77_3: ( $i * $i * $i ) > $i ).

tff(decl_384,type,
    esk78_3: ( $i * $i * $i ) > $i ).

tff(decl_385,type,
    esk79_1: $i > $i ).

tff(decl_386,type,
    esk80_2: ( $i * $i ) > $i ).

tff(decl_387,type,
    esk81_2: ( $i * $i ) > $i ).

tff(decl_388,type,
    esk82_2: ( $i * $i ) > $i ).

tff(decl_389,type,
    esk83_2: ( $i * $i ) > $i ).

tff(decl_390,type,
    esk84_2: ( $i * $i ) > $i ).

tff(decl_391,type,
    esk85_1: $i > $i ).

tff(decl_392,type,
    esk86_1: $i > $i ).

tff(decl_393,type,
    esk87_1: $i > $i ).

tff(decl_394,type,
    esk88_1: $i > $i ).

tff(decl_395,type,
    esk89_1: $i > $i ).

tff(decl_396,type,
    esk90_1: $i > $i ).

tff(decl_397,type,
    esk91_1: $i > $i ).

tff(decl_398,type,
    esk92_1: $i > $i ).

tff(decl_399,type,
    esk93_1: $i > $i ).

tff(decl_400,type,
    esk94_1: $i > $i ).

tff(decl_401,type,
    esk95_1: $i > $i ).

tff(decl_402,type,
    esk96_1: $i > $i ).

tff(decl_403,type,
    esk97_1: $i > $i ).

tff(decl_404,type,
    esk98_1: $i > $i ).

tff(decl_405,type,
    esk99_1: $i > $i ).

tff(decl_406,type,
    esk100_1: $i > $i ).

tff(decl_407,type,
    esk101_1: $i > $i ).

tff(decl_408,type,
    esk102_1: $i > $i ).

tff(decl_409,type,
    esk103_3: ( $i * $i * $i ) > $i ).

tff(decl_410,type,
    esk104_3: ( $i * $i * $i ) > $i ).

tff(decl_411,type,
    esk105_3: ( $i * $i * $i ) > $i ).

tff(decl_412,type,
    esk106_3: ( $i * $i * $i ) > $i ).

tff(decl_413,type,
    esk107_3: ( $i * $i * $i ) > $i ).

tff(decl_414,type,
    esk108_3: ( $i * $i * $i ) > $i ).

tff(decl_415,type,
    esk109_3: ( $i * $i * $i ) > $i ).

tff(decl_416,type,
    esk110_3: ( $i * $i * $i ) > $i ).

tff(decl_417,type,
    esk111_3: ( $i * $i * $i ) > $i ).

tff(decl_418,type,
    esk112_3: ( $i * $i * $i ) > $i ).

tff(decl_419,type,
    esk113_3: ( $i * $i * $i ) > $i ).

tff(decl_420,type,
    esk114_3: ( $i * $i * $i ) > $i ).

tff(decl_421,type,
    esk115_2: ( $i * $i ) > $i ).

tff(decl_422,type,
    esk116_2: ( $i * $i ) > $i ).

tff(decl_423,type,
    esk117_2: ( $i * $i ) > $i ).

tff(decl_424,type,
    esk118_2: ( $i * $i ) > $i ).

tff(decl_425,type,
    esk119_2: ( $i * $i ) > $i ).

tff(decl_426,type,
    esk120_2: ( $i * $i ) > $i ).

tff(decl_427,type,
    esk121_2: ( $i * $i ) > $i ).

tff(decl_428,type,
    esk122_2: ( $i * $i ) > $i ).

tff(decl_429,type,
    esk123_1: $i > $i ).

tff(decl_430,type,
    esk124_2: ( $i * $i ) > $i ).

tff(decl_431,type,
    esk125_2: ( $i * $i ) > $i ).

tff(decl_432,type,
    esk126_3: ( $i * $i * $i ) > $i ).

tff(decl_433,type,
    esk127_3: ( $i * $i * $i ) > $i ).

tff(decl_434,type,
    esk128_3: ( $i * $i * $i ) > $i ).

tff(decl_435,type,
    esk129_2: ( $i * $i ) > $i ).

tff(decl_436,type,
    esk130_2: ( $i * $i ) > $i ).

