TSTP Solution File: ITP114^2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP114^2 : 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 : n025.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 22:52:21 EDT 2024

% Result   : Theorem 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :  535
% Syntax   : Number of formulae    : 1235 ( 535 unt; 218 typ;   0 def)
%            Number of atoms       : 4008 (1036 equ;   0 cnn)
%            Maximal formula atoms :    4 (   3 avg)
%            Number of connectives : 1051 ( 372   ~; 366   |;  25   &;   0   @)
%                                         ( 161 <=>; 127  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    7 (   6 usr)
%            Number of type conns  :  384 ( 383   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :  376 ( 373 usr; 166 con; 0-6 aty)
%            Number of variables   :  742 (   0   ^ 610   !;  33   ?; 742   :)
%                                         (  99  !>;   0  ?*;   0  @-;   0  @+)

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

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

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

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

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

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

thf(type_def_11,type,
    set: $tType > $tType ).

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

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

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

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

thf(func_def_3,type,
    set: $tType > $tType ).

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

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

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

thf(func_def_7,type,
    type: 
      !>[X0: $tType] : $o ).

thf(func_def_8,type,
    zero: 
      !>[X0: $tType] : $o ).

thf(func_def_9,type,
    numeral: 
      !>[X0: $tType] : $o ).

thf(func_def_10,type,
    uminus: 
      !>[X0: $tType] : $o ).

thf(func_def_11,type,
    ord: 
      !>[X0: $tType] : $o ).

thf(func_def_12,type,
    ring_char_0: 
      !>[X0: $tType] : $o ).

thf(func_def_13,type,
    neg_numeral: 
      !>[X0: $tType] : $o ).

thf(func_def_14,type,
    order: 
      !>[X0: $tType] : $o ).

thf(func_def_15,type,
    group_add: 
      !>[X0: $tType] : $o ).

thf(func_def_16,type,
    linorder: 
      !>[X0: $tType] : $o ).

thf(func_def_17,type,
    preorder: 
      !>[X0: $tType] : $o ).

thf(func_def_18,type,
    semiring_char_0: 
      !>[X0: $tType] : $o ).

thf(func_def_19,type,
    linordered_idom: 
      !>[X0: $tType] : $o ).

thf(func_def_20,type,
    linordered_field: 
      !>[X0: $tType] : $o ).

thf(func_def_21,type,
    boolean_algebra: 
      !>[X0: $tType] : $o ).

thf(func_def_22,type,
    ordered_ab_group_add: 
      !>[X0: $tType] : $o ).

thf(func_def_23,type,
    linord219039673up_add: 
      !>[X0: $tType] : $o ).

thf(func_def_24,type,
    ordere142940540dd_abs: 
      !>[X0: $tType] : $o ).

thf(func_def_25,type,
    real_V2090557954_space: 
      !>[X0: $tType] : $o ).

thf(func_def_26,type,
    linord1659791738miring: 
      !>[X0: $tType] : $o ).

thf(func_def_27,type,
    topolo259154727pology: 
      !>[X0: $tType] : $o ).

thf(func_def_28,type,
    topolo503727757_space: 
      !>[X0: $tType] : $o ).

thf(func_def_29,type,
    canoni770627133id_add: 
      !>[X0: $tType] : $o ).

thf(func_def_30,type,
    extended_enat2: nat > extended_enat ).

thf(func_def_31,type,
    extended_case_enat: 
      !>[X0: $tType] : ( ( nat > X0 ) > X0 > extended_enat > X0 ) ).

thf(func_def_32,type,
    extended_rec_enat: 
      !>[X0: $tType] : ( ( nat > X0 ) > X0 > extended_enat > X0 ) ).

thf(func_def_33,type,
    extend1396239628finity: 
      !>[X0: $tType] : X0 ).

thf(func_def_34,type,
    extended_the_enat: extended_enat > nat ).

thf(func_def_35,type,
    extended_MInfty: extended_ereal ).

thf(func_def_36,type,
    extended_PInfty: extended_ereal ).

thf(func_def_37,type,
    extended_ereal2: real > extended_ereal ).

thf(func_def_38,type,
    extended_size_ereal: extended_ereal > nat ).

thf(func_def_39,type,
    extend1771934483f_enat: extended_enat > extended_ereal ).

thf(func_def_40,type,
    extend1716541707_ereal: extended_ereal > real ).

thf(func_def_41,type,
    abs_abs: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_42,type,
    uminus_uminus: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_43,type,
    zero_zero: 
      !>[X0: $tType] : X0 ).

thf(func_def_44,type,
    lower_107104146le_lsc: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > $o ) ).

thf(func_def_45,type,
    lower_582600101lsc_at: 
      !>[X0: $tType,X1: $tType] : ( X0 > ( X0 > X1 ) > $o ) ).

thf(func_def_46,type,
    lower_1879122655c_hull: 
      !>[X0: $tType] : ( ( X0 > extended_ereal ) > X0 > extended_ereal ) ).

thf(func_def_47,type,
    neg_numeral_dbl: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_48,type,
    neg_numeral_sub: 
      !>[X0: $tType] : ( num > num > X0 ) ).

thf(func_def_49,type,
    numeral_numeral: 
      !>[X0: $tType] : ( num > X0 ) ).

thf(func_def_50,type,
    ord_less_eq: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_51,type,
    order_Greatest: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_52,type,
    order_antimono: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > $o ) ).

thf(func_def_53,type,
    order_strict_mono: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > $o ) ).

thf(func_def_54,type,
    divide_divide: 
      !>[X0: $tType] : ( X0 > X0 > X0 ) ).

thf(func_def_55,type,
    member: 
      !>[X0: $tType] : ( X0 > set(X0) > $o ) ).

thf(func_def_56,type,
    f: a > extended_ereal ).

thf(func_def_57,type,
    g: a > extended_ereal ).

thf(func_def_58,type,
    x: a ).

thf(func_def_62,type,
    vPI: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_63,type,
    vAND: $o > $o > $o ).

thf(func_def_64,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_65,type,
    iCOMB: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_66,type,
    cCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).

thf(func_def_67,type,
    sCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_68,type,
    vSIGMA: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_69,type,
    vOR: $o > $o > $o ).

thf(func_def_70,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_71,type,
    vNOT: $o > $o ).

thf(func_def_72,type,
    vIMP: $o > $o > $o ).

thf(func_def_73,type,
    sP0: 
      !>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).

thf(func_def_74,type,
    sP1: 
      !>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).

thf(func_def_75,type,
    sP2: 
      !>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).

thf(func_def_76,type,
    sP3: 
      !>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).

thf(func_def_77,type,
    sP4: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).

thf(func_def_78,type,
    sP5: extended_ereal > real > $o ).

thf(func_def_79,type,
    sP6: extended_ereal > extended_ereal > $o ).

thf(func_def_80,type,
    sP7: extended_ereal > extended_ereal > $o ).

thf(func_def_81,type,
    sP8: extended_ereal > extended_ereal > $o ).

thf(func_def_82,type,
    sP9: extended_ereal > extended_ereal > $o ).

thf(func_def_83,type,
    sP10: extended_ereal > extended_ereal > $o ).

thf(func_def_84,type,
    sP11: extended_ereal > extended_ereal > $o ).

thf(func_def_85,type,
    sP12: extended_ereal > extended_ereal > $o ).

thf(func_def_86,type,
    sP13: extended_ereal > extended_ereal > $o ).

thf(func_def_87,type,
    sP14: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_88,type,
    sP15: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_89,type,
    sP16: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_90,type,
    sP17: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_91,type,
    sP18: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_92,type,
    sP19: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_93,type,
    sP20: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_94,type,
    sP21: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_95,type,
    sP22: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_96,type,
    sP23: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_97,type,
    sP24: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_98,type,
    sP25: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_99,type,
    sP26: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_100,type,
    sP27: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_101,type,
    sP28: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_102,type,
    sP29: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_103,type,
    sP30: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_104,type,
    sP31: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_105,type,
    sP32: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_106,type,
    sP33: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_107,type,
    sP34: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_108,type,
    sP35: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_109,type,
    sP36: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_110,type,
    sP37: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_111,type,
    sP38: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_112,type,
    sP39: extended_ereal > extended_ereal > extended_ereal > $o ).

thf(func_def_113,type,
    sK40: extended_ereal > real ).

thf(func_def_114,type,
    sK41: extended_ereal > real ).

thf(func_def_115,type,
    sK42: extended_ereal > real ).

thf(func_def_116,type,
    sK43: extended_ereal > real ).

thf(func_def_117,type,
    sK44: extended_ereal > real ).

thf(func_def_118,type,
    sK45: extended_ereal > real ).

thf(func_def_119,type,
    sK46: extended_ereal > real ).

thf(func_def_120,type,
    sK47: extended_ereal > real ).

thf(func_def_121,type,
    sK48: 
      !>[X0: $tType] : ( ( X0 > extended_ereal ) > ( X0 > extended_ereal ) > X0 ) ).

thf(func_def_122,type,
    sK49: 
      !>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).

