TSTP Solution File: ITP110^1 by Vampire---4.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : ITP110^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n002.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 : Mon Jun 24 09:35:57 EDT 2024

% Result   : Theorem 0.20s 0.43s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   32 (   9 unt;   0 typ;   0 def)
%            Number of atoms       :  120 (  32 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :  125 (  19   ~;  16   |;   0   &;  82   @)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Number of types       :   17 (  16 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  176 ( 173 usr;  20 con; 0-3 aty)
%            Number of variables   :    5 (   0   ^   5   !;   0   ?;   5   :)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    set_Extended_ereal_o: $tType ).

thf(type_def_6,type,
    extended_ereal: $tType ).

thf(type_def_8,type,
    set_a_o: $tType ).

thf(type_def_9,type,
    a: $tType ).

thf(type_def_10,type,
    set_Extended_ereal: $tType ).

thf(type_def_11,type,
    set_real: $tType ).

thf(type_def_12,type,
    real: $tType ).

thf(type_def_13,type,
    set_se767749006_ereal: $tType ).

thf(type_def_14,type,
    set_se1849684334_ereal: $tType ).

thf(type_def_15,type,
    set_set_set_a: $tType ).

thf(type_def_16,type,
    set_set_a: $tType ).

thf(type_def_17,type,
    set_a: $tType ).

thf(type_def_18,type,
    set_Pr1158285382l_real: $tType ).

thf(type_def_19,type,
    set_Pr1928503567a_real: $tType ).

thf(type_def_20,type,
    set_Pr597221087l_real: $tType ).

thf(type_def_21,type,
    product_prod_a_real: $tType ).

thf(func_def_0,type,
    set_Pr1158285382l_real: $tType ).

thf(func_def_1,type,
    set_Pr597221087l_real: $tType ).

thf(func_def_2,type,
    set_se1849684334_ereal: $tType ).

thf(func_def_3,type,
    set_Pr1928503567a_real: $tType ).

thf(func_def_4,type,
    set_se767749006_ereal: $tType ).

thf(func_def_5,type,
    set_Extended_ereal_o: $tType ).

thf(func_def_6,type,
    set_set_set_a: $tType ).

thf(func_def_7,type,
    product_prod_a_real: $tType ).

thf(func_def_8,type,
    set_Extended_ereal: $tType ).

thf(func_def_9,type,
    set_set_a: $tType ).

thf(func_def_10,type,
    set_a_o: $tType ).

thf(func_def_11,type,
    set_real: $tType ).

thf(func_def_12,type,
    extended_ereal: $tType ).

thf(func_def_13,type,
    set_a: $tType ).

thf(func_def_14,type,
    real: $tType ).

thf(func_def_15,type,
    a: $tType ).

thf(func_def_16,type,
    comple179807490real_o: set_Extended_ereal_o > extended_ereal > $o ).

thf(func_def_17,type,
    complete_Sup_Sup_a_o: set_a_o > a > $o ).

thf(func_def_18,type,
    comple1161760187_ereal: set_Extended_ereal > extended_ereal ).

thf(func_def_19,type,
    comple2129349247p_real: set_real > real ).

thf(func_def_20,type,
    comple767846299_ereal: set_se767749006_ereal > set_Extended_ereal ).

thf(func_def_21,type,
    comple1517911419_ereal: set_se1849684334_ereal > set_se767749006_ereal ).

thf(func_def_22,type,
    comple968993579_set_a: set_set_set_a > set_set_a ).

thf(func_def_23,type,
    comple1766734283_set_a: set_set_a > set_a ).

thf(func_def_24,type,
    convex291263275l_real: set_Pr1158285382l_real > $o ).

thf(func_def_25,type,
    convex78185044a_real: set_Pr1928503567a_real > $o ).

thf(func_def_26,type,
    convex_a: set_a > $o ).

thf(func_def_27,type,
    extend1289208545_ereal: extended_ereal ).

thf(func_def_28,type,
    extended_MInfty: extended_ereal ).

thf(func_def_29,type,
    extended_PInfty: extended_ereal ).

thf(func_def_30,type,
    extended_ereal2: real > extended_ereal ).

thf(func_def_31,type,
    extend1716541707_ereal: extended_ereal > real ).

