TSTP Solution File: ITP118^1 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP118^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n015.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 May 20 22:52:22 EDT 2024

% Result   : Theorem 4.65s 1.03s
% Output   : Refutation 4.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :  212
% Syntax   : Number of formulae    :  232 (  26 unt; 205 typ;   0 def)
%            Number of atoms       :  190 (  27 equ;   0 cnn)
%            Maximal formula atoms :    2 (   7 avg)
%            Number of connectives :   10 (   9   ~;   0   |;   0   &;   0   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :   17 (  16 usr)
%            Number of type conns  :  331 ( 330   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :  176 ( 174 usr;  18 con; 0-6 aty)
%            Number of variables   :   31 (   0   ^  14   !;   2   ?;  31   :)
%                                         (  15  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(type_def_7,type,
    sTfun: ( $tType * $tType ) > $tType ).

thf(type_def_8,type,
    numeral_num1: $tType ).

thf(type_def_9,type,
    finite2063899472l_num1: $tType ).

thf(type_def_10,type,
    finite1183840848l_num1: $tType ).

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

thf(type_def_12,type,
    finite964658038_int_n: $tType ).

thf(type_def_13,type,
    finite1489363574real_n: $tType ).

thf(type_def_14,type,
    finite463740460l_num1: $tType ).

thf(type_def_15,type,
    finite337957458num1_n: $tType ).

thf(type_def_16,type,
    finite121157254l_num1: $tType ).

thf(type_def_17,type,
    finite318270636al_n_n: $tType ).

thf(type_def_18,type,
    set_Fi1257234438l_num1: $tType ).

thf(type_def_19,type,
    set_Fi1058188332real_n: $tType ).

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

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

thf(func_def_0,type,
    finite463740460l_num1: $tType ).

thf(func_def_1,type,
    finite121157254l_num1: $tType ).

thf(func_def_2,type,
    finite337957458num1_n: $tType ).

thf(func_def_3,type,
    finite318270636al_n_n: $tType ).

thf(func_def_4,type,
    set_Fi1257234438l_num1: $tType ).

thf(func_def_5,type,
    finite1183840848l_num1: $tType ).

thf(func_def_6,type,
    finite2063899472l_num1: $tType ).

thf(func_def_7,type,
    set_Fi1058188332real_n: $tType ).

thf(func_def_8,type,
    finite1489363574real_n: $tType ).

thf(func_def_9,type,
    finite964658038_int_n: $tType ).

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

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

thf(func_def_12,type,
    numeral_num1: $tType ).

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

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

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

thf(func_def_16,type,
    archim1371465213g_real: real > int ).

thf(func_def_17,type,
    archim1031974863r_real: real > int ).

thf(func_def_18,type,
    finite627713486m1_int: numeral_num1 > int > finite2063899472l_num1 ).

thf(func_def_19,type,
    finite15144922381_real: numeral_num1 > real > finite1183840848l_num1 ).

thf(func_def_20,type,
    finite1888777460_n_int: n > int > finite964658038_int_n ).

thf(func_def_21,type,
    finite703491444n_real: n > real > finite1489363574real_n ).

thf(func_def_22,type,
    finite1470207077l_num1: int > finite2063899472l_num1 ).

thf(func_def_23,type,
    finite55766923_int_n: int > finite964658038_int_n ).

thf(func_def_24,type,
    finite1329045861l_num1: real > finite1183840848l_num1 ).

thf(func_def_25,type,
    finite667548811real_n: real > finite1489363574real_n ).

thf(func_def_26,type,
    finite1449546019l_num1: finite463740460l_num1 > numeral_num1 > finite1183840848l_num1 ).

thf(func_def_27,type,
    finite1639785033num1_n: finite337957458num1_n > n > finite1183840848l_num1 ).

thf(func_def_28,type,
    finite1503577981l_num1: finite121157254l_num1 > numeral_num1 > finite1489363574real_n ).

thf(func_def_29,type,
    finite625646243al_n_n: finite318270636al_n_n > n > finite1489363574real_n ).