tff(decl_437,type,
    esk131_3: ( $i * $i * $i ) > $i ).

tff(decl_438,type,
    esk132_3: ( $i * $i * $i ) > $i ).

tff(decl_439,type,
    esk133_2: ( $i * $i ) > $i ).

tff(decl_440,type,
    esk134_2: ( $i * $i ) > $i ).

fof(fact_403_Collect__empty__eq,axiom,
    ! [X13] :
      ( collect_nat(X13) = bot_bot_fun_nat_bool
    <=> ! [X30] : ~ hBOOL(hAPP_nat_bool(X13,X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_Collect__empty__eq) ).

fof(help_fFalse_1_1_T,axiom,
    ! [X92] :
      ( is_bool(X92)
     => ( X92 = fTrue
        | X92 = fFalse ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
    ! [X1,X2] : is_bool(hAPP_f54304608l_bool(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).

fof(fact_295_Collect__def,axiom,
    ! [X13] : collect_nat(X13) = X13,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_Collect__def) ).

fof(fact_391_finite_OemptyI,axiom,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_finite_OemptyI) ).

fof(help_fFalse_1_1_U,axiom,
    ~ hBOOL(fFalse),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

fof(fact_426_bot__fun__def,axiom,
    ! [X30] :
      ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X30))
    <=> hBOOL(bot_bot_bool) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_426_bot__fun__def) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool,hypothesis,
    ! [X1,X2] : is_bool(hAPP_nat_bool(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) ).

fof(gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool,axiom,
    is_bool(bot_bot_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool) ).

fof(fact_416_all__not__in__conv,axiom,
    ! [X5] :
      ( ! [X30] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
    <=> X5 = bot_bot_fun_nat_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_416_all__not__in__conv) ).

fof(fact_383_emptyE,axiom,
    ! [X8] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),bot_bot_fun_nat_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_383_emptyE) ).

fof(fact_287_mem__def,axiom,
    ! [X11,X5] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
    <=> hBOOL(hAPP_nat_bool(X5,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_mem__def) ).

fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
    ! [X92,X93] :
      ( is_bool(X92)
     => hAPP_nat_bool(cOMBK_bool_nat(X92),X93) = X92 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U) ).

fof(fact_484_singleton__conv,axiom,
    ! [X8] : collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X8)) = insert_a(X8,bot_bot_fun_a_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_singleton__conv) ).

fof(fact_238_insert__compr,axiom,
    ! [X8,X10] : insert_a(X8,X10) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X8)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X10))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_insert__compr) ).

fof(fact_490_singleton__conv2,axiom,
    ! [X8] : collect_a(hAPP_a_fun_a_bool(fequal_a,X8)) = insert_a(X8,bot_bot_fun_a_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_singleton__conv2) ).

fof(fact_307_imageI,axiom,
    ! [X9,X11,X5] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X9,X11)),image_pname_a(X9,X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_imageI) ).

fof(fact_302_image__iff,axiom,
    ! [X38,X9,X5] :
      ( is_a(X38)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X38),image_pname_a(X9,X5)))
      <=> ? [X30] :
            ( is_pname(X30)
            & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5))
            & X38 = hAPP_pname_a(X9,X30) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_image__iff) ).

fof(conj_4,hypothesis,
    hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).

fof(fact_290_Collect__def,axiom,
    ! [X13] :
      ( is_fun_a_bool(X13)
     => collect_a(X13) = X13 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_Collect__def) ).

fof(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
    ! [X1,X2] :
      ( is_pname(X2)
     => is_fun_a_bool(hAPP_p1534023578a_bool(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J) ).

fof(help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna,axiom,
    ! [X92,X93,X94] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X92,X93),X94) = hAPP_a_fun_a_bool(X92,hAPP_pname_a(X93,X94)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna) ).

fof(gsy_c_hAPP_000tc__Com__Opname_000t__a,hypothesis,
    ! [X1,X2] :
      ( is_pname(X2)
     => is_a(hAPP_pname_a(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000t__a) ).

fof(fact_337_image__insert,axiom,
    ! [X9,X8,X10] : image_pname_a(X9,insert_pname(X8,X10)) = insert_a(hAPP_pname_a(X9,X8),image_pname_a(X9,X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_image__insert) ).