thf(func_def_32,type,
    times_1966848393_ereal: extended_ereal > extended_ereal > extended_ereal ).

thf(func_def_33,type,
    times_times_real: real > real > real ).

thf(func_def_34,type,
    uminus1208298309_ereal: extended_ereal > extended_ereal ).

thf(func_def_35,type,
    uminus_uminus_real: real > real ).

thf(func_def_36,type,
    uminus360668453_ereal: set_Extended_ereal > set_Extended_ereal ).

thf(func_def_37,type,
    uminus_uminus_set_a: set_a > set_a ).

thf(func_def_38,type,
    zero_z163181189_ereal: extended_ereal ).

thf(func_def_39,type,
    zero_zero_real: real ).

thf(func_def_40,type,
    lower_331963542_ereal: set_Extended_ereal > ( extended_ereal > extended_ereal ) > set_Pr597221087l_real ).

thf(func_def_41,type,
    lower_870348689a_real: set_Pr1928503567a_real > ( product_prod_a_real > extended_ereal ) > set_Pr1158285382l_real ).

thf(func_def_42,type,
    lower_930854854raph_a: set_a > ( a > extended_ereal ) > set_Pr1928503567a_real ).

thf(func_def_43,type,
    lower_128423320e_on_a: set_a > ( a > extended_ereal ) > $o ).

thf(func_def_44,type,
    lower_1023700310e_on_a: set_a > ( a > extended_ereal ) > $o ).

thf(func_def_45,type,
    lower_591730471a_real: set_Pr1928503567a_real > ( product_prod_a_real > extended_ereal ) > $o ).

thf(func_def_46,type,
    lower_311861424x_on_a: set_a > ( a > extended_ereal ) > $o ).

thf(func_def_47,type,
    lower_1359521925a_real: ( product_prod_a_real > extended_ereal ) > set_Pr1928503567a_real ).

thf(func_def_48,type,
    lower_1391529426main_a: ( a > extended_ereal ) > set_a ).

thf(func_def_49,type,
    lower_1486931688e_on_a: set_a > ( a > extended_ereal ) > $o ).

thf(func_def_50,type,
    ord_le824540014_ereal: extended_ereal > extended_ereal > $o ).

thf(func_def_51,type,
    ord_less_eq_real: real > real > $o ).

thf(func_def_52,type,
    ord_le88246606_ereal: set_Extended_ereal > set_Extended_ereal > $o ).

thf(func_def_53,type,
    ord_le1586073967a_real: set_Pr1928503567a_real > set_Pr1928503567a_real > $o ).

thf(func_def_54,type,
    ord_less_eq_set_real: set_real > set_real > $o ).

thf(func_def_55,type,
    ord_le1153389358_ereal: set_se767749006_ereal > set_se767749006_ereal > $o ).

thf(func_def_56,type,
    ord_le318720350_set_a: set_set_a > set_set_a > $o ).

thf(func_def_57,type,
    ord_less_eq_set_a: set_a > set_a > $o ).

thf(func_def_58,type,
    order_1158471719_ereal: ( extended_ereal > $o ) > extended_ereal ).

thf(func_def_59,type,
    order_Greatest_real: ( real > $o ) > real ).

thf(func_def_60,type,
    top_to398855007real_o: extended_ereal > $o ).

thf(func_def_61,type,
    top_top_a_o: a > $o ).

thf(func_def_63,type,
    top_to802031902_ereal: extended_ereal ).

thf(func_def_64,type,
    top_to772344469real_o: set_Extended_ereal_o ).

thf(func_def_65,type,
    top_top_set_a_o: set_a_o ).

thf(func_def_66,type,
    top_to1767659262_ereal: set_Extended_ereal ).

thf(func_def_67,type,
    top_to2138011583a_real: set_Pr1928503567a_real ).

thf(func_def_68,type,
    top_top_set_real: set_real ).

thf(func_def_69,type,
    top_to692740318_ereal: set_se767749006_ereal ).

thf(func_def_70,type,
    top_to1791633086_ereal: set_se1849684334_ereal ).

thf(func_def_71,type,
    top_to1486684270_set_a: set_set_set_a ).

thf(func_def_72,type,
    top_top_set_set_a: set_set_a ).

thf(func_def_73,type,
    top_top_set_a: set_a ).