thf(func_def_30,type,
    finite1800583751l_num1: finite2063899472l_num1 > numeral_num1 > int ).

thf(func_def_31,type,
    finite566214509_int_n: finite964658038_int_n > n > int ).

thf(func_def_32,type,
    finite1106245191l_num1: finite1183840848l_num1 > numeral_num1 > real ).

thf(func_def_33,type,
    finite772340589real_n: finite1489363574real_n > n > real ).

thf(func_def_34,type,
    finite1961675766l_num1: real > finite1183840848l_num1 > finite1183840848l_num1 ).

thf(func_def_35,type,
    finite2053577756real_n: real > finite1489363574real_n > finite1489363574real_n ).

thf(func_def_36,type,
    abs_ab948591917l_num1: finite1183840848l_num1 > finite1183840848l_num1 ).

thf(func_def_37,type,
    abs_ab1599551059real_n: finite1489363574real_n > finite1489363574real_n ).

thf(func_def_38,type,
    abs_abs_int: int > int ).

thf(func_def_39,type,
    abs_abs_real: real > real ).

thf(func_def_40,type,
    minus_779068585l_num1: finite2063899472l_num1 > finite2063899472l_num1 > finite2063899472l_num1 ).

thf(func_def_41,type,
    minus_1196255695_int_n: finite964658038_int_n > finite964658038_int_n > finite964658038_int_n ).

thf(func_def_42,type,
    minus_249161513l_num1: finite1183840848l_num1 > finite1183840848l_num1 > finite1183840848l_num1 ).

thf(func_def_43,type,
    minus_1037315151real_n: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).

thf(func_def_44,type,
    minus_minus_int: int > int > int ).

thf(func_def_45,type,
    minus_minus_real: real > real > real ).

thf(func_def_46,type,
    one_on601734293l_num1: finite2063899472l_num1 ).

thf(func_def_47,type,
    one_on1516019131_int_n: finite964658038_int_n ).

thf(func_def_48,type,
    one_on1961019669l_num1: finite1183840848l_num1 ).

thf(func_def_49,type,
    one_on1253059131real_n: finite1489363574real_n ).

thf(func_def_50,type,
    one_one_int: int ).

thf(func_def_51,type,
    one_one_Numeral_num1: numeral_num1 ).

thf(func_def_52,type,
    one_one_real: real ).

thf(func_def_53,type,
    if_Fin1570437642l_num1: $o > finite2063899472l_num1 > finite2063899472l_num1 > finite2063899472l_num1 ).

thf(func_def_54,type,
    if_Fin1767949360_int_n: $o > finite964658038_int_n > finite964658038_int_n > finite964658038_int_n ).

thf(func_def_55,type,
    if_Fin1668193290l_num1: $o > finite1183840848l_num1 > finite1183840848l_num1 > finite1183840848l_num1 ).

thf(func_def_56,type,
    if_Fin127821360real_n: $o > finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).

thf(func_def_57,type,
    ring_11529266783l_num1: set_Fi1257234438l_num1 ).

thf(func_def_58,type,
    ring_1723899781real_n: set_Fi1058188332real_n ).

thf(func_def_59,type,
    ring_1_Ints_int: set_int ).

thf(func_def_60,type,
    ring_1_Ints_real: set_real ).

thf(func_def_61,type,
    ring_1154201247l_num1: int > finite1183840848l_num1 ).

thf(func_def_62,type,
    ring_11737179077real_n: int > finite1489363574real_n ).

thf(func_def_63,type,
    ring_1_of_int_int: int > int ).

thf(func_def_64,type,
    ring_1_of_int_real: int > real ).

thf(func_def_65,type,
    minkow781993583real_n: finite2063899472l_num1 > finite121157254l_num1 ).

thf(func_def_66,type,
    minkow2063319845m1_int: finite2063899472l_num1 > finite2063899472l_num1 ).

thf(func_def_67,type,
    minkow19073400691_real: finite2063899472l_num1 > finite1183840848l_num1 ).