thf(func_def_123,type,
    sK50: 
      !>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).

thf(func_def_124,type,
    sK51: 
      !>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).

thf(func_def_125,type,
    sK52: 
      !>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).

thf(func_def_126,type,
    sK53: 
      !>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 ) ).

thf(func_def_127,type,
    sK54: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_128,type,
    sK55: 
      !>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 ) ).

thf(func_def_129,type,
    sK56: set(extended_ereal) > extended_ereal ).

thf(func_def_130,type,
    sK57: extended_ereal > set(extended_ereal) > extended_ereal ).

thf(func_def_131,type,
    sK58: set(extended_ereal) > extended_ereal ).

thf(func_def_132,type,
    sK59: extended_ereal > set(extended_ereal) > extended_ereal ).

thf(func_def_133,type,
    sK60: extended_ereal > real > real ).

thf(func_def_134,type,
    sK61: extended_ereal > extended_ereal > real ).

thf(func_def_135,type,
    sK62: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_136,type,
    sK63: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_137,type,
    sK64: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).

thf(func_def_138,type,
    sK65: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).

thf(func_def_139,type,
    sK66: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_140,type,
    sK67: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_141,type,
    sK68: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).

thf(func_def_142,type,
    sK69: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).

thf(func_def_143,type,
    sK70: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_144,type,
    sK71: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_145,type,
    sK72: extended_ereal > real ).

thf(func_def_146,type,
    sK73: extended_ereal > real ).

thf(func_def_147,type,
    sK74: extended_ereal > real ).

thf(func_def_148,type,
    sK75: extended_ereal > real ).

thf(func_def_149,type,
    sK76: extended_ereal > real ).

thf(func_def_150,type,
    sK77: extended_ereal > real ).

thf(func_def_151,type,
    sK78: extended_ereal > extended_ereal > real ).

thf(func_def_152,type,
    sK79: ( extended_ereal > $o ) > real ).

thf(func_def_153,type,
    sK80: ( extended_ereal > $o ) > real ).

thf(func_def_154,type,
    sK81: ( extended_ereal > $o ) > real ).

thf(func_def_155,type,
    sK82: ( extended_ereal > $o ) > real ).

thf(func_def_156,type,
    sK83: nat > ( nat > $o ) > nat ).

thf(func_def_157,type,
    sK84: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).

thf(func_def_158,type,
    sK85: extended_enat > nat ).

thf(func_def_159,type,
    sK86: extended_ereal > real ).

thf(func_def_160,type,
    sK87: extended_ereal > real ).

thf(func_def_161,type,
    sK88: extended_ereal > real ).

thf(func_def_162,type,
    sK89: extended_ereal > real ).

thf(func_def_163,type,
    sK90: extended_ereal > real ).

thf(func_def_164,type,
    sK91: extended_ereal > real ).

thf(func_def_165,type,
    sK92: extended_ereal > real ).

thf(func_def_166,type,
    sK93: extended_ereal > real ).

thf(func_def_167,type,
    sK94: extended_ereal > real ).

thf(func_def_168,type,
    sK95: extended_ereal > real ).

thf(func_def_169,type,
    sK96: extended_ereal > real ).

thf(func_def_170,type,
    sK97: extended_ereal > real ).

thf(func_def_171,type,
    sK98: extended_ereal > real ).

thf(func_def_172,type,
    sK99: extended_ereal > real ).

thf(func_def_173,type,
    sK100: extended_ereal > real ).

thf(func_def_174,type,
    sK101: extended_ereal > real ).

thf(func_def_175,type,
    sK102: extended_ereal > real ).

thf(func_def_176,type,
    sK103: extended_ereal > real ).

thf(func_def_177,type,
    sK104: extended_ereal > real ).

thf(func_def_178,type,
    sK105: extended_ereal > real ).

thf(func_def_179,type,
    sK106: extended_ereal > real ).

thf(func_def_180,type,
    sK107: extended_ereal > real ).

thf(func_def_181,type,
    sK108: extended_ereal > real ).

thf(func_def_182,type,
    sK109: extended_ereal > real ).

thf(func_def_183,type,
    sK110: extended_ereal > real ).

thf(func_def_184,type,
    sK111: extended_ereal > real ).

thf(func_def_185,type,
    sK112: extended_ereal > real ).

thf(func_def_186,type,
    sK113: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_187,type,
    sK114: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_188,type,
    sK115: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).

thf(func_def_189,type,
    sK116: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).

thf(func_def_190,type,
    sK117: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_191,type,
    sK118: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_192,type,
    sK119: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_193,type,
    sK120: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_194,type,
    sK121: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).

thf(func_def_195,type,
    sK122: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).

thf(func_def_196,type,
    sK123: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_197,type,
    sK124: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_198,type,
    sK125: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_199,type,
    sK126: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_200,type,
    sK127: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_201,type,
    sK128: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_202,type,
    sK129: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_203,type,
    sK130: ( extended_ereal > extended_ereal > $o ) > real ).

thf(func_def_204,type,
    sK131: ( nat > $o ) > nat ).

thf(func_def_205,type,
    sK132: nat > ( nat > $o ) > nat ).

thf(func_def_206,type,
    sK133: nat > ( nat > $o ) > nat ).

thf(func_def_207,type,
    sK134: nat > ( nat > $o ) > nat ).

thf(func_def_208,type,
    sK135: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).

thf(func_def_210,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_211,type,
    sK137: 
      !>[X0: $tType] : ( ( X0 > extended_ereal ) > ( X0 > extended_ereal ) > X0 > extended_ereal ) ).

thf(func_def_212,type,
    sK138: 
      !>[X0: $tType] : ( ( X0 > extended_ereal ) > ( X0 > extended_ereal ) > X0 ) ).

thf(func_def_213,type,
    sK139: extended_ereal > real ).

thf(f3523,plain,
    $false,
    inference(avatar_sat_refutation,[],[f2481,f2486,f2491,f2496,f2501,f2506,f2511,f2516,f2521,f2526,f2531,f2536,f2541,f2546,f2551,f2556,f2561,f2566,f2571,f2576,f2581,f2586,f2591,f2596,f2601,f2606,f2611,f2616,f2621,f2626,f2631,f2636,f2641,f2646,f2651,f2656,f2661,f2666,f2671,f2676,f2681,f2686,f2691,f2696,f2701,f2706,f2711,f2716,f2721,f2726,f2731,f2736,f2741,f2746,f2751,f2756,f2761,f2766,f2771,f2776,f2781,f2786,f2791,f2796,f2801,f2806,f2811,f2816,f2821,f2826,f2830,f2864,f2868,f2873,f2878,f2883,f2888,f2893,f2897,f2901,f2906,f2911,f2919,f2924,f2941,f2946,f2951,f2956,f2961,f2968,f2973,f2978,f2982,f2986,f2990,f2994,f2998,f3002,f3072,f3076,f3084,f3089,f3093,f3101,f3105,f3109,f3113,f3118,f3122,f3126,f3142,f3146,f3150,f3154,f3159,f3165,f3169,f3173,f3177,f3181,f3185,f3189,f3193,f3197,f3201,f3209,f3225,f3229,f3233,f3237,f3241,f3245,f3249,f3253,f3257,f3261,f3287,f3305,f3309,f3313,f3317,f3330,f3362,f3366,f3370,f3374,f3378,f3382,f3396,f3417,f3421,f3425,f3449,f3453,f3457,f3476,f3480,f3484,f3488,f3492,f3501,f3518,f3520,f3522]) ).

thf(f3522,plain,
    ( ~ spl136_74
    | ~ spl136_160 ),
    inference(avatar_contradiction_clause,[],[f3521]) ).

thf(f3521,plain,
    ( $false
    | ~ spl136_74
    | ~ spl136_160 ),
    inference(trivial_inequality_removal,[],[f3514]) ).

thf(f3514,plain,
    ( ( $true = $false )
    | ~ spl136_74
    | ~ spl136_160 ),
    inference(superposition,[],[f3491,f2872]) ).

thf(f2872,plain,
    ( ( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)) = $false )
    | ~ spl136_74 ),
    inference(avatar_component_clause,[],[f2870]) ).

thf(f2870,plain,
    ( spl136_74
  <=> ( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)) = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_74])]) ).

thf(f3491,plain,
    ( ! [X0: a] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,X0)),vAPP(a,extended_ereal,f,X0)) )
    | ~ spl136_160 ),
    inference(avatar_component_clause,[],[f3490]) ).

thf(f3490,plain,
    ( spl136_160
  <=> ! [X0: a] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,X0)),vAPP(a,extended_ereal,f,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_160])]) ).

thf(f3520,plain,
    ( ~ spl136_74
    | ~ spl136_160 ),
    inference(avatar_contradiction_clause,[],[f3519]) ).

thf(f3519,plain,
    ( $false
    | ~ spl136_74
    | ~ spl136_160 ),
    inference(trivial_inequality_removal,[],[f3515]) ).