fof(fact_237_insert__compr,axiom,
    ! [X8,X10] : insert_pname(X8,X10) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X8)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X10))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_insert__compr) ).

fof(fact_489_singleton__conv2,axiom,
    ! [X8] : collect_pname(hAPP_p61793385e_bool(fequal_pname,X8)) = insert_pname(X8,bot_bo844097828e_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_singleton__conv2) ).

fof(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool,hypothesis,
    ! [X1,X2] :
      ( ( is_fun949378684l_bool(X1)
        & is_fun_a_bool(X2) )
     => is_bool(hAPP_fun_a_bool_bool(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).

fof(conj_6,conjecture,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).

fof(gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
    ! [X1,X2] :
      ( is_a(X2)
     => is_fun_a_bool(hAPP_a_fun_a_bool(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J) ).

fof(gsy_v_pn,hypothesis,
    is_pname(pn),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_pn) ).

fof(fact_468_image__empty,axiom,
    ! [X9] : image_pname_a(X9,bot_bo844097828e_bool) = bot_bot_fun_a_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_image__empty) ).

fof(fact_324_insert__subset,axiom,
    ! [X11,X5,X10] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X11,X5)),X10))
    <=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X10))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_insert__subset) ).

fof(conj_1,hypothesis,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

fof(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__a_Mtc__HOL,hypothesis,
    ! [X1,X2] :
      ( is_fun_a_bool(X2)
     => is_fun949378684l_bool(hAPP_f1631501043l_bool(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__a_Mtc__HOL) ).

fof(gsy_v_G,hypothesis,
    is_fun_a_bool(g),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_G) ).

fof(gsy_c_Set_Oimage_000tc__Com__Opname_000t__a,hypothesis,
    ! [X1,X2] :
      ( is_fun_pname_bool(X2)
     => is_fun_a_bool(image_pname_a(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000t__a) ).

fof(gsy_v_U,hypothesis,
    is_fun_pname_bool(u),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_U) ).

fof(c_0_37,plain,
    ! [X13] :
      ( collect_nat(X13) = bot_bot_fun_nat_bool
    <=> ! [X30] : ~ hBOOL(hAPP_nat_bool(X13,X30)) ),
    inference(fof_simplification,[status(thm)],[fact_403_Collect__empty__eq]) ).

fof(c_0_38,plain,
    ! [X1995] :
      ( ~ is_bool(X1995)
      | X1995 = fTrue
      | X1995 = fFalse ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_fFalse_1_1_T])]) ).

fof(c_0_39,plain,
    ! [X229,X230] : is_bool(hAPP_f54304608l_bool(X229,X230)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool]) ).

fof(c_0_40,plain,
    ! [X1312,X1313,X1314] :
      ( ( collect_nat(X1312) != bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_nat_bool(X1312,X1313)) )
      & ( hBOOL(hAPP_nat_bool(X1314,esk90_1(X1314)))
        | collect_nat(X1314) = bot_bot_fun_nat_bool ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])])]) ).

fof(c_0_41,plain,
    ! [X990] : collect_nat(X990) = X990,
    inference(variable_rename,[status(thm)],[fact_295_Collect__def]) ).

cnf(c_0_42,plain,
    ( X1 = fTrue
    | X1 = fFalse
    | ~ is_bool(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_43,plain,
    is_bool(hAPP_f54304608l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_44,plain,
    ( collect_nat(X1) != bot_bot_fun_nat_bool
    | ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_45,plain,
    collect_nat(X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_46,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)),
    inference(split_conjunct,[status(thm)],[fact_391_finite_OemptyI]) ).

cnf(c_0_47,plain,
    ( hAPP_f54304608l_bool(X1,X2) = fTrue
    | hAPP_f54304608l_bool(X1,X2) = fFalse ),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

fof(c_0_48,plain,
    ~ hBOOL(fFalse),
    inference(fof_simplification,[status(thm)],[help_fFalse_1_1_U]) ).

fof(c_0_49,plain,
    ! [X1364] :
      ( ( ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X1364))
        | hBOOL(bot_bot_bool) )
      & ( ~ hBOOL(bot_bot_bool)
        | hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X1364)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_426_bot__fun__def])]) ).