thf(func_def_68,type,
    minkow371489429real_n: finite964658038_int_n > finite318270636al_n_n ).

thf(func_def_69,type,
    minkow1468704075_n_int: finite964658038_int_n > finite964658038_int_n ).

thf(func_def_70,type,
    minkow1134813771n_real: finite964658038_int_n > finite1489363574real_n ).

thf(func_def_71,type,
    ord_le2035778724l_num1: finite1183840848l_num1 > finite1183840848l_num1 > $o ).

thf(func_def_72,type,
    ord_le1017090250real_n: finite1489363574real_n > finite1489363574real_n > $o ).

thf(func_def_73,type,
    ord_less_int: int > int > $o ).

thf(func_def_74,type,
    ord_less_real: real > real > $o ).

thf(func_def_75,type,
    ord_le1202326448l_num1: finite2063899472l_num1 > finite2063899472l_num1 > $o ).

thf(func_def_76,type,
    ord_le1908593622_int_n: finite964658038_int_n > finite964658038_int_n > $o ).

thf(func_def_77,type,
    ord_le1724070576l_num1: finite1183840848l_num1 > finite1183840848l_num1 > $o ).

thf(func_def_78,type,
    ord_le866583254real_n: finite1489363574real_n > finite1489363574real_n > $o ).

thf(func_def_79,type,
    ord_less_eq_int: int > int > $o ).

thf(func_def_80,type,
    ord_less_eq_real: real > real > $o ).

thf(func_def_81,type,
    real_V1974343547l_num1: finite463740460l_num1 > finite463740460l_num1 > real ).

thf(func_def_82,type,
    real_V845814485l_num1: finite121157254l_num1 > finite121157254l_num1 > real ).

thf(func_def_83,type,
    real_V488409631l_num1: finite1183840848l_num1 > finite1183840848l_num1 > real ).

thf(func_def_84,type,
    real_V783965509real_n: finite1489363574real_n > finite1489363574real_n > real ).

thf(func_def_85,type,
    real_V1934908667t_real: real > real > real ).

thf(func_def_86,type,
    real_V316032763l_num1: finite463740460l_num1 > real ).

thf(func_def_87,type,
    real_V1121707553num1_n: finite337957458num1_n > real ).

thf(func_def_88,type,
    real_V400292255l_num1: finite1183840848l_num1 > real ).

thf(func_def_89,type,
    real_V739724485real_n: finite1489363574real_n > real ).

thf(func_def_90,type,
    real_V646646907m_real: real > real ).

thf(func_def_91,type,
    collec321817931real_n: ( finite1489363574real_n > $o ) > set_Fi1058188332real_n ).

thf(func_def_92,type,
    collect_real: ( real > $o ) > set_real ).

thf(func_def_93,type,
    member1413569767l_num1: finite1183840848l_num1 > set_Fi1257234438l_num1 > $o ).

thf(func_def_94,type,
    member1352538125real_n: finite1489363574real_n > set_Fi1058188332real_n > $o ).

thf(func_def_95,type,
    member_int: int > set_int > $o ).

thf(func_def_96,type,
    member_real: real > set_real > $o ).

thf(func_def_97,type,
    a: set_Fi1058188332real_n ).

thf(func_def_98,type,
    i: n ).

thf(func_def_99,type,
    m: int ).

thf(func_def_100,type,
    x: finite1489363574real_n ).

thf(func_def_101,type,
    y: finite1489363574real_n ).

thf(func_def_105,type,
    vPI: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_106,type,
    iCOMB: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_107,type,
    cCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).

thf(func_def_108,type,
    vSIGMA: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_109,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_110,type,
    vAND: $o > $o > $o ).

thf(func_def_111,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_112,type,
    sCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_113,type,
    vNOT: $o > $o ).

thf(func_def_114,type,
    vOR: $o > $o > $o ).

thf(func_def_115,type,
    vIMP: $o > $o > $o ).

thf(func_def_116,type,
    sP0: set_real > $o ).

thf(func_def_117,type,
    sP1: int > int > int > $o ).