thf(f3515,plain,
    ( ( $true = $false )
    | ~ spl136_74
    | ~ spl136_160 ),
    inference(superposition,[],[f2872,f3491]) ).

thf(f3518,plain,
    ( spl136_70
    | ~ spl136_160 ),
    inference(avatar_contradiction_clause,[],[f3517]) ).

thf(f3517,plain,
    ( $false
    | spl136_70
    | ~ spl136_160 ),
    inference(trivial_inequality_removal,[],[f3516]) ).

thf(f3516,plain,
    ( ( $true != $true )
    | spl136_70
    | ~ spl136_160 ),
    inference(superposition,[],[f2825,f3491]) ).

thf(f2825,plain,
    ( ( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)) != $true )
    | spl136_70 ),
    inference(avatar_component_clause,[],[f2823]) ).

thf(f2823,plain,
    ( spl136_70
  <=> ( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_70])]) ).

thf(f3501,plain,
    ( spl136_161
    | ~ spl136_38
    | ~ spl136_95 ),
    inference(avatar_split_clause,[],[f3025,f2988,f2663,f3499]) ).

thf(f3499,plain,
    ( spl136_161
  <=> ! [X0: $tType] : ( $true = topolo503727757_space(sTfun(X0,nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_161])]) ).

thf(f2663,plain,
    ( spl136_38
  <=> ( topolo503727757_space(nat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_38])]) ).

thf(f2988,plain,
    ( spl136_95
  <=> ! [X1: $tType,X0: $tType] :
        ( ( $true = topolo503727757_space(sTfun(X0,X1)) )
        | ( $true != topolo503727757_space(X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_95])]) ).

thf(f3025,plain,
    ( ! [X0: $tType] : ( $true = topolo503727757_space(sTfun(X0,nat)) )
    | ~ spl136_38
    | ~ spl136_95 ),
    inference(trivial_inequality_removal,[],[f3016]) ).

thf(f3016,plain,
    ( ! [X0: $tType] :
        ( ( $true != $true )
        | ( $true = topolo503727757_space(sTfun(X0,nat)) ) )
    | ~ spl136_38
    | ~ spl136_95 ),
    inference(superposition,[],[f2989,f2665]) ).

thf(f2665,plain,
    ( ( topolo503727757_space(nat) = $true )
    | ~ spl136_38 ),
    inference(avatar_component_clause,[],[f2663]) ).

thf(f2989,plain,
    ( ! [X1: $tType,X0: $tType] :
        ( ( $true != topolo503727757_space(X1) )
        | ( $true = topolo503727757_space(sTfun(X0,X1)) ) )
    | ~ spl136_95 ),
    inference(avatar_component_clause,[],[f2988]) ).

thf(f3492,plain,
    spl136_160,
    inference(avatar_split_clause,[],[f1624,f3490]) ).

thf(f1624,plain,
    ! [X0: a] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,X0)),vAPP(a,extended_ereal,f,X0)) ),
    inference(cnf_transformation,[],[f604]) ).

thf(f604,plain,
    ! [X0: a] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,X0)),vAPP(a,extended_ereal,f,X0)) ),
    inference(fool_elimination,[],[f603]) ).

thf(f603,plain,
    ! [X0: a] : vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,X0)),vAPP(a,extended_ereal,f,X0)),
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    ! [X3: a] : vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,X3)),vAPP(a,extended_ereal,f,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms) ).

thf(f3488,plain,
    spl136_159,
    inference(avatar_split_clause,[],[f1568,f3486]) ).

thf(f3486,plain,
    ( spl136_159
  <=> ! [X0: $tType,X1: X0] :
        ( ( vAPP(X0,X0,abs_abs(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) )
        | ( ordere142940540dd_abs(X0) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_159])]) ).

thf(f1568,plain,
    ! [X0: $tType,X1: X0] :
      ( ( vAPP(X0,X0,abs_abs(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) )
      | ( ordere142940540dd_abs(X0) != $true ) ),
    inference(cnf_transformation,[],[f992]) ).

thf(f992,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] : ( vAPP(X0,X0,abs_abs(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) )
      | ( ordere142940540dd_abs(X0) != $true ) ),
    inference(ennf_transformation,[],[f510]) ).

thf(f510,plain,
    ! [X0: $tType] :
      ( ( ordere142940540dd_abs(X0) = $true )
     => ! [X1: X0] : ( vAPP(X0,X0,abs_abs(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) ) ),
    inference(fool_elimination,[],[f509]) ).

thf(f509,plain,
    ! [X0: $tType] :
      ( ordere142940540dd_abs(X0)
     => ! [X1: X0] : ( vAPP(X0,X0,abs_abs(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) ) ),
    inference(rectify,[],[f218]) ).

thf(f218,axiom,
    ! [X0: $tType] :
      ( ordere142940540dd_abs(X0)
     => ! [X15: X0] : ( vAPP(X0,X0,abs_abs(X0),X15) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,uminus_uminus(X0),X15)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_abs__minus__cancel) ).

thf(f3484,plain,
    spl136_158,
    inference(avatar_split_clause,[],[f1567,f3482]) ).

thf(f3482,plain,
    ( spl136_158
  <=> ! [X0: $tType,X1: X0] :
        ( ( vAPP(X0,X0,abs_abs(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,abs_abs(X0),X1)) )
        | ( ordere142940540dd_abs(X0) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_158])]) ).

thf(f1567,plain,
    ! [X0: $tType,X1: X0] :
      ( ( vAPP(X0,X0,abs_abs(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,abs_abs(X0),X1)) )
      | ( ordere142940540dd_abs(X0) != $true ) ),
    inference(cnf_transformation,[],[f991]) ).

thf(f991,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] : ( vAPP(X0,X0,abs_abs(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,abs_abs(X0),X1)) )
      | ( ordere142940540dd_abs(X0) != $true ) ),
    inference(ennf_transformation,[],[f508]) ).

thf(f508,plain,
    ! [X0: $tType] :
      ( ( ordere142940540dd_abs(X0) = $true )
     => ! [X1: X0] : ( vAPP(X0,X0,abs_abs(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,abs_abs(X0),X1)) ) ),
    inference(fool_elimination,[],[f507]) ).

thf(f507,plain,
    ! [X0: $tType] :
      ( ordere142940540dd_abs(X0)
     => ! [X1: X0] : ( vAPP(X0,X0,abs_abs(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,abs_abs(X0),X1)) ) ),
    inference(rectify,[],[f213]) ).

thf(f213,axiom,
    ! [X0: $tType] :
      ( ordere142940540dd_abs(X0)
     => ! [X15: X0] : ( vAPP(X0,X0,abs_abs(X0),X15) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,abs_abs(X0),X15)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_abs__idempotent) ).

thf(f3480,plain,
    spl136_157,
    inference(avatar_split_clause,[],[f1534,f3478]) ).

thf(f3478,plain,
    ( spl136_157
  <=> ! [X0: $tType,X1: num] :
        ( ( vAPP(num,X0,numeral_numeral(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(num,X0,numeral_numeral(X0),X1)) )
        | ( linordered_idom(X0) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_157])]) ).

thf(f1534,plain,
    ! [X0: $tType,X1: num] :
      ( ( vAPP(num,X0,numeral_numeral(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(num,X0,numeral_numeral(X0),X1)) )
      | ( linordered_idom(X0) != $true ) ),
    inference(cnf_transformation,[],[f969]) ).

thf(f969,plain,
    ! [X0: $tType] :
      ( ! [X1: num] : ( vAPP(num,X0,numeral_numeral(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(num,X0,numeral_numeral(X0),X1)) )
      | ( linordered_idom(X0) != $true ) ),
    inference(ennf_transformation,[],[f470]) ).

thf(f470,plain,
    ! [X0: $tType] :
      ( ( linordered_idom(X0) = $true )
     => ! [X1: num] : ( vAPP(num,X0,numeral_numeral(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(num,X0,numeral_numeral(X0),X1)) ) ),
    inference(fool_elimination,[],[f469]) ).

thf(f469,plain,
    ! [X0: $tType] :
      ( linordered_idom(X0)
     => ! [X1: num] : ( vAPP(num,X0,numeral_numeral(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(num,X0,numeral_numeral(X0),X1)) ) ),
    inference(rectify,[],[f217]) ).

thf(f217,axiom,
    ! [X0: $tType] :
      ( linordered_idom(X0)
     => ! [X36: num] : ( vAPP(num,X0,numeral_numeral(X0),X36) = vAPP(X0,X0,abs_abs(X0),vAPP(num,X0,numeral_numeral(X0),X36)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_abs__numeral) ).

thf(f3476,plain,
    spl136_156,
    inference(avatar_split_clause,[],[f1499,f3474]) ).

thf(f3474,plain,
    ( spl136_156
  <=> ! [X0: $tType,X2: num,X1: num] :
        ( ( vAPP(num,X0,numeral_numeral(X0),X1) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X2)) )
        | ( ring_char_0(X0) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_156])]) ).