thf(func_def_74,type,
    divide595620860_ereal: extended_ereal > extended_ereal > extended_ereal ).

thf(func_def_75,type,
    divide_divide_real: real > real > real ).

thf(func_def_76,type,
    collec247695033_ereal: ( extended_ereal > $o ) > set_Extended_ereal ).

thf(func_def_77,type,
    collec1714955950a_real: ( product_prod_a_real > $o ) > set_Pr1928503567a_real ).

thf(func_def_78,type,
    collect_a: ( a > $o ) > set_a ).

thf(func_def_79,type,
    member1900190071_ereal: extended_ereal > set_Extended_ereal > $o ).

thf(func_def_80,type,
    member1103263856a_real: product_prod_a_real > set_Pr1928503567a_real > $o ).

thf(func_def_81,type,
    member_real: real > set_real > $o ).

thf(func_def_82,type,
    member450560855_ereal: set_Extended_ereal > set_se767749006_ereal > $o ).

thf(func_def_83,type,
    member_set_a: set_a > set_set_a > $o ).

thf(func_def_84,type,
    member_a: a > set_a > $o ).

thf(func_def_85,type,
    f: a > extended_ereal ).

thf(func_def_99,type,
    sP0: extended_ereal > extended_ereal > $o ).

thf(func_def_100,type,
    sP1: extended_ereal > extended_ereal > $o ).

thf(func_def_101,type,
    sP2: extended_ereal > extended_ereal > $o ).

thf(func_def_102,type,
    sP3: extended_ereal > extended_ereal > $o ).

thf(func_def_103,type,
    sP4: extended_ereal > extended_ereal > $o ).

thf(func_def_104,type,
    sP5: extended_ereal > extended_ereal > $o ).

thf(func_def_105,type,
    sP6: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_106,type,
    sP7: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_107,type,
    sP8: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_108,type,
    sP9: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_109,type,
    sP10: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_110,type,
    sP11: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_111,type,
    sP12: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_112,type,
    sP13: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_113,type,
    sP14: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_114,type,
    sP15: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_115,type,
    sP16: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_116,type,
    sP17: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_117,type,
    sP18: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_118,type,
    sP19: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_119,type,
    sP20: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_120,type,
    sP21: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_121,type,
    sP22: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_122,type,
    sP23: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_123,type,
    sP24: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_124,type,
    sP25: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_125,type,
    sP26: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_126,type,
    sP27: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_127,type,
    sP28: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_128,type,
    sP29: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_129,type,
    sP30: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_130,type,
    sP31: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_131,type,
    sK32: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_132,type,
    sK33: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_133,type,
    sK34: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_134,type,
    sK35: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_135,type,
    sK36: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_136,type,
    sK37: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_137,type,
    sK38: ( extended_ereal > $o ) > real ).

thf(func_def_138,type,
    sK39: ( extended_ereal > set_a ) > extended_ereal ).

thf(func_def_139,type,
    sK40: ( extended_ereal > set_a ) > extended_ereal ).

thf(func_def_140,type,
    sK41: ( real > set_a ) > real ).

thf(func_def_141,type,
    sK42: ( real > set_a ) > real ).

thf(func_def_142,type,
    sK43: ( set_a > extended_ereal ) > set_a ).

thf(func_def_143,type,
    sK44: ( set_a > extended_ereal ) > set_a ).

thf(func_def_144,type,
    sK45: ( extended_ereal > $o ) > real ).

thf(func_def_145,type,
    sK46: extended_ereal > real ).

thf(func_def_146,type,
    sK47: extended_ereal > real ).

thf(func_def_147,type,
    sK48: extended_ereal > real ).

thf(func_def_148,type,
    sK49: extended_ereal > real ).

thf(func_def_149,type,
    sK50: extended_ereal > real ).

thf(func_def_150,type,
    sK51: extended_ereal > real ).

thf(func_def_151,type,
    sK52: ( a > extended_ereal ) > set_a ).

thf(func_def_152,type,
    sK53: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).

thf(func_def_153,type,
    sK54: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_154,type,
    sK55: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_155,type,
    sK56: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_156,type,
    sK57: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).

thf(func_def_157,type,
    sK58: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_158,type,
    sK59: extended_ereal > real ).