thf(func_def_118,type,
    sP2: int > int > int > $o ).

thf(func_def_119,type,
    sP3: int > int > int > $o ).

thf(func_def_120,type,
    sP4: int > int > int > $o ).

thf(func_def_121,type,
    sP5: real > real > real > $o ).

thf(func_def_122,type,
    sP6: real > real > real > $o ).

thf(func_def_123,type,
    sP7: real > real > real > $o ).

thf(func_def_124,type,
    sP8: real > real > real > $o ).

thf(func_def_125,type,
    sP9: int > ( int > $o ) > int > $o ).

thf(func_def_126,type,
    sP10: real > ( real > $o ) > real > $o ).

thf(func_def_127,type,
    sK11: int ).

thf(func_def_128,type,
    sK12: set_real > real ).

thf(func_def_129,type,
    sK13: real > set_real > real ).

thf(func_def_130,type,
    sK14: real > set_real > real ).

thf(func_def_131,type,
    sK15: int > int ).

thf(func_def_132,type,
    sK16: finite1489363574real_n > int ).

thf(func_def_133,type,
    sK17: real > int ).

thf(func_def_134,type,
    sK18: real > int ).

thf(func_def_135,type,
    sK19: real > int ).

thf(func_def_136,type,
    sK20: real > int ).

thf(func_def_137,type,
    sK21: finite1489363574real_n > finite337957458num1_n > n ).

thf(func_def_138,type,
    sK22: finite1183840848l_num1 > finite463740460l_num1 > numeral_num1 ).

thf(func_def_139,type,
    sK23: finite337957458num1_n > finite1489363574real_n > n ).

thf(func_def_140,type,
    sK24: finite1489363574real_n > finite1489363574real_n > n ).

thf(func_def_141,type,
    sK25: finite463740460l_num1 > finite1183840848l_num1 > numeral_num1 ).

thf(func_def_142,type,
    sK26: finite1183840848l_num1 > finite1183840848l_num1 > numeral_num1 ).

thf(func_def_143,type,
    sK27: ( int > $o ) > int ).

thf(func_def_144,type,
    sK28: ( finite1489363574real_n > $o ) > int ).

thf(func_def_145,type,
    sK29: ( real > $o ) > int ).

thf(func_def_146,type,
    sK30: ( int > int > $o ) > int ).

thf(func_def_147,type,
    sK31: ( int > int > $o ) > int ).

thf(func_def_148,type,
    sK32: ( int > int > $o ) > int ).

thf(func_def_149,type,
    sK33: ( int > int > $o ) > int ).

thf(func_def_150,type,
    sK34: ( real > real > $o ) > real ).

thf(func_def_151,type,
    sK35: ( real > real > $o ) > real ).

thf(func_def_152,type,
    sK36: ( real > real > $o ) > real ).

thf(func_def_153,type,
    sK37: ( real > real > $o ) > real ).

thf(func_def_154,type,
    sK38: int > int > ( int > $o ) > int ).

thf(func_def_155,type,
    sK39: ( int > $o ) > int > int > int ).

thf(func_def_156,type,
    sK40: ( int > $o ) > int > int ).

thf(func_def_157,type,
    sK41: ( int > $o ) > int > int ).

thf(func_def_158,type,
    sK42: real > real > ( real > $o ) > real ).

thf(func_def_159,type,
    sK43: ( real > $o ) > real > real > real ).

thf(func_def_160,type,
    sK44: ( int > int ) > int ).

thf(func_def_161,type,
    sK45: ( int > int ) > int ).

thf(func_def_162,type,
    sK46: ( int > real ) > int ).

thf(func_def_163,type,
    sK47: ( int > real ) > int ).

thf(func_def_164,type,
    sK48: ( real > int ) > real ).

thf(func_def_165,type,
    sK49: ( real > int ) > real ).

thf(func_def_166,type,
    sK50: ( real > real ) > real ).

thf(func_def_167,type,
    sK51: ( real > real ) > real ).

thf(func_def_168,type,
    sK52: ( int > int ) > int ).