thf(f1499,plain,
    ! [X0: $tType,X2: num,X1: num] :
      ( ( vAPP(num,X0,numeral_numeral(X0),X1) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X2)) )
      | ( ring_char_0(X0) != $true ) ),
    inference(cnf_transformation,[],[f933]) ).

thf(f933,plain,
    ! [X0: $tType] :
      ( ! [X1: num,X2: num] : ( vAPP(num,X0,numeral_numeral(X0),X1) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X2)) )
      | ( ring_char_0(X0) != $true ) ),
    inference(ennf_transformation,[],[f400]) ).

thf(f400,plain,
    ! [X0: $tType] :
      ( ( ring_char_0(X0) = $true )
     => ! [X1: num,X2: num] : ( vAPP(num,X0,numeral_numeral(X0),X1) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X2)) ) ),
    inference(fool_elimination,[],[f399]) ).

thf(f399,plain,
    ! [X0: $tType] :
      ( ring_char_0(X0)
     => ! [X1: num,X2: num] : ( vAPP(num,X0,numeral_numeral(X0),X1) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X2)) ) ),
    inference(rectify,[],[f113]) ).

thf(f113,axiom,
    ! [X0: $tType] :
      ( ring_char_0(X0)
     => ! [X35: num,X36: num] : ( vAPP(num,X0,numeral_numeral(X0),X35) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X36)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_numeral__neq__neg__numeral) ).

thf(f3457,plain,
    spl136_155,
    inference(avatar_split_clause,[],[f1452,f3455]) ).

thf(f3455,plain,
    ( spl136_155
  <=> ! [X0: real] : ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),vAPP(real,extended_ereal,extended_ereal2,X0)) = vAPP(real,extended_ereal,extended_ereal2,vAPP(real,real,uminus_uminus(real),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_155])]) ).

thf(f1452,plain,
    ! [X0: real] : ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),vAPP(real,extended_ereal,extended_ereal2,X0)) = vAPP(real,extended_ereal,extended_ereal2,vAPP(real,real,uminus_uminus(real),X0)) ),
    inference(cnf_transformation,[],[f861]) ).

thf(f861,plain,
    ! [X0: real] : ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),vAPP(real,extended_ereal,extended_ereal2,X0)) = vAPP(real,extended_ereal,extended_ereal2,vAPP(real,real,uminus_uminus(real),X0)) ),
    inference(rectify,[],[f195]) ).

thf(f195,axiom,
    ! [X41: real] : ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),vAPP(real,extended_ereal,extended_ereal2,X41)) = vAPP(real,extended_ereal,extended_ereal2,vAPP(real,real,uminus_uminus(real),X41)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_uminus__ereal_Osimps_I1_J) ).

thf(f3453,plain,
    spl136_154,
    inference(avatar_split_clause,[],[f1451,f3451]) ).

thf(f3451,plain,
    ( spl136_154
  <=> ! [X0: extended_ereal] : ( vAPP(extended_ereal,real,extend1716541707_ereal,vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X0)) = vAPP(real,real,uminus_uminus(real),vAPP(extended_ereal,real,extend1716541707_ereal,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_154])]) ).

thf(f1451,plain,
    ! [X0: extended_ereal] : ( vAPP(extended_ereal,real,extend1716541707_ereal,vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X0)) = vAPP(real,real,uminus_uminus(real),vAPP(extended_ereal,real,extend1716541707_ereal,X0)) ),
    inference(cnf_transformation,[],[f860]) ).

thf(f860,plain,
    ! [X0: extended_ereal] : ( vAPP(extended_ereal,real,extend1716541707_ereal,vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X0)) = vAPP(real,real,uminus_uminus(real),vAPP(extended_ereal,real,extend1716541707_ereal,X0)) ),
    inference(rectify,[],[f87]) ).

thf(f87,axiom,
    ! [X4: extended_ereal] : ( vAPP(extended_ereal,real,extend1716541707_ereal,vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X4)) = vAPP(real,real,uminus_uminus(real),vAPP(extended_ereal,real,extend1716541707_ereal,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_real__of__ereal) ).

thf(f3449,plain,
    ( spl136_153
    | ~ spl136_37
    | ~ spl136_95 ),
    inference(avatar_split_clause,[],[f3024,f2988,f2658,f3447]) ).

thf(f3447,plain,
    ( spl136_153
  <=> ! [X0: $tType] : ( $true = topolo503727757_space(sTfun(X0,extended_enat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_153])]) ).

thf(f2658,plain,
    ( spl136_37
  <=> ( topolo503727757_space(extended_enat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_37])]) ).

thf(f3024,plain,
    ( ! [X0: $tType] : ( $true = topolo503727757_space(sTfun(X0,extended_enat)) )
    | ~ spl136_37
    | ~ spl136_95 ),
    inference(trivial_inequality_removal,[],[f3017]) ).

thf(f3017,plain,
    ( ! [X0: $tType] :
        ( ( $true != $true )
        | ( $true = topolo503727757_space(sTfun(X0,extended_enat)) ) )
    | ~ spl136_37
    | ~ spl136_95 ),
    inference(superposition,[],[f2989,f2660]) ).

thf(f2660,plain,
    ( ( topolo503727757_space(extended_enat) = $true )
    | ~ spl136_37 ),
    inference(avatar_component_clause,[],[f2658]) ).

thf(f3425,plain,
    spl136_152,
    inference(avatar_split_clause,[],[f2285,f3423]) ).

thf(f3423,plain,
    ( spl136_152
  <=> ! [X0: extended_ereal] :
        ( ( extended_PInfty != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
        | ( zero_zero(extended_ereal) = vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_152])]) ).

thf(f2285,plain,
    ! [X0: extended_ereal] :
      ( ( extended_PInfty != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
      | ( zero_zero(extended_ereal) = vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X0)) ) ),
    inference(forward_demodulation,[],[f1472,f1416]) ).

thf(f1416,plain,
    extend1396239628finity(extended_ereal) = extended_PInfty,
    inference(cnf_transformation,[],[f203]) ).

thf(f203,axiom,
    extend1396239628finity(extended_ereal) = extended_PInfty,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_infinity__ereal__def) ).

thf(f1472,plain,
    ! [X0: extended_ereal] :
      ( ( zero_zero(extended_ereal) = vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X0)) )
      | ( extend1396239628finity(extended_ereal) != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) ) ),
    inference(cnf_transformation,[],[f901]) ).

thf(f901,plain,
    ! [X0: extended_ereal] :
      ( ( ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X0)) = X0 )
        | ( extend1396239628finity(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) ) )
      & ( ( zero_zero(extended_ereal) = vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X0)) )
        | ( extend1396239628finity(extended_ereal) != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) ) ) ),
    inference(ennf_transformation,[],[f867]) ).

thf(f867,plain,
    ! [X0: extended_ereal] :
      ( ( ( extend1396239628finity(extended_ereal) != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
       => ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X0)) = X0 ) )
      & ( ( extend1396239628finity(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
       => ( zero_zero(extended_ereal) = vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X0)) ) ) ),
    inference(rectify,[],[f250]) ).

thf(f250,axiom,
    ! [X4: extended_ereal] :
      ( ( ( extend1396239628finity(extended_ereal) != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X4) )
       => ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X4)) = X4 ) )
      & ( ( extend1396239628finity(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X4) )
       => ( zero_zero(extended_ereal) = vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X4)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_ereal__real) ).

thf(f3421,plain,
    spl136_151,
    inference(avatar_split_clause,[],[f1622,f3419]) ).

thf(f3419,plain,
    ( spl136_151
  <=> ! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_151])]) ).

thf(f1622,plain,
    ! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0)) ),
    inference(cnf_transformation,[],[f600]) ).

thf(f600,plain,
    ! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0)) ),
    inference(fool_elimination,[],[f599]) ).

thf(f599,plain,
    ! [X0: extended_ereal] : vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0)),
    inference(rectify,[],[f237]) ).

thf(f237,axiom,
    ! [X4: extended_ereal] : vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_abs__ereal__pos) ).

thf(f3417,plain,
    spl136_150,
    inference(avatar_split_clause,[],[f1506,f3415]) ).

thf(f3415,plain,
    ( spl136_150
  <=> ! [X0: $tType] :
        ( ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),zero_zero(X0)) = $true )
        | ( linord1659791738miring(X0) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_150])]) ).

thf(f1506,plain,
    ! [X0: $tType] :
      ( ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),zero_zero(X0)) = $true )
      | ( linord1659791738miring(X0) != $true ) ),
    inference(cnf_transformation,[],[f940]) ).

thf(f940,plain,
    ! [X0: $tType] :
      ( ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),zero_zero(X0)) = $true )
      | ( linord1659791738miring(X0) != $true ) ),
    inference(ennf_transformation,[],[f414]) ).

thf(f414,plain,
    ! [X0: $tType] :
      ( ( linord1659791738miring(X0) = $true )
     => ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),zero_zero(X0)) = $true ) ),
    inference(fool_elimination,[],[f413]) ).

thf(f413,plain,
    ! [X0: $tType] :
      ( linord1659791738miring(X0)
     => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),zero_zero(X0)) ),
    inference(rectify,[],[f71]) ).