cnf(c_0_50,plain,
    ( X1 != bot_bot_fun_nat_bool
    | ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
    inference(rw,[status(thm)],[c_0_44,c_0_45]) ).

fof(c_0_51,hypothesis,
    ! [X197,X198] : is_bool(hAPP_nat_bool(X197,X198)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool]) ).

cnf(c_0_52,plain,
    ( hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool) = fFalse
    | hBOOL(fTrue) ),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_53,plain,
    ~ hBOOL(fFalse),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_54,plain,
    is_bool(bot_bot_bool),
    inference(split_conjunct,[status(thm)],[gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool]) ).

cnf(c_0_55,plain,
    ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X1))
    | ~ hBOOL(bot_bot_bool) ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_56,plain,
    ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X1)),
    inference(er,[status(thm)],[c_0_50]) ).

fof(c_0_57,plain,
    ! [X5] :
      ( ! [X30] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
    <=> X5 = bot_bot_fun_nat_bool ),
    inference(fof_simplification,[status(thm)],[fact_416_all__not__in__conv]) ).

cnf(c_0_58,hypothesis,
    is_bool(hAPP_nat_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

cnf(c_0_59,plain,
    hBOOL(fTrue),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_52]),c_0_53]) ).

cnf(c_0_60,plain,
    ( fTrue = bot_bot_bool
    | fFalse = bot_bot_bool ),
    inference(spm,[status(thm)],[c_0_42,c_0_54]) ).

cnf(c_0_61,plain,
    ~ hBOOL(bot_bot_bool),
    inference(sr,[status(thm)],[c_0_55,c_0_56]) ).

fof(c_0_62,plain,
    ! [X8] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),bot_bot_fun_nat_bool)),
    inference(fof_simplification,[status(thm)],[fact_383_emptyE]) ).

fof(c_0_63,plain,
    ! [X979,X980] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X979),X980))
        | hBOOL(hAPP_nat_bool(X980,X979)) )
      & ( ~ hBOOL(hAPP_nat_bool(X980,X979))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X979),X980)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_287_mem__def])]) ).

fof(c_0_64,plain,
    ! [X1353,X1355,X1356] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk100_1(X1353)),X1353))
        | X1353 = bot_bot_fun_nat_bool )
      & ( X1355 != bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1356),X1355)) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])])]) ).

fof(c_0_65,plain,
    ! [X2021,X2022] :
      ( ~ is_bool(X2021)
      | hAPP_nat_bool(cOMBK_bool_nat(X2021),X2022) = X2021 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U])]) ).

cnf(c_0_66,hypothesis,
    ( hAPP_nat_bool(X1,X2) = fTrue
    | hAPP_nat_bool(X1,X2) = fFalse ),
    inference(spm,[status(thm)],[c_0_42,c_0_58]) ).

cnf(c_0_67,plain,
    fFalse = bot_bot_bool,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).

fof(c_0_68,plain,
    ! [X1280] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1280),bot_bot_fun_nat_bool)),
    inference(variable_rename,[status(thm)],[c_0_62]) ).

fof(c_0_69,plain,
    ! [X1460] : collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1460)) = insert_a(X1460,bot_bot_fun_a_bool),
    inference(variable_rename,[status(thm)],[fact_484_singleton__conv]) ).

fof(c_0_70,plain,
    ! [X860,X861] : insert_a(X860,X861) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X860)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X861))),
    inference(variable_rename,[status(thm)],[fact_238_insert__compr]) ).

fof(c_0_71,plain,
    ! [X1466] : collect_a(hAPP_a_fun_a_bool(fequal_a,X1466)) = insert_a(X1466,bot_bot_fun_a_bool),
    inference(variable_rename,[status(thm)],[fact_490_singleton__conv2]) ).

fof(c_0_72,plain,
    ! [X1025,X1026,X1027] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1026),X1027))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X1025,X1026)),image_pname_a(X1025,X1027))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_307_imageI])]) ).

cnf(c_0_73,plain,
    ( hBOOL(hAPP_nat_bool(X2,X1))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_63]) ).

cnf(c_0_74,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk100_1(X1)),X1))
    | X1 = bot_bot_fun_nat_bool ),
    inference(split_conjunct,[status(thm)],[c_0_64]) ).