thf(func_def_169,type,
    sK53: ( int > int ) > int ).

thf(func_def_170,type,
    sK54: ( int > real ) > int ).

thf(func_def_171,type,
    sK55: ( int > real ) > int ).

thf(func_def_172,type,
    sK56: ( real > int ) > real ).

thf(func_def_173,type,
    sK57: ( real > int ) > real ).

thf(func_def_174,type,
    sK58: ( real > real ) > real ).

thf(func_def_175,type,
    sK59: ( real > real ) > real ).

thf(func_def_177,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_178,type,
    sK61: set_real > real > real > real ).

thf(func_def_179,type,
    sK62: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).

thf(func_def_180,type,
    sK63: set_Fi1257234438l_num1 > finite1183840848l_num1 > finite1183840848l_num1 > finite1183840848l_num1 ).

thf(func_def_181,type,
    sK64: real > ( int > $o ) > int ).

thf(func_def_182,type,
    sK65: ( numeral_num1 > real > $o ) > numeral_num1 ).

thf(func_def_183,type,
    sK66: ( numeral_num1 > real > $o ) > finite1183840848l_num1 ).

thf(func_def_184,type,
    sK67: ( n > real > $o ) > n ).

thf(func_def_185,type,
    sK68: ( n > real > $o ) > finite1489363574real_n ).

thf(func_def_186,type,
    sK69: ( numeral_num1 > int > $o ) > numeral_num1 ).

thf(func_def_187,type,
    sK70: ( numeral_num1 > int > $o ) > finite2063899472l_num1 ).

thf(func_def_188,type,
    sK71: ( n > int > $o ) > n ).

thf(func_def_189,type,
    sK72: ( n > int > $o ) > finite964658038_int_n ).

thf(func_def_190,type,
    sK73: real > int ).

thf(func_def_191,type,
    sK74: real > int ).

thf(f14501,plain,
    $false,
    inference(trivial_inequality_removal,[],[f14500]) ).

thf(f14500,plain,
    vAPP(real,real,real_V646646907m_real,vAPP(int,real,ring_1_of_int_real,sK11)) != vAPP(real,real,real_V646646907m_real,vAPP(int,real,ring_1_of_int_real,sK11)),
    inference(backward_demodulation,[],[f1984,f14475]) ).

thf(f14475,plain,
    vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,vAPP(finite1489363574real_n,finite1489363574real_n,vAPP(finite1489363574real_n,sTfun(finite1489363574real_n,finite1489363574real_n),minus_1037315151real_n,x),y)),i) = vAPP(int,real,ring_1_of_int_real,sK11),
    inference(superposition,[],[f1538,f1315]) ).

thf(f1315,plain,
    vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,x),i)),vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,y),i)) = vAPP(int,real,ring_1_of_int_real,sK11),
    inference(cnf_transformation,[],[f1175]) ).

thf(f1175,plain,
    vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,x),i)),vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,y),i)) = vAPP(int,real,ring_1_of_int_real,sK11),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f975,f1174]) ).

thf(f1174,plain,
    ( ? [X0: int] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,x),i)),vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,y),i)) = vAPP(int,real,ring_1_of_int_real,X0) )
   => ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,x),i)),vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,y),i)) = vAPP(int,real,ring_1_of_int_real,sK11) ) ),
    introduced(choice_axiom,[]) ).

thf(f975,plain,
    ? [X0: int] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,x),i)),vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,y),i)) = vAPP(int,real,ring_1_of_int_real,X0) ),
    inference(ennf_transformation,[],[f4]) ).

thf(f4,axiom,
    ~ ! [X0: int] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,x),i)),vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,y),i)) != vAPP(int,real,ring_1_of_int_real,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_Areal__of__int_Am_A_061_Ax_A_E_Ai_A_N_Ay_A_E_Ai_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).

thf(f1538,plain,
    ! [X2: n,X0: finite1489363574real_n,X1: finite1489363574real_n] : ( vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,vAPP(finite1489363574real_n,finite1489363574real_n,vAPP(finite1489363574real_n,sTfun(finite1489363574real_n,finite1489363574real_n),minus_1037315151real_n,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,X0),X2)),vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,X1),X2)) ),
    inference(cnf_transformation,[],[f948]) ).