thf(f71,axiom,
    ! [X0: $tType] :
      ( linord1659791738miring(X0)
     => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),zero_zero(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_le__numeral__extra_I3_J) ).

thf(f3396,plain,
    ( spl136_149
    | ~ spl136_42
    | ~ spl136_95 ),
    inference(avatar_split_clause,[],[f3023,f2988,f2683,f3394]) ).

thf(f3394,plain,
    ( spl136_149
  <=> ! [X0: $tType] : ( $true = topolo503727757_space(sTfun(X0,extended_ereal)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_149])]) ).

thf(f2683,plain,
    ( spl136_42
  <=> ( topolo503727757_space(extended_ereal) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_42])]) ).

thf(f3023,plain,
    ( ! [X0: $tType] : ( $true = topolo503727757_space(sTfun(X0,extended_ereal)) )
    | ~ spl136_42
    | ~ spl136_95 ),
    inference(trivial_inequality_removal,[],[f3018]) ).

thf(f3018,plain,
    ( ! [X0: $tType] :
        ( ( $true != $true )
        | ( $true = topolo503727757_space(sTfun(X0,extended_ereal)) ) )
    | ~ spl136_42
    | ~ spl136_95 ),
    inference(superposition,[],[f2989,f2685]) ).

thf(f2685,plain,
    ( ( topolo503727757_space(extended_ereal) = $true )
    | ~ spl136_42 ),
    inference(avatar_component_clause,[],[f2683]) ).

thf(f3382,plain,
    spl136_148,
    inference(avatar_split_clause,[],[f2293,f3380]) ).

thf(f3380,plain,
    ( spl136_148
  <=> ! [X0: extended_ereal] :
        ( ( extended_PInfty = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
        | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK40,X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_148])]) ).

thf(f2293,plain,
    ! [X0: extended_ereal] :
      ( ( extended_PInfty = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
      | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK40,X0)) = X0 ) ),
    inference(forward_demodulation,[],[f1478,f1416]) ).

thf(f1478,plain,
    ! [X0: extended_ereal] :
      ( ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK40,X0)) = X0 )
      | ( extend1396239628finity(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) ) ),
    inference(cnf_transformation,[],[f1180]) ).

thf(f1180,plain,
    ! [X0: extended_ereal] :
      ( ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK40,X0)) = X0 )
      | ( extend1396239628finity(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK40])],[f906,f1179]) ).

thf(f1179,plain,
    ! [X0: extended_ereal] :
      ( ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 )
     => ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK40,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f906,plain,
    ! [X0: extended_ereal] :
      ( ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 )
      | ( extend1396239628finity(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) ) ),
    inference(ennf_transformation,[],[f871]) ).

thf(f871,plain,
    ! [X0: extended_ereal] :
      ( ( extend1396239628finity(extended_ereal) != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
     => ~ ! [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) != X0 ) ),
    inference(rectify,[],[f232]) ).

thf(f232,axiom,
    ! [X4: extended_ereal] :
      ( ( extend1396239628finity(extended_ereal) != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X4) )
     => ~ ! [X58: real] : ( vAPP(real,extended_ereal,extended_ereal2,X58) != X4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_abs__neq__infinity__cases) ).

thf(f3378,plain,
    spl136_147,
    inference(avatar_split_clause,[],[f2291,f3376]) ).

thf(f3376,plain,
    ( spl136_147
  <=> ! [X0: extended_ereal] :
        ( ( extended_PInfty = X0 )
        | ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty) = X0 )
        | ( extended_PInfty != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_147])]) ).

thf(f2291,plain,
    ! [X0: extended_ereal] :
      ( ( extended_PInfty = X0 )
      | ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty) = X0 )
      | ( extended_PInfty != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) ) ),
    inference(forward_demodulation,[],[f2290,f1416]) ).

thf(f2290,plain,
    ! [X0: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty) = X0 )
      | ( extended_PInfty != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
      | ( extend1396239628finity(extended_ereal) = X0 ) ),
    inference(forward_demodulation,[],[f2289,f1416]) ).

thf(f2289,plain,
    ! [X0: extended_ereal] :
      ( ( extended_PInfty != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
      | ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
      | ( extend1396239628finity(extended_ereal) = X0 ) ),
    inference(forward_demodulation,[],[f1476,f1416]) ).

thf(f1476,plain,
    ! [X0: extended_ereal] :
      ( ( extend1396239628finity(extended_ereal) != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
      | ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
      | ( extend1396239628finity(extended_ereal) = X0 ) ),
    inference(cnf_transformation,[],[f904]) ).

thf(f904,plain,
    ! [X0: extended_ereal] :
      ( ( extend1396239628finity(extended_ereal) != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
      | ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
      | ( extend1396239628finity(extended_ereal) = X0 ) ),
    inference(flattening,[],[f903]) ).

thf(f903,plain,
    ! [X0: extended_ereal] :
      ( ( extend1396239628finity(extended_ereal) != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
      | ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
      | ( extend1396239628finity(extended_ereal) = X0 ) ),
    inference(ennf_transformation,[],[f869]) ).

thf(f869,plain,
    ! [X0: extended_ereal] :
      ( ( extend1396239628finity(extended_ereal) != X0 )
     => ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X0 )
       => ( extend1396239628finity(extended_ereal) != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) ) ) ),
    inference(rectify,[],[f234]) ).

thf(f234,axiom,
    ! [X15: extended_ereal] :
      ( ( extend1396239628finity(extended_ereal) != X15 )
     => ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X15 )
       => ( extend1396239628finity(extended_ereal) != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X15) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_ereal__infinity__cases) ).

thf(f3374,plain,
    spl136_146,
    inference(avatar_split_clause,[],[f2284,f3372]) ).

thf(f3372,plain,
    ( spl136_146
  <=> ! [X0: extended_ereal] :
        ( ( extended_PInfty = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
        | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_146])]) ).

thf(f2284,plain,
    ! [X0: extended_ereal] :
      ( ( extended_PInfty = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
      | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X0)) = X0 ) ),
    inference(forward_demodulation,[],[f1473,f1416]) ).

thf(f1473,plain,
    ! [X0: extended_ereal] :
      ( ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X0)) = X0 )
      | ( extend1396239628finity(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) ) ),
    inference(cnf_transformation,[],[f901]) ).

thf(f3370,plain,
    spl136_145,
    inference(avatar_split_clause,[],[f1621,f3368]) ).

thf(f3368,plain,
    ( spl136_145
  <=> ! [X0: extended_enat] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_enat,extended_ereal,extend1771934483f_enat,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_145])]) ).

thf(f1621,plain,
    ! [X0: extended_enat] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_enat,extended_ereal,extend1771934483f_enat,X0)) ),
    inference(cnf_transformation,[],[f598]) ).

thf(f598,plain,
    ! [X0: extended_enat] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_enat,extended_ereal,extend1771934483f_enat,X0)) ),
    inference(fool_elimination,[],[f597]) ).

thf(f597,plain,
    ! [X0: extended_enat] : vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_enat,extended_ereal,extend1771934483f_enat,X0)),
    inference(rectify,[],[f49]) ).

thf(f49,axiom,
    ! [X36: extended_enat] : vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_enat,extended_ereal,extend1771934483f_enat,X36)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_ereal__of__enat__nonneg) ).

thf(f3366,plain,
    spl136_144,
    inference(avatar_split_clause,[],[f1605,f3364]) ).

thf(f3364,plain,
    ( spl136_144
  <=> ! [X0: nat] :
        ( ( zero_zero(nat) = X0 )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_144])]) ).

thf(f1605,plain,
    ! [X0: nat] :
      ( ( zero_zero(nat) = X0 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat)) ) ),
    inference(cnf_transformation,[],[f1035]) ).

thf(f1035,plain,
    ! [X0: nat] :
      ( ( zero_zero(nat) = X0 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat)) ) ),
    inference(ennf_transformation,[],[f574]) ).

thf(f574,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat)) )
     => ( zero_zero(nat) = X0 ) ),
    inference(fool_elimination,[],[f573]) ).

thf(f573,plain,
    ! [X0: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat))
     => ( zero_zero(nat) = X0 ) ),
    inference(rectify,[],[f144]) ).

thf(f144,axiom,
    ! [X15: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X15),zero_zero(nat))
     => ( zero_zero(nat) = X15 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_bot__nat__0_Oextremum__uniqueI) ).

thf(f3362,plain,
    spl136_143,
    inference(avatar_split_clause,[],[f1491,f3360]) ).

thf(f3360,plain,
    ( spl136_143
  <=> ! [X0: $tType,X1: X0] :
        ( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1) )
        | ( canoni770627133id_add(X0) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_143])]) ).

thf(f1491,plain,
    ! [X0: $tType,X1: X0] :
      ( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1) )
      | ( canoni770627133id_add(X0) != $true ) ),
    inference(cnf_transformation,[],[f925]) ).

thf(f925,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] : ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1) )
      | ( canoni770627133id_add(X0) != $true ) ),
    inference(ennf_transformation,[],[f384]) ).