cnf(c_0_75,plain,
    ( hAPP_nat_bool(cOMBK_bool_nat(X1),X2) = X1
    | ~ is_bool(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_65]) ).

cnf(c_0_76,hypothesis,
    ( hAPP_nat_bool(X1,X2) = bot_bot_bool
    | hAPP_nat_bool(X1,X2) = fTrue ),
    inference(rw,[status(thm)],[c_0_66,c_0_67]) ).

cnf(c_0_77,plain,
    ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),bot_bot_fun_nat_bool)),
    inference(split_conjunct,[status(thm)],[c_0_68]) ).

cnf(c_0_78,plain,
    collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)) = insert_a(X1,bot_bot_fun_a_bool),
    inference(split_conjunct,[status(thm)],[c_0_69]) ).

cnf(c_0_79,plain,
    insert_a(X1,X2) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))),
    inference(split_conjunct,[status(thm)],[c_0_70]) ).

cnf(c_0_80,plain,
    collect_a(hAPP_a_fun_a_bool(fequal_a,X1)) = insert_a(X1,bot_bot_fun_a_bool),
    inference(split_conjunct,[status(thm)],[c_0_71]) ).

fof(c_0_81,plain,
    ! [X1006,X1007,X1008,X1010,X1011,X1012] :
      ( ( is_pname(esk59_3(X1006,X1007,X1008))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1006),image_pname_a(X1007,X1008)))
        | ~ is_a(X1006) )
      & ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk59_3(X1006,X1007,X1008)),X1008))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1006),image_pname_a(X1007,X1008)))
        | ~ is_a(X1006) )
      & ( X1006 = hAPP_pname_a(X1007,esk59_3(X1006,X1007,X1008))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1006),image_pname_a(X1007,X1008)))
        | ~ is_a(X1006) )
      & ( ~ is_pname(X1012)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1012),X1011))
        | X1006 != hAPP_pname_a(X1010,X1012)
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1006),image_pname_a(X1010,X1011)))
        | ~ is_a(X1006) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_302_image__iff])])])])])]) ).

cnf(c_0_82,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X3,X1)),image_pname_a(X3,X2)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_72]) ).

cnf(c_0_83,hypothesis,
    hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
    inference(split_conjunct,[status(thm)],[conj_4]) ).

cnf(c_0_84,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
    | ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_63]) ).

cnf(c_0_85,plain,
    ( X1 = bot_bot_fun_nat_bool
    | hBOOL(hAPP_nat_bool(X1,esk100_1(X1))) ),
    inference(spm,[status(thm)],[c_0_73,c_0_74]) ).

cnf(c_0_86,hypothesis,
    ( hAPP_nat_bool(cOMBK_bool_nat(X1),X2) = bot_bot_bool
    | fTrue = X1
    | ~ is_bool(X1) ),
    inference(spm,[status(thm)],[c_0_75,c_0_76]) ).

cnf(c_0_87,plain,
    ( hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),bot_bot_fun_nat_bool) = fFalse
    | ~ hBOOL(fTrue) ),
    inference(spm,[status(thm)],[c_0_77,c_0_47]) ).

cnf(c_0_88,plain,
    collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool))),
    inference(rw,[status(thm)],[c_0_78,c_0_79]) ).

cnf(c_0_89,plain,
    collect_a(hAPP_a_fun_a_bool(fequal_a,X1)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool))),
    inference(rw,[status(thm)],[c_0_80,c_0_79]) ).

fof(c_0_90,plain,
    ! [X985] :
      ( ~ is_fun_a_bool(X985)
      | collect_a(X985) = X985 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_290_Collect__def])]) ).

fof(c_0_91,plain,
    ! [X183,X184] :
      ( ~ is_pname(X184)
      | is_fun_a_bool(hAPP_p1534023578a_bool(X183,X184)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J])]) ).

fof(c_0_92,plain,
    ! [X2090,X2091,X2092] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X2090,X2091),X2092) = hAPP_a_fun_a_bool(X2090,hAPP_pname_a(X2091,X2092)),
    inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna]) ).

cnf(c_0_93,plain,
    ( X1 = hAPP_pname_a(X2,esk59_3(X1,X2,X3))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
    | ~ is_a(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_81]) ).