thf(f948,plain,
    ! [X0: finite1489363574real_n,X1: finite1489363574real_n,X2: n] : ( vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,vAPP(finite1489363574real_n,finite1489363574real_n,vAPP(finite1489363574real_n,sTfun(finite1489363574real_n,finite1489363574real_n),minus_1037315151real_n,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,X0),X2)),vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,X1),X2)) ),
    inference(rectify,[],[f7]) ).

thf(f7,axiom,
    ! [X1: finite1489363574real_n,X2: finite1489363574real_n,X3: n] : ( vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,vAPP(finite1489363574real_n,finite1489363574real_n,vAPP(finite1489363574real_n,sTfun(finite1489363574real_n,finite1489363574real_n),minus_1037315151real_n,X1),X2)),X3) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,X1),X3)),vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,X2),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_vector__minus__component) ).

thf(f1984,plain,
    vAPP(real,real,real_V646646907m_real,vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,vAPP(finite1489363574real_n,finite1489363574real_n,vAPP(finite1489363574real_n,sTfun(finite1489363574real_n,finite1489363574real_n),minus_1037315151real_n,x),y)),i)) != vAPP(real,real,real_V646646907m_real,vAPP(int,real,ring_1_of_int_real,sK11)),
    inference(forward_demodulation,[],[f1983,f1977]) ).

thf(f1977,plain,
    vAPP(int,real,ring_1_of_int_real,m) = vAPP(int,real,ring_1_of_int_real,sK11),
    inference(backward_demodulation,[],[f1282,f1315]) ).

thf(f1282,plain,
    vAPP(int,real,ring_1_of_int_real,m) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,x),i)),vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,y),i)),
    inference(cnf_transformation,[],[f3]) ).

thf(f3,axiom,
    vAPP(int,real,ring_1_of_int_real,m) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,x),i)),vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,y),i)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_m) ).

thf(f1983,plain,
    vAPP(real,real,real_V646646907m_real,vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,vAPP(finite1489363574real_n,finite1489363574real_n,vAPP(finite1489363574real_n,sTfun(finite1489363574real_n,finite1489363574real_n),minus_1037315151real_n,x),y)),i)) != vAPP(real,real,real_V646646907m_real,vAPP(int,real,ring_1_of_int_real,m)),
    inference(backward_demodulation,[],[f1966,f1982]) ).

thf(f1982,plain,
    ! [X0: int] : ( vAPP(int,real,ring_1_of_int_real,vAPP(int,int,abs_abs_int,X0)) = vAPP(real,real,real_V646646907m_real,vAPP(int,real,ring_1_of_int_real,X0)) ),
    inference(forward_demodulation,[],[f1334,f1271]) ).

thf(f1271,plain,
    abs_abs_real = real_V646646907m_real,
    inference(cnf_transformation,[],[f157]) ).

thf(f157,axiom,
    abs_abs_real = real_V646646907m_real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_real__norm__def) ).

thf(f1334,plain,
    ! [X0: int] : ( vAPP(int,real,ring_1_of_int_real,vAPP(int,int,abs_abs_int,X0)) = vAPP(real,real,abs_abs_real,vAPP(int,real,ring_1_of_int_real,X0)) ),
    inference(cnf_transformation,[],[f871]) ).

thf(f871,plain,
    ! [X0: int] : ( vAPP(int,real,ring_1_of_int_real,vAPP(int,int,abs_abs_int,X0)) = vAPP(real,real,abs_abs_real,vAPP(int,real,ring_1_of_int_real,X0)) ),
    inference(rectify,[],[f10]) ).

thf(f10,axiom,
    ! [X1: int] : ( vAPP(int,real,ring_1_of_int_real,vAPP(int,int,abs_abs_int,X1)) = vAPP(real,real,abs_abs_real,vAPP(int,real,ring_1_of_int_real,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_of__int__abs) ).