thf(func_def_159,type,
    sK60: extended_ereal > real ).

thf(func_def_160,type,
    sK61: extended_ereal > real ).

thf(func_def_161,type,
    sK62: extended_ereal > real ).

thf(func_def_162,type,
    sK63: extended_ereal > real ).

thf(func_def_163,type,
    sK64: extended_ereal > real ).

thf(func_def_164,type,
    sK65: extended_ereal > real ).

thf(func_def_165,type,
    sK66: extended_ereal > real ).

thf(func_def_166,type,
    sK67: extended_ereal > real ).

thf(func_def_167,type,
    sK68: extended_ereal > real ).

thf(func_def_168,type,
    sK69: extended_ereal > real ).

thf(func_def_169,type,
    sK70: extended_ereal > real ).

thf(func_def_170,type,
    sK71: extended_ereal > real ).

thf(func_def_171,type,
    sK72: extended_ereal > real ).

thf(func_def_172,type,
    sK73: extended_ereal > real ).

thf(func_def_173,type,
    sK74: extended_ereal > real ).

thf(func_def_174,type,
    sK75: extended_ereal > real ).

thf(func_def_175,type,
    sK76: extended_ereal > real ).

thf(func_def_176,type,
    sK77: extended_ereal > real ).

thf(func_def_177,type,
    sK78: extended_ereal > real ).

thf(func_def_178,type,
    sK79: extended_ereal > real ).

thf(func_def_179,type,
    sK80: extended_ereal > real ).

thf(func_def_180,type,
    sK81: extended_ereal > real ).

thf(func_def_181,type,
    sK82: extended_ereal > real ).

thf(func_def_182,type,
    sK83: extended_ereal > real ).

thf(func_def_183,type,
    sK84: extended_ereal > real ).

thf(func_def_184,type,
    sK85: extended_ereal > real ).

thf(func_def_185,type,
    sK86: extended_ereal > real ).

thf(func_def_186,type,
    sK87: ( a > extended_ereal ) > set_a ).

thf(func_def_187,type,
    sK88: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).

thf(func_def_188,type,
    sK89: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_189,type,
    sK90: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_190,type,
    sK91: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_191,type,
    sK92: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_192,type,
    sK93: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).

thf(func_def_193,type,
    sK94: extended_ereal > real ).

thf(func_def_194,type,
    sK95: extended_ereal > real ).

thf(func_def_195,type,
    sK96: ( set_a > real ) > set_a ).

thf(func_def_196,type,
    sK97: ( set_a > real ) > set_a ).

thf(func_def_197,type,
    sK98: extended_ereal > real ).

thf(func_def_198,type,
    sK99: extended_ereal > real ).

thf(func_def_199,type,
    sK100: extended_ereal > real ).

thf(func_def_201,type,
    ph102: 
      !>[X0: $tType] : X0 ).

thf(f1396,plain,
    $false,
    inference(avatar_sat_refutation,[],[f1346,f1372,f1395]) ).

thf(f1395,plain,
    ~ spl101_1,
    inference(avatar_contradiction_clause,[],[f1394]) ).

thf(f1394,plain,
    ( $false
    | ~ spl101_1 ),
    inference(trivial_inequality_removal,[],[f1390]) ).

thf(f1390,plain,
    ( ( $true = $false )
    | ~ spl101_1 ),
    inference(superposition,[],[f1348,f1341]) ).

thf(f1341,plain,
    ( ( ( convex_a @ ( lower_1391529426main_a @ f ) )
      = $false )
    | ~ spl101_1 ),
    inference(avatar_component_clause,[],[f1339]) ).

thf(f1339,plain,
    ( spl101_1
  <=> ( ( convex_a @ ( lower_1391529426main_a @ f ) )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl101_1])]) ).

thf(f1348,plain,
    ( ( convex_a @ ( lower_1391529426main_a @ f ) )
    = $true ),
    inference(trivial_inequality_removal,[],[f1347]) ).

thf(f1347,plain,
    ( ( $true != $true )
    | ( ( convex_a @ ( lower_1391529426main_a @ f ) )
      = $true ) ),
    inference(superposition,[],[f1187,f1337]) ).