cnf(c_0_94,hypothesis,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X1,pn)),image_pname_a(X1,u))),
    inference(spm,[status(thm)],[c_0_82,c_0_83]) ).

fof(c_0_95,hypothesis,
    ! [X177,X178] :
      ( ~ is_pname(X178)
      | is_a(hAPP_pname_a(X177,X178)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000t__a])]) ).

cnf(c_0_96,plain,
    ( is_pname(esk59_3(X1,X2,X3))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
    | ~ is_a(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_81]) ).

fof(c_0_97,plain,
    ! [X1111,X1112,X1113] : image_pname_a(X1111,insert_pname(X1112,X1113)) = insert_a(hAPP_pname_a(X1111,X1112),image_pname_a(X1111,X1113)),
    inference(variable_rename,[status(thm)],[fact_337_image__insert]) ).

fof(c_0_98,plain,
    ! [X858,X859] : insert_pname(X858,X859) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X858)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X859))),
    inference(variable_rename,[status(thm)],[fact_237_insert__compr]) ).

fof(c_0_99,plain,
    ! [X1465] : collect_pname(hAPP_p61793385e_bool(fequal_pname,X1465)) = insert_pname(X1465,bot_bo844097828e_bool),
    inference(variable_rename,[status(thm)],[fact_489_singleton__conv2]) ).

cnf(c_0_100,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),cOMBK_bool_nat(X2)))
    | ~ hBOOL(X2)
    | ~ is_bool(X2) ),
    inference(spm,[status(thm)],[c_0_84,c_0_75]) ).

cnf(c_0_101,hypothesis,
    ( cOMBK_bool_nat(X1) = bot_bot_fun_nat_bool
    | fTrue = X1
    | ~ is_bool(X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_61]) ).

cnf(c_0_102,plain,
    hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),bot_bot_fun_nat_bool) = bot_bot_bool,
    inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_59])]),c_0_67]) ).

fof(c_0_103,hypothesis,
    ! [X209,X210] :
      ( ~ is_fun949378684l_bool(X209)
      | ~ is_fun_a_bool(X210)
      | is_bool(hAPP_fun_a_bool_bool(X209,X210)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool])]) ).

fof(c_0_104,negated_conjecture,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_6])]) ).

cnf(c_0_105,plain,
    collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)) = collect_a(hAPP_a_fun_a_bool(fequal_a,X1)),
    inference(rw,[status(thm)],[c_0_88,c_0_89]) ).

cnf(c_0_106,plain,
    ( collect_a(X1) = X1
    | ~ is_fun_a_bool(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_90]) ).

fof(c_0_107,plain,
    ! [X169,X170] :
      ( ~ is_a(X170)
      | is_fun_a_bool(hAPP_a_fun_a_bool(X169,X170)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J])]) ).

cnf(c_0_108,plain,
    ( is_fun_a_bool(hAPP_p1534023578a_bool(X2,X1))
    | ~ is_pname(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_91]) ).

cnf(c_0_109,plain,
    hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X1,X2),X3) = hAPP_a_fun_a_bool(X1,hAPP_pname_a(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_92]) ).

cnf(c_0_110,hypothesis,
    ( hAPP_pname_a(X1,esk59_3(hAPP_pname_a(X1,pn),X1,u)) = hAPP_pname_a(X1,pn)
    | ~ is_a(hAPP_pname_a(X1,pn)) ),
    inference(spm,[status(thm)],[c_0_93,c_0_94]) ).

cnf(c_0_111,hypothesis,
    ( is_a(hAPP_pname_a(X2,X1))
    | ~ is_pname(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_95]) ).

cnf(c_0_112,hypothesis,
    is_pname(pn),
    inference(split_conjunct,[status(thm)],[gsy_v_pn]) ).

cnf(c_0_113,hypothesis,
    ( is_pname(esk59_3(hAPP_pname_a(X1,pn),X1,u))
    | ~ is_a(hAPP_pname_a(X1,pn)) ),
    inference(spm,[status(thm)],[c_0_96,c_0_94]) ).

cnf(c_0_114,plain,
    image_pname_a(X1,insert_pname(X2,X3)) = insert_a(hAPP_pname_a(X1,X2),image_pname_a(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_97]) ).

cnf(c_0_115,plain,
    insert_pname(X1,X2) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))),
    inference(split_conjunct,[status(thm)],[c_0_98]) ).