thf(f384,plain,
    ! [X0: $tType] :
      ( ( canoni770627133id_add(X0) = $true )
     => ! [X1: X0] : ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1) ) ),
    inference(fool_elimination,[],[f383]) ).

thf(f383,plain,
    ! [X0: $tType] :
      ( canoni770627133id_add(X0)
     => ! [X1: X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1) ),
    inference(rectify,[],[f70]) ).

thf(f70,axiom,
    ! [X0: $tType] :
      ( canoni770627133id_add(X0)
     => ! [X4: X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_zero__le) ).

thf(f3330,plain,
    ( spl136_142
    | ~ spl136_40
    | ~ spl136_95 ),
    inference(avatar_split_clause,[],[f3022,f2988,f2673,f3328]) ).

thf(f3328,plain,
    ( spl136_142
  <=> ! [X0: $tType] : ( $true = topolo503727757_space(sTfun(X0,real)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_142])]) ).

thf(f2673,plain,
    ( spl136_40
  <=> ( topolo503727757_space(real) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_40])]) ).

thf(f3022,plain,
    ( ! [X0: $tType] : ( $true = topolo503727757_space(sTfun(X0,real)) )
    | ~ spl136_40
    | ~ spl136_95 ),
    inference(trivial_inequality_removal,[],[f3019]) ).

thf(f3019,plain,
    ( ! [X0: $tType] :
        ( ( $true != $true )
        | ( $true = topolo503727757_space(sTfun(X0,real)) ) )
    | ~ spl136_40
    | ~ spl136_95 ),
    inference(superposition,[],[f2989,f2675]) ).

thf(f2675,plain,
    ( ( topolo503727757_space(real) = $true )
    | ~ spl136_40 ),
    inference(avatar_component_clause,[],[f2673]) ).

thf(f3317,plain,
    spl136_141,
    inference(avatar_split_clause,[],[f1590,f3315]) ).

thf(f3315,plain,
    ( spl136_141
  <=> ! [X0: $tType,X1: X0] :
        ( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1) )
        | ( order(X0) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_141])]) ).

thf(f1590,plain,
    ! [X0: $tType,X1: X0] :
      ( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1) )
      | ( order(X0) != $true ) ),
    inference(cnf_transformation,[],[f1017]) ).

thf(f1017,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] : ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1) )
      | ( order(X0) != $true ) ),
    inference(ennf_transformation,[],[f554]) ).

thf(f554,plain,
    ! [X0: $tType] :
      ( ( order(X0) = $true )
     => ! [X1: X0] : ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1) ) ),
    inference(fool_elimination,[],[f553]) ).

thf(f553,plain,
    ! [X0: $tType] :
      ( order(X0)
     => ! [X1: X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1) ),
    inference(rectify,[],[f20]) ).

thf(f20,axiom,
    ! [X0: $tType] :
      ( order(X0)
     => ! [X15: X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X15),X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_dual__order_Orefl) ).

thf(f3313,plain,
    spl136_140,
    inference(avatar_split_clause,[],[f1544,f3311]) ).

thf(f3311,plain,
    ( spl136_140
  <=> ! [X0: $tType,X1: X0] :
        ( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1) )
        | ( preorder(X0) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_140])]) ).

thf(f1544,plain,
    ! [X0: $tType,X1: X0] :
      ( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1) )
      | ( preorder(X0) != $true ) ),
    inference(cnf_transformation,[],[f979]) ).

thf(f979,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] : ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1) )
      | ( preorder(X0) != $true ) ),
    inference(ennf_transformation,[],[f490]) ).

thf(f490,plain,
    ! [X0: $tType] :
      ( ( preorder(X0) = $true )
     => ! [X1: X0] : ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1) ) ),
    inference(fool_elimination,[],[f489]) ).

thf(f489,plain,
    ! [X0: $tType] :
      ( preorder(X0)
     => ! [X1: X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1) ),
    inference(rectify,[],[f3]) ).

thf(f3,axiom,
    ! [X0: $tType] :
      ( preorder(X0)
     => ! [X4: X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X4),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_order__refl) ).

thf(f3309,plain,
    spl136_139,
    inference(avatar_split_clause,[],[f1493,f3307]) ).

thf(f3307,plain,
    ( spl136_139
  <=> ! [X0: $tType,X1: num] :
        ( ( zero_zero(X0) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X1)) )
        | ( ring_char_0(X0) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_139])]) ).

thf(f1493,plain,
    ! [X0: $tType,X1: num] :
      ( ( zero_zero(X0) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X1)) )
      | ( ring_char_0(X0) != $true ) ),
    inference(cnf_transformation,[],[f927]) ).

thf(f927,plain,
    ! [X0: $tType] :
      ( ! [X1: num] : ( zero_zero(X0) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X1)) )
      | ( ring_char_0(X0) != $true ) ),
    inference(ennf_transformation,[],[f388]) ).

thf(f388,plain,
    ! [X0: $tType] :
      ( ( ring_char_0(X0) = $true )
     => ! [X1: num] : ( zero_zero(X0) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X1)) ) ),
    inference(fool_elimination,[],[f387]) ).

thf(f387,plain,
    ! [X0: $tType] :
      ( ring_char_0(X0)
     => ! [X1: num] : ( zero_zero(X0) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X1)) ) ),
    inference(rectify,[],[f126]) ).

thf(f126,axiom,
    ! [X0: $tType] :
      ( ring_char_0(X0)
     => ! [X36: num] : ( zero_zero(X0) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X36)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_zero__neq__neg__numeral) ).

thf(f3305,plain,
    spl136_138,
    inference(avatar_split_clause,[],[f1449,f3303]) ).

thf(f3303,plain,
    ( spl136_138
  <=> ! [X0: extended_ereal] : ( vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_138])]) ).

thf(f1449,plain,
    ! [X0: extended_ereal] : ( vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X0)) ),
    inference(cnf_transformation,[],[f858]) ).

thf(f858,plain,
    ! [X0: extended_ereal] : ( vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X0)) ),
    inference(rectify,[],[f219]) ).

thf(f219,axiom,
    ! [X4: extended_ereal] : ( vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X4)) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_abs__ereal__uminus) ).

thf(f3287,plain,
    ( spl136_137
    | ~ spl136_36
    | ~ spl136_94 ),
    inference(avatar_split_clause,[],[f3014,f2984,f2653,f3285]) ).

thf(f3285,plain,
    ( spl136_137
  <=> ! [X0: $tType] : ( $true = boolean_algebra(sTfun(X0,$o)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_137])]) ).

thf(f2653,plain,
    ( spl136_36
  <=> ( boolean_algebra($o) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_36])]) ).

thf(f2984,plain,
    ( spl136_94
  <=> ! [X1: $tType,X0: $tType] :
        ( ( $true = boolean_algebra(sTfun(X0,X1)) )
        | ( $true != boolean_algebra(X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_94])]) ).

thf(f3014,plain,
    ( ! [X0: $tType] : ( $true = boolean_algebra(sTfun(X0,$o)) )
    | ~ spl136_36
    | ~ spl136_94 ),
    inference(trivial_inequality_removal,[],[f3011]) ).

thf(f3011,plain,
    ( ! [X0: $tType] :
        ( ( $true != $true )
        | ( $true = boolean_algebra(sTfun(X0,$o)) ) )
    | ~ spl136_36
    | ~ spl136_94 ),
    inference(superposition,[],[f2985,f2655]) ).

thf(f2655,plain,
    ( ( boolean_algebra($o) = $true )
    | ~ spl136_36 ),
    inference(avatar_component_clause,[],[f2653]) ).

thf(f2985,plain,
    ( ! [X1: $tType,X0: $tType] :
        ( ( $true != boolean_algebra(X1) )
        | ( $true = boolean_algebra(sTfun(X0,X1)) ) )
    | ~ spl136_94 ),
    inference(avatar_component_clause,[],[f2984]) ).

thf(f3261,plain,
    spl136_136,
    inference(avatar_split_clause,[],[f2365,f3259]) ).

thf(f3259,plain,
    ( spl136_136
  <=> ! [X0: extended_ereal] :
        ( ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),extended_MInfty) )
        | ( extended_MInfty = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_136])]) ).

thf(f2365,plain,
    ! [X0: extended_ereal] :
      ( ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),extended_MInfty) )
      | ( extended_MInfty = X0 ) ),
    inference(forward_demodulation,[],[f2364,f1419]) ).

thf(f1419,plain,
    extended_MInfty = vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty),
    inference(cnf_transformation,[],[f209]) ).

thf(f209,axiom,
    extended_MInfty = vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_uminus__ereal_Osimps_I2_J) ).

thf(f2364,plain,
    ! [X0: extended_ereal] :
      ( ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty)) )
      | ( extended_MInfty = X0 ) ),
    inference(forward_demodulation,[],[f2363,f1416]) ).

thf(f2363,plain,
    ! [X0: extended_ereal] :
      ( ( extended_MInfty = X0 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))) ) ),
    inference(forward_demodulation,[],[f2362,f1419]) ).