thf(f1337,plain,
    ( ( lower_311861424x_on_a @ top_top_set_a @ f )
    = $true ),
    inference(subsumption_resolution,[],[f1335,f1169]) ).

thf(f1169,plain,
    ( ( ( lower_311861424x_on_a @ top_top_set_a @ f )
      = $true )
    | ( ( convex_a @ ( lower_1391529426main_a @ f ) )
     != $true ) ),
    inference(cnf_transformation,[],[f945]) ).

thf(f945,plain,
    ( ( ( lower_311861424x_on_a @ top_top_set_a @ f )
      = $true )
    | ( ( convex_a @ ( lower_1391529426main_a @ f ) )
     != $true ) ),
    inference(ennf_transformation,[],[f393]) ).

thf(f393,plain,
    ( ( ( convex_a @ ( lower_1391529426main_a @ f ) )
      = $true )
   => ( ( lower_311861424x_on_a @ top_top_set_a @ f )
      = $true ) ),
    inference(fool_elimination,[],[f392]) ).

thf(f392,plain,
    ( ( convex_a @ ( lower_1391529426main_a @ f ) )
   => ( lower_311861424x_on_a @ top_top_set_a @ f ) ),
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    ( ( convex_a @ ( lower_1391529426main_a @ f ) )
   => ( lower_311861424x_on_a @ top_top_set_a @ f ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062convex_A_Idomain_Af_J_A_092_060Longrightarrow_062_ALower__Semicontinuous__Mirabelle__mxyexokbxt_Oconvex__on_AUNIV_Af_092_060close_062) ).

thf(f1335,plain,
    ( ( ( convex_a @ ( lower_1391529426main_a @ f ) )
      = $true )
    | ( ( lower_311861424x_on_a @ top_top_set_a @ f )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f1298]) ).

thf(f1298,plain,
    ( ( convex_a @ ( lower_1391529426main_a @ f ) )
   != ( lower_311861424x_on_a @ top_top_set_a @ f ) ),
    inference(cnf_transformation,[],[f888]) ).

thf(f888,plain,
    ( ( convex_a @ ( lower_1391529426main_a @ f ) )
   != ( lower_311861424x_on_a @ top_top_set_a @ f ) ),
    inference(flattening,[],[f356]) ).

thf(f356,negated_conjecture,
    ( ( convex_a @ ( lower_1391529426main_a @ f ) )
   != ( lower_311861424x_on_a @ top_top_set_a @ f ) ),
    inference(negated_conjecture,[],[f355]) ).

thf(f355,conjecture,
    ( ( convex_a @ ( lower_1391529426main_a @ f ) )
    = ( lower_311861424x_on_a @ top_top_set_a @ f ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(f1187,plain,
    ! [X0: a > extended_ereal] :
      ( ( ( lower_311861424x_on_a @ top_top_set_a @ X0 )
       != $true )
      | ( ( convex_a @ ( lower_1391529426main_a @ X0 ) )
        = $true ) ),
    inference(cnf_transformation,[],[f901]) ).

thf(f901,plain,
    ! [X0: a > extended_ereal] :
      ( ( ( convex_a @ ( lower_1391529426main_a @ X0 ) )
        = $true )
      | ( ( lower_311861424x_on_a @ top_top_set_a @ X0 )
       != $true ) ),
    inference(ennf_transformation,[],[f441]) ).

thf(f441,plain,
    ! [X0: a > extended_ereal] :
      ( ( ( lower_311861424x_on_a @ top_top_set_a @ X0 )
        = $true )
     => ( ( convex_a @ ( lower_1391529426main_a @ X0 ) )
        = $true ) ),
    inference(fool_elimination,[],[f440]) ).

thf(f440,plain,
    ! [X0: a > extended_ereal] :
      ( ( lower_311861424x_on_a @ top_top_set_a @ X0 )
     => ( convex_a @ ( lower_1391529426main_a @ X0 ) ) ),
    inference(rectify,[],[f3]) ).

thf(f3,axiom,
    ! [X0: a > extended_ereal] :
      ( ( lower_311861424x_on_a @ top_top_set_a @ X0 )
     => ( convex_a @ ( lower_1391529426main_a @ X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_convex__domain) ).

thf(f1372,plain,
    ~ spl101_2,
    inference(avatar_contradiction_clause,[],[f1371]) ).