fof(c_0_116,plain,
    ! [X1431] : image_pname_a(X1431,bot_bo844097828e_bool) = bot_bot_fun_a_bool,
    inference(variable_rename,[status(thm)],[fact_468_image__empty]) ).

cnf(c_0_117,plain,
    collect_pname(hAPP_p61793385e_bool(fequal_pname,X1)) = insert_pname(X1,bot_bo844097828e_bool),
    inference(split_conjunct,[status(thm)],[c_0_99]) ).

cnf(c_0_118,hypothesis,
    ( fTrue = X1
    | ~ hBOOL(X1)
    | ~ is_bool(X1) ),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102]),c_0_61]) ).

cnf(c_0_119,hypothesis,
    ( is_bool(hAPP_fun_a_bool_bool(X1,X2))
    | ~ is_fun949378684l_bool(X1)
    | ~ is_fun_a_bool(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_103]) ).

cnf(c_0_120,negated_conjecture,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
    inference(split_conjunct,[status(thm)],[c_0_104]) ).

cnf(c_0_121,plain,
    ( hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1) = collect_a(hAPP_a_fun_a_bool(fequal_a,X1))
    | ~ is_fun_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)) ),
    inference(spm,[status(thm)],[c_0_105,c_0_106]) ).

cnf(c_0_122,plain,
    ( is_fun_a_bool(hAPP_a_fun_a_bool(X2,X1))
    | ~ is_a(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_107]) ).

fof(c_0_123,plain,
    ! [X1072,X1073,X1074] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1072),X1074))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1072,X1073)),X1074)) )
      & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1073),X1074))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1072,X1073)),X1074)) )
      & ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1072),X1074))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1073),X1074))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1072,X1073)),X1074)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_324_insert__subset])])]) ).

cnf(c_0_124,plain,
    ( is_fun_a_bool(hAPP_a_fun_a_bool(X1,hAPP_pname_a(X2,X3)))
    | ~ is_pname(X3) ),
    inference(spm,[status(thm)],[c_0_108,c_0_109]) ).

cnf(c_0_125,hypothesis,
    hAPP_pname_a(X1,esk59_3(hAPP_pname_a(X1,pn),X1,u)) = hAPP_pname_a(X1,pn),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112])]) ).

cnf(c_0_126,hypothesis,
    is_pname(esk59_3(hAPP_pname_a(X1,pn),X1,u)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_111]),c_0_112])]) ).

cnf(c_0_127,plain,
    image_pname_a(X1,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X3)))) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(X1,X2))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X1,X3)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_79]),c_0_115]) ).

cnf(c_0_128,plain,
    image_pname_a(X1,bot_bo844097828e_bool) = bot_bot_fun_a_bool,
    inference(split_conjunct,[status(thm)],[c_0_116]) ).

cnf(c_0_129,plain,
    collect_pname(hAPP_p61793385e_bool(fequal_pname,X1)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),bot_bo844097828e_bool))),
    inference(rw,[status(thm)],[c_0_117,c_0_115]) ).

cnf(c_0_130,hypothesis,
    ( hAPP_fun_a_bool_bool(X1,X2) = fTrue
    | ~ hBOOL(hAPP_fun_a_bool_bool(X1,X2))
    | ~ is_fun949378684l_bool(X1)
    | ~ is_fun_a_bool(X2) ),
    inference(spm,[status(thm)],[c_0_118,c_0_119]) ).

cnf(c_0_131,hypothesis,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
    inference(split_conjunct,[status(thm)],[conj_1]) ).

fof(c_0_132,hypothesis,
    ! [X215,X216] :
      ( ~ is_fun_a_bool(X216)
      | is_fun949378684l_bool(hAPP_f1631501043l_bool(X215,X216)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__a_Mtc__HOL])]) ).

cnf(c_0_133,negated_conjecture,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(mgt_call,pn))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),image_pname_a(mgt_call,u))),
    inference(rw,[status(thm)],[c_0_120,c_0_79]) ).

cnf(c_0_134,plain,
    ( hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1) = collect_a(hAPP_a_fun_a_bool(fequal_a,X1))
    | ~ is_a(X1) ),
    inference(spm,[status(thm)],[c_0_121,c_0_122]) ).