thf(f2362,plain,
    ! [X0: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty) = X0 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))) ) ),
    inference(forward_demodulation,[],[f1903,f1416]) ).

thf(f1903,plain,
    ! [X0: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))) ) ),
    inference(equality_resolution,[],[f1715]) ).

thf(f1715,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
      | ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X1 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),X1) ) ),
    inference(cnf_transformation,[],[f1104]) ).

thf(f1104,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
      | ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X1 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),X1) ) ),
    inference(flattening,[],[f1103]) ).

thf(f1103,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
      | ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X1 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),X1) ) ),
    inference(ennf_transformation,[],[f692]) ).

thf(f692,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),X1) )
     => ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X1 )
       => ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 ) ) ),
    inference(fool_elimination,[],[f691]) ).

thf(f691,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),X1)
     => ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X1 )
       => ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 ) ) ),
    inference(rectify,[],[f128]) ).

thf(f128,axiom,
    ! [X15: extended_ereal,X16: extended_ereal] :
      ( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X15),X16)
     => ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X16 )
       => ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X15 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_ereal__infty__less__eq2_I2_J) ).

thf(f3257,plain,
    spl136_135,
    inference(avatar_split_clause,[],[f2327,f3255]) ).

thf(f3255,plain,
    ( spl136_135
  <=> ! [X0: extended_ereal] :
        ( ( extended_PInfty = X0 )
        | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),extended_PInfty),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_135])]) ).

thf(f2327,plain,
    ! [X0: extended_ereal] :
      ( ( extended_PInfty = X0 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),extended_PInfty),X0) ) ),
    inference(forward_demodulation,[],[f2326,f1416]) ).

thf(f2326,plain,
    ! [X0: extended_ereal] :
      ( ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),extended_PInfty),X0) )
      | ( extend1396239628finity(extended_ereal) = X0 ) ),
    inference(forward_demodulation,[],[f1889,f1416]) ).

thf(f1889,plain,
    ! [X0: extended_ereal] :
      ( ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),extend1396239628finity(extended_ereal)),X0) )
      | ( extend1396239628finity(extended_ereal) = X0 ) ),
    inference(equality_resolution,[],[f1644]) ).

thf(f1644,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( extend1396239628finity(extended_ereal) != X1 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X1),X0) )
      | ( extend1396239628finity(extended_ereal) = X0 ) ),
    inference(cnf_transformation,[],[f1044]) ).

thf(f1044,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( extend1396239628finity(extended_ereal) != X1 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X1),X0) )
      | ( extend1396239628finity(extended_ereal) = X0 ) ),
    inference(flattening,[],[f1043]) ).

thf(f1043,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( extend1396239628finity(extended_ereal) != X1 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X1),X0) )
      | ( extend1396239628finity(extended_ereal) = X0 ) ),
    inference(ennf_transformation,[],[f624]) ).

thf(f624,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( extend1396239628finity(extended_ereal) != X0 )
     => ( ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X1),X0) )
       => ( extend1396239628finity(extended_ereal) != X1 ) ) ),
    inference(fool_elimination,[],[f623]) ).

thf(f623,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( extend1396239628finity(extended_ereal) != X0 )
     => ( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X1),X0)
       => ( extend1396239628finity(extended_ereal) != X1 ) ) ),
    inference(rectify,[],[f58]) ).

thf(f58,axiom,
    ! [X27: extended_ereal,X4: extended_ereal] :
      ( ( extend1396239628finity(extended_ereal) != X27 )
     => ( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X4),X27)
       => ( extend1396239628finity(extended_ereal) != X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_neq__PInf__trans) ).

thf(f3253,plain,
    spl136_134,
    inference(avatar_split_clause,[],[f2305,f3251]) ).

thf(f3251,plain,
    ( spl136_134
  <=> ! [X0: extended_ereal] :
        ( ( extended_MInfty = X0 )
        | ( extended_PInfty = X0 )
        | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK45,X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_134])]) ).

thf(f2305,plain,
    ! [X0: extended_ereal] :
      ( ( extended_MInfty = X0 )
      | ( extended_PInfty = X0 )
      | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK45,X0)) = X0 ) ),
    inference(forward_demodulation,[],[f2304,f1419]) ).

thf(f2304,plain,
    ! [X0: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty) = X0 )
      | ( extended_PInfty = X0 )
      | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK45,X0)) = X0 ) ),
    inference(forward_demodulation,[],[f2303,f1416]) ).

thf(f2303,plain,
    ! [X0: extended_ereal] :
      ( ( extended_PInfty = X0 )
      | ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
      | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK45,X0)) = X0 ) ),
    inference(forward_demodulation,[],[f1484,f1416]) ).

thf(f1484,plain,
    ! [X0: extended_ereal] :
      ( ( extend1396239628finity(extended_ereal) = X0 )
      | ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
      | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK45,X0)) = X0 ) ),
    inference(cnf_transformation,[],[f1190]) ).

thf(f1190,plain,
    ! [X0: extended_ereal] :
      ( ( extend1396239628finity(extended_ereal) = X0 )
      | ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
      | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK45,X0)) = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK45])],[f918,f1189]) ).

thf(f1189,plain,
    ! [X0: extended_ereal] :
      ( ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 )
     => ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK45,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f918,plain,
    ! [X0: extended_ereal] :
      ( ( extend1396239628finity(extended_ereal) = X0 )
      | ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
      | ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 ) ),
    inference(flattening,[],[f917]) ).

thf(f917,plain,
    ! [X0: extended_ereal] :
      ( ( extend1396239628finity(extended_ereal) = X0 )
      | ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
      | ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 ) ),
    inference(ennf_transformation,[],[f877]) ).

thf(f877,plain,
    ! [X0: extended_ereal] :
      ( ! [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) != X0 )
     => ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X0 )
       => ( extend1396239628finity(extended_ereal) = X0 ) ) ),
    inference(rectify,[],[f188]) ).

thf(f188,axiom,
    ! [X4: extended_ereal] :
      ( ! [X58: real] : ( vAPP(real,extended_ereal,extended_ereal2,X58) != X4 )
     => ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X4 )
       => ( extend1396239628finity(extended_ereal) = X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_abs__ereal_Ocases) ).

thf(f3249,plain,
    spl136_133,
    inference(avatar_split_clause,[],[f2302,f3247]) ).

thf(f3247,plain,
    ( spl136_133
  <=> ! [X0: extended_ereal] :
        ( ( extended_PInfty = X0 )
        | ( extended_MInfty = X0 )
        | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK44,X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_133])]) ).

thf(f2302,plain,
    ! [X0: extended_ereal] :
      ( ( extended_PInfty = X0 )
      | ( extended_MInfty = X0 )
      | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK44,X0)) = X0 ) ),
    inference(forward_demodulation,[],[f2301,f1416]) ).

thf(f2301,plain,
    ! [X0: extended_ereal] :
      ( ( extended_MInfty = X0 )
      | ( extend1396239628finity(extended_ereal) = X0 )
      | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK44,X0)) = X0 ) ),
    inference(forward_demodulation,[],[f2300,f1419]) ).

thf(f2300,plain,
    ! [X0: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty) = X0 )
      | ( extend1396239628finity(extended_ereal) = X0 )
      | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK44,X0)) = X0 ) ),
    inference(forward_demodulation,[],[f1483,f1416]) ).

thf(f1483,plain,
    ! [X0: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
      | ( extend1396239628finity(extended_ereal) = X0 )
      | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK44,X0)) = X0 ) ),
    inference(cnf_transformation,[],[f1188]) ).

thf(f1188,plain,
    ! [X0: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
      | ( extend1396239628finity(extended_ereal) = X0 )
      | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK44,X0)) = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK44])],[f916,f1187]) ).

thf(f1187,plain,
    ! [X0: extended_ereal] :
      ( ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 )
     => ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK44,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f916,plain,
    ! [X0: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
      | ( extend1396239628finity(extended_ereal) = X0 )
      | ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 ) ),
    inference(flattening,[],[f915]) ).

thf(f915,plain,
    ! [X0: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
      | ( extend1396239628finity(extended_ereal) = X0 )
      | ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 ) ),
    inference(ennf_transformation,[],[f876]) ).

thf(f876,plain,
    ! [X0: extended_ereal] :
      ( ! [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) != X0 )
     => ( ( extend1396239628finity(extended_ereal) != X0 )
       => ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 ) ) ),
    inference(rectify,[],[f192]) ).

thf(f192,axiom,
    ! [X4: extended_ereal] :
      ( ! [X58: real] : ( vAPP(real,extended_ereal,extended_ereal2,X58) != X4 )
     => ( ( extend1396239628finity(extended_ereal) != X4 )
       => ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_ereal__cases) ).

thf(f3245,plain,
    spl136_132,
    inference(avatar_split_clause,[],[f2299,f3243]) ).

thf(f3243,plain,
    ( spl136_132
  <=> ! [X0: extended_ereal] :
        ( ( extended_PInfty = X0 )
        | ( extended_MInfty = X0 )
        | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK43,X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_132])]) ).