thf(f1371,plain,
    ( $false
    | ~ spl101_2 ),
    inference(subsumption_resolution,[],[f1358,f1348]) ).

thf(f1358,plain,
    ( ( ( convex_a @ ( lower_1391529426main_a @ f ) )
     != $true )
    | ~ spl101_2 ),
    inference(trivial_inequality_removal,[],[f1354]) ).

thf(f1354,plain,
    ( ( $true = $false )
    | ( ( convex_a @ ( lower_1391529426main_a @ f ) )
     != $true )
    | ~ spl101_2 ),
    inference(superposition,[],[f1169,f1345]) ).

thf(f1345,plain,
    ( ( ( lower_311861424x_on_a @ top_top_set_a @ f )
      = $false )
    | ~ spl101_2 ),
    inference(avatar_component_clause,[],[f1343]) ).

thf(f1343,plain,
    ( spl101_2
  <=> ( ( lower_311861424x_on_a @ top_top_set_a @ f )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl101_2])]) ).

thf(f1346,plain,
    ( spl101_1
    | spl101_2 ),
    inference(avatar_split_clause,[],[f1336,f1343,f1339]) ).

thf(f1336,plain,
    ( ( ( lower_311861424x_on_a @ top_top_set_a @ f )
      = $false )
    | ( ( convex_a @ ( lower_1391529426main_a @ f ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f1298]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : ITP110^1 : TPTP v8.2.0. Released v7.5.0.
% 0.10/0.12  % Command    : run_vampire %s %d THM
% 0.12/0.33  % Computer : n002.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Wed Jun 19 03:44:39 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.12/0.35  This is a TH0_THM_EQU_NAR problem
% 0.12/0.35  Running higher-order theorem proving
% 0.12/0.35  Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.12/0.39  % (8798)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.12/0.39  % (8797)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.12/0.39  % (8799)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.39  % (8796)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.39  % (8800)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.39  % (8801)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.12/0.39  % (8802)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.39  % (8799)Instruction limit reached!
% 0.12/0.39  % (8799)------------------------------
% 0.12/0.39  % (8799)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.39  % (8799)Termination reason: Unknown
% 0.12/0.39  % (8799)Termination phase: shuffling
% 0.12/0.39  % (8800)Instruction limit reached!
% 0.12/0.39  % (8800)------------------------------
% 0.12/0.39  % (8800)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.39  % (8800)Termination reason: Unknown
% 0.12/0.39  % (8800)Termination phase: shuffling
% 0.12/0.39  
% 0.12/0.39  % (8800)Memory used [KB]: 1407
% 0.12/0.39  % (8800)Time elapsed: 0.004 s
% 0.12/0.39  % (8800)Instructions burned: 3 (million)
% 0.12/0.39  % (8800)------------------------------
% 0.12/0.39  % (8800)------------------------------
% 0.12/0.39  
% 0.12/0.39  % (8799)Memory used [KB]: 1407
% 0.12/0.39  % (8799)Time elapsed: 0.004 s
% 0.12/0.39  % (8799)Instructions burned: 2 (million)
% 0.12/0.39  % (8799)------------------------------
% 0.12/0.39  % (8799)------------------------------
% 0.12/0.39  % (8797)Instruction limit reached!
% 0.12/0.39  % (8797)------------------------------
% 0.12/0.39  % (8797)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.39  % (8797)Termination reason: Unknown
% 0.12/0.39  % (8797)Termination phase: shuffling
% 0.12/0.39  
% 0.12/0.39  % (8797)Memory used [KB]: 1407
% 0.12/0.39  % (8797)Time elapsed: 0.005 s
% 0.12/0.39  % (8797)Instructions burned: 4 (million)
% 0.12/0.39  % (8797)------------------------------
% 0.12/0.39  % (8797)------------------------------
% 0.12/0.40  % (8802)Instruction limit reached!
% 0.12/0.40  % (8802)------------------------------
% 0.12/0.40  % (8802)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.40  % (8802)Termination reason: Unknown
% 0.12/0.40  % (8802)Termination phase: Property scanning
% 0.12/0.40  
% 0.12/0.40  % (8802)Memory used [KB]: 1791
% 0.12/0.40  % (8802)Time elapsed: 0.014 s