thf(f1966,plain,
    vAPP(int,real,ring_1_of_int_real,vAPP(int,int,abs_abs_int,m)) != vAPP(real,real,real_V646646907m_real,vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,vAPP(finite1489363574real_n,finite1489363574real_n,vAPP(finite1489363574real_n,sTfun(finite1489363574real_n,finite1489363574real_n),minus_1037315151real_n,x),y)),i)),
    inference(backward_demodulation,[],[f1270,f1271]) ).

thf(f1270,plain,
    vAPP(int,real,ring_1_of_int_real,vAPP(int,int,abs_abs_int,m)) != vAPP(real,real,abs_abs_real,vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,vAPP(finite1489363574real_n,finite1489363574real_n,vAPP(finite1489363574real_n,sTfun(finite1489363574real_n,finite1489363574real_n),minus_1037315151real_n,x),y)),i)),
    inference(cnf_transformation,[],[f852]) ).

thf(f852,plain,
    vAPP(int,real,ring_1_of_int_real,vAPP(int,int,abs_abs_int,m)) != vAPP(real,real,abs_abs_real,vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,vAPP(finite1489363574real_n,finite1489363574real_n,vAPP(finite1489363574real_n,sTfun(finite1489363574real_n,finite1489363574real_n),minus_1037315151real_n,x),y)),i)),
    inference(flattening,[],[f365]) ).

thf(f365,negated_conjecture,
    vAPP(int,real,ring_1_of_int_real,vAPP(int,int,abs_abs_int,m)) != vAPP(real,real,abs_abs_real,vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,vAPP(finite1489363574real_n,finite1489363574real_n,vAPP(finite1489363574real_n,sTfun(finite1489363574real_n,finite1489363574real_n),minus_1037315151real_n,x),y)),i)),
    inference(negated_conjecture,[],[f364]) ).

thf(f364,conjecture,
    vAPP(int,real,ring_1_of_int_real,vAPP(int,int,abs_abs_int,m)) = vAPP(real,real,abs_abs_real,vAPP(n,real,vAPP(finite1489363574real_n,sTfun(n,real),finite772340589real_n,vAPP(finite1489363574real_n,finite1489363574real_n,vAPP(finite1489363574real_n,sTfun(finite1489363574real_n,finite1489363574real_n),minus_1037315151real_n,x),y)),i)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : ITP118^1 : TPTP v8.2.0. Released v7.5.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n015.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sat May 18 16:20:53 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (23668)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.39  % (23671)WARNING: value z3 for option sas not known
% 0.20/0.39  % (23675)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.20/0.39  % (23674)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.20/0.39  % (23673)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.20/0.39  % (23672)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.39  % (23670)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.39  % (23671)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.20/0.39  % (23669)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.42  % (23675)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.43  % Exception at run slice level
% 0.20/0.43  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.44  % Exception at run slice level
% 0.20/0.44  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.44  % Exception at run slice level
% 0.20/0.44  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.45  % (23677)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.20/0.45  % (23676)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.46  % (23678)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.20/0.47  % (23677)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.48  % (23676)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.49  % Exception at run slice level
% 0.20/0.49  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.51  % (23679)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 4.21/1.02  % (23678)First to succeed.
% 4.65/1.02  % (23678)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-23668"
% 4.65/1.03  % (23678)Refutation found. Thanks to Tanya!
% 4.65/1.03  % SZS status Theorem for theBenchmark
% 4.65/1.03  % SZS output start Proof for theBenchmark
% See solution above
% 4.65/1.03  % (23678)------------------------------
% 4.65/1.03  % (23678)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 4.65/1.03  % (23678)Termination reason: Refutation
% 4.65/1.03  
% 4.65/1.03  % (23678)Memory used [KB]: 6570
% 4.65/1.03  % (23678)Time elapsed: 0.565 s
% 4.65/1.03  % (23678)Instructions burned: 1495 (million)
% 4.65/1.03  % (23668)Success in time 0.667 s
%------------------------------------------------------------------------------