cnf(c_0_135,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1,X3)),X2))
    | ~ 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,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_123]) ).

cnf(c_0_136,hypothesis,
    is_fun_a_bool(hAPP_a_fun_a_bool(X1,hAPP_pname_a(X2,pn))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_126])]) ).

cnf(c_0_137,plain,
    collect_a(hAPP_a_fun_a_bool(fequal_a,hAPP_pname_a(X1,X2))) = image_pname_a(X1,collect_pname(hAPP_p61793385e_bool(fequal_pname,X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_89]),c_0_129]) ).

cnf(c_0_138,hypothesis,
    ( hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)) = fTrue
    | ~ is_fun949378684l_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g))
    | ~ is_fun_a_bool(image_pname_a(mgt_call,u)) ),
    inference(spm,[status(thm)],[c_0_130,c_0_131]) ).

cnf(c_0_139,hypothesis,
    ( is_fun949378684l_bool(hAPP_f1631501043l_bool(X2,X1))
    | ~ is_fun_a_bool(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_132]) ).

cnf(c_0_140,hypothesis,
    is_fun_a_bool(g),
    inference(split_conjunct,[status(thm)],[gsy_v_G]) ).

fof(c_0_141,hypothesis,
    ! [X127,X128] :
      ( ~ is_fun_pname_bool(X128)
      | is_fun_a_bool(image_pname_a(X127,X128)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Com__Opname_000t__a])]) ).

cnf(c_0_142,negated_conjecture,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,collect_a(hAPP_a_fun_a_bool(fequal_a,hAPP_pname_a(mgt_call,pn)))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),image_pname_a(mgt_call,u)))
    | ~ is_a(hAPP_pname_a(mgt_call,pn)) ),
    inference(spm,[status(thm)],[c_0_133,c_0_134]) ).

cnf(c_0_143,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3)))),X2))
    | ~ 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,X3),X2)) ),
    inference(rw,[status(thm)],[c_0_135,c_0_79]) ).

cnf(c_0_144,hypothesis,
    hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(X1,pn)) = image_pname_a(X1,collect_pname(hAPP_p61793385e_bool(fequal_pname,pn))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_136]),c_0_137]) ).

cnf(c_0_145,hypothesis,
    ( hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)) = fTrue
    | ~ is_fun_a_bool(image_pname_a(mgt_call,u)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_140])]) ).

cnf(c_0_146,hypothesis,
    ( is_fun_a_bool(image_pname_a(X2,X1))
    | ~ is_fun_pname_bool(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_141]) ).

cnf(c_0_147,hypothesis,
    is_fun_pname_bool(u),
    inference(split_conjunct,[status(thm)],[gsy_v_U]) ).

cnf(c_0_148,hypothesis,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,collect_a(hAPP_a_fun_a_bool(fequal_a,hAPP_pname_a(mgt_call,pn)))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),image_pname_a(mgt_call,u))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_111]),c_0_112])]) ).

cnf(c_0_149,hypothesis,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,image_pname_a(X1,collect_pname(hAPP_p61793385e_bool(fequal_pname,pn)))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))),image_pname_a(X1,u)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X1,u))) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_94]),c_0_144]) ).

cnf(c_0_150,hypothesis,
    hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u)) = fTrue,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_147])]) ).

cnf(c_0_151,hypothesis,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,image_pname_a(mgt_call,collect_pname(hAPP_p61793385e_bool(fequal_pname,pn)))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),image_pname_a(mgt_call,u))),
    inference(spm,[status(thm)],[c_0_148,c_0_137]) ).

cnf(c_0_152,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_59])]),c_0_151]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWW473+2 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.33  % Computer : n020.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Sun Aug 27 22:13:44 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.55  start to proof: theBenchmark
% 30.50/30.57  % Version  : CSE_E---1.5
% 30.50/30.57  % Problem  : theBenchmark.p
% 30.50/30.57  % Proof found
% 30.50/30.57  % SZS status Theorem for theBenchmark.p
% 30.50/30.57  % SZS output start Proof
% See solution above
% 30.59/30.60  % Total time : 30.002000 s
% 30.59/30.60  % SZS output end Proof
% 30.59/30.60  % Total time : 30.022000 s
%------------------------------------------------------------------------------