% 0.12/0.40  % (8802)Instructions burned: 18 (million)
% 0.12/0.40  % (8802)------------------------------
% 0.12/0.40  % (8802)------------------------------
% 0.20/0.41  % (8805)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.41  % (8798)Instruction limit reached!
% 0.20/0.41  % (8798)------------------------------
% 0.20/0.41  % (8798)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.41  % (8798)Termination reason: Unknown
% 0.20/0.41  % (8798)Termination phase: Property scanning
% 0.20/0.41  
% 0.20/0.41  % (8798)Memory used [KB]: 1791
% 0.20/0.41  % (8798)Time elapsed: 0.019 s
% 0.20/0.41  % (8798)Instructions burned: 28 (million)
% 0.20/0.41  % (8798)------------------------------
% 0.20/0.41  % (8798)------------------------------
% 0.20/0.41  % (8803)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.41  % (8804)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.20/0.41  % (8803)Instruction limit reached!
% 0.20/0.41  % (8803)------------------------------
% 0.20/0.41  % (8803)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.41  % (8803)Termination reason: Unknown
% 0.20/0.41  % (8803)Termination phase: shuffling
% 0.20/0.41  
% 0.20/0.41  % (8803)Memory used [KB]: 1407
% 0.20/0.41  % (8803)Time elapsed: 0.004 s
% 0.20/0.41  % (8803)Instructions burned: 3 (million)
% 0.20/0.41  % (8803)------------------------------
% 0.20/0.41  % (8803)------------------------------
% 0.20/0.41  % (8805)Instruction limit reached!
% 0.20/0.41  % (8805)------------------------------
% 0.20/0.41  % (8805)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.41  % (8805)Termination reason: Unknown
% 0.20/0.41  % (8805)Termination phase: shuffling
% 0.20/0.41  
% 0.20/0.41  % (8805)Memory used [KB]: 1663
% 0.20/0.41  % (8805)Time elapsed: 0.009 s
% 0.20/0.41  % (8805)Instructions burned: 15 (million)
% 0.20/0.41  % (8805)------------------------------
% 0.20/0.41  % (8805)------------------------------
% 0.20/0.42  % (8806)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.42  % (8806)Instruction limit reached!
% 0.20/0.42  % (8806)------------------------------
% 0.20/0.42  % (8806)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.42  % (8806)Termination reason: Unknown
% 0.20/0.42  % (8806)Termination phase: shuffling
% 0.20/0.42  
% 0.20/0.42  % (8806)Memory used [KB]: 1407
% 0.20/0.42  % (8806)Time elapsed: 0.005 s
% 0.20/0.42  % (8806)Instructions burned: 4 (million)
% 0.20/0.42  % (8806)------------------------------
% 0.20/0.42  % (8806)------------------------------
% 0.20/0.42  % (8807)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.20/0.43  % (8808)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.43  % (8801)First to succeed.
% 0.20/0.43  % (8804)Instruction limit reached!
% 0.20/0.43  % (8804)------------------------------
% 0.20/0.43  % (8804)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.43  % (8804)Termination reason: Unknown
% 0.20/0.43  % (8804)Termination phase: shuffling
% 0.20/0.43  
% 0.20/0.43  % (8804)Memory used [KB]: 2174
% 0.20/0.43  % (8804)Time elapsed: 0.022 s
% 0.20/0.43  % (8804)Instructions burned: 38 (million)
% 0.20/0.43  % (8804)------------------------------
% 0.20/0.43  % (8804)------------------------------
% 0.20/0.43  % (8801)Refutation found. Thanks to Tanya!
% 0.20/0.43  % SZS status Theorem for theBenchmark
% 0.20/0.43  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.43  % (8801)------------------------------
% 0.20/0.43  % (8801)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.43  % (8801)Termination reason: Refutation
% 0.20/0.43  
% 0.20/0.43  % (8801)Memory used [KB]: 6780
% 0.20/0.43  % (8801)Time elapsed: 0.039 s
% 0.20/0.43  % (8801)Instructions burned: 60 (million)
% 0.20/0.43  % (8801)------------------------------
% 0.20/0.43  % (8801)------------------------------
% 0.20/0.43  % (8795)Success in time 0.08 s
%------------------------------------------------------------------------------