thf(f2299,plain,
    ! [X0: extended_ereal] :
      ( ( extended_PInfty = X0 )
      | ( extended_MInfty = X0 )
      | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK43,X0)) = X0 ) ),
    inference(forward_demodulation,[],[f2298,f1416]) ).

thf(f2298,plain,
    ! [X0: extended_ereal] :
      ( ( extended_MInfty = X0 )
      | ( extend1396239628finity(extended_ereal) = X0 )
      | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK43,X0)) = X0 ) ),
    inference(forward_demodulation,[],[f2297,f1419]) ).

thf(f2297,plain,
    ! [X0: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty) = X0 )
      | ( extend1396239628finity(extended_ereal) = X0 )
      | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK43,X0)) = X0 ) ),
    inference(forward_demodulation,[],[f1482,f1416]) ).

thf(f1482,plain,
    ! [X0: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
      | ( extend1396239628finity(extended_ereal) = X0 )
      | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK43,X0)) = X0 ) ),
    inference(cnf_transformation,[],[f1186]) ).

thf(f1186,plain,
    ! [X0: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
      | ( extend1396239628finity(extended_ereal) = X0 )
      | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK43,X0)) = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK43])],[f914,f1185]) ).

thf(f1185,plain,
    ! [X0: extended_ereal] :
      ( ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 )
     => ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK43,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f914,plain,
    ! [X0: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
      | ( extend1396239628finity(extended_ereal) = X0 )
      | ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 ) ),
    inference(flattening,[],[f913]) ).

thf(f913,plain,
    ! [X0: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
      | ( extend1396239628finity(extended_ereal) = X0 )
      | ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 ) ),
    inference(ennf_transformation,[],[f875]) ).

thf(f875,plain,
    ! [X0: extended_ereal] :
      ( ! [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) != X0 )
     => ( ( extend1396239628finity(extended_ereal) != X0 )
       => ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 ) ) ),
    inference(rectify,[],[f182]) ).

thf(f182,axiom,
    ! [X4: extended_ereal] :
      ( ! [X58: real] : ( vAPP(real,extended_ereal,extended_ereal2,X58) != X4 )
     => ( ( extend1396239628finity(extended_ereal) != X4 )
       => ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_real__of__ereal_Ocases) ).

thf(f3241,plain,
    ( spl136_131
    | ~ spl136_29
    | ~ spl136_93 ),
    inference(avatar_split_clause,[],[f3010,f2980,f2618,f3239]) ).

thf(f3239,plain,
    ( spl136_131
  <=> ! [X0: $tType] : ( $true = uminus(sTfun(X0,real)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_131])]) ).

thf(f2618,plain,
    ( spl136_29
  <=> ( uminus(real) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_29])]) ).

thf(f2980,plain,
    ( spl136_93
  <=> ! [X1: $tType,X0: $tType] :
        ( ( $true = uminus(sTfun(X0,X1)) )
        | ( $true != uminus(X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_93])]) ).

thf(f3010,plain,
    ( ! [X0: $tType] : ( $true = uminus(sTfun(X0,real)) )
    | ~ spl136_29
    | ~ spl136_93 ),
    inference(trivial_inequality_removal,[],[f3003]) ).

thf(f3003,plain,
    ( ! [X0: $tType] :
        ( ( $true != $true )
        | ( $true = uminus(sTfun(X0,real)) ) )
    | ~ spl136_29
    | ~ spl136_93 ),
    inference(superposition,[],[f2981,f2620]) ).

thf(f2620,plain,
    ( ( uminus(real) = $true )
    | ~ spl136_29 ),
    inference(avatar_component_clause,[],[f2618]) ).

thf(f2981,plain,
    ( ! [X1: $tType,X0: $tType] :
        ( ( $true != uminus(X1) )
        | ( $true = uminus(sTfun(X0,X1)) ) )
    | ~ spl136_93 ),
    inference(avatar_component_clause,[],[f2980]) ).

thf(f3237,plain,
    spl136_130,
    inference(avatar_split_clause,[],[f1523,f3235]) ).

thf(f3235,plain,
    ( spl136_130
  <=> ! [X0: $tType,X1: X0] :
        ( ( vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1 )
        | ( boolean_algebra(X0) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_130])]) ).

thf(f1523,plain,
    ! [X0: $tType,X1: X0] :
      ( ( vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1 )
      | ( boolean_algebra(X0) != $true ) ),
    inference(cnf_transformation,[],[f958]) ).

thf(f958,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] : ( vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1 )
      | ( boolean_algebra(X0) != $true ) ),
    inference(ennf_transformation,[],[f448]) ).

thf(f448,plain,
    ! [X0: $tType] :
      ( ( boolean_algebra(X0) = $true )
     => ! [X1: X0] : ( vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1 ) ),
    inference(fool_elimination,[],[f447]) ).

thf(f447,plain,
    ! [X0: $tType] :
      ( boolean_algebra(X0)
     => ! [X1: X0] : ( vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1 ) ),
    inference(rectify,[],[f151]) ).

thf(f151,axiom,
    ! [X0: $tType] :
      ( boolean_algebra(X0)
     => ! [X4: X0] : ( vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X4)) = X4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_double__compl) ).

thf(f3233,plain,
    spl136_129,
    inference(avatar_split_clause,[],[f1521,f3231]) ).

thf(f3231,plain,
    ( spl136_129
  <=> ! [X0: $tType,X1: X0] :
        ( ( vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1 )
        | ( group_add(X0) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_129])]) ).

thf(f1521,plain,
    ! [X0: $tType,X1: X0] :
      ( ( vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1 )
      | ( group_add(X0) != $true ) ),
    inference(cnf_transformation,[],[f956]) ).

thf(f956,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] : ( vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1 )
      | ( group_add(X0) != $true ) ),
    inference(ennf_transformation,[],[f444]) ).

thf(f444,plain,
    ! [X0: $tType] :
      ( ( group_add(X0) = $true )
     => ! [X1: X0] : ( vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1 ) ),
    inference(fool_elimination,[],[f443]) ).

thf(f443,plain,
    ! [X0: $tType] :
      ( group_add(X0)
     => ! [X1: X0] : ( vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1 ) ),
    inference(rectify,[],[f82]) ).

thf(f82,axiom,
    ! [X2: $tType] :
      ( group_add(X2)
     => ! [X16: X2] : ( vAPP(X2,X2,uminus_uminus(X2),vAPP(X2,X2,uminus_uminus(X2),X16)) = X16 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_verit__minus__simplify_I4_J) ).

thf(f3229,plain,
    spl136_128,
    inference(avatar_split_clause,[],[f1481,f3227]) ).

thf(f3227,plain,
    ( spl136_128
  <=> ! [X0: extended_ereal] :
        ( ( extended_MInfty = X0 )
        | ( extended_PInfty = X0 )
        | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK42,X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_128])]) ).

thf(f1481,plain,
    ! [X0: extended_ereal] :
      ( ( extended_MInfty = X0 )
      | ( extended_PInfty = X0 )
      | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK42,X0)) = X0 ) ),
    inference(cnf_transformation,[],[f1184]) ).

thf(f1184,plain,
    ! [X0: extended_ereal] :
      ( ( extended_MInfty = X0 )
      | ( extended_PInfty = X0 )
      | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK42,X0)) = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK42])],[f912,f1183]) ).

thf(f1183,plain,
    ! [X0: extended_ereal] :
      ( ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 )
     => ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK42,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f912,plain,
    ! [X0: extended_ereal] :
      ( ( extended_MInfty = X0 )
      | ( extended_PInfty = X0 )
      | ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 ) ),
    inference(flattening,[],[f911]) ).

thf(f911,plain,
    ! [X0: extended_ereal] :
      ( ( extended_MInfty = X0 )
      | ( extended_PInfty = X0 )
      | ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 ) ),
    inference(ennf_transformation,[],[f874]) ).

thf(f874,plain,
    ! [X0: extended_ereal] :
      ( ! [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) != X0 )
     => ( ( extended_PInfty != X0 )
       => ( extended_MInfty = X0 ) ) ),
    inference(rectify,[],[f207]) ).

thf(f207,axiom,
    ! [X27: extended_ereal] :
      ( ! [X70: real] : ( vAPP(real,extended_ereal,extended_ereal2,X70) != X27 )
     => ( ( extended_PInfty != X27 )
       => ( extended_MInfty = X27 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_ereal_Oexhaust) ).

thf(f3225,plain,
    spl136_127,
    inference(avatar_split_clause,[],[f1480,f3223]) ).

thf(f3223,plain,
    ( spl136_127
  <=> ! [X0: extended_ereal] :
        ( ( extended_MInfty = X0 )
        | ( extended_PInfty = X0 )
        | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK41,X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_127])]) ).

thf(f1480,plain,
    ! [X0: extended_ereal] :
      ( ( extended_MInfty = X0 )
      | ( extended_PInfty = X0 )
      | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK41,X0)) = X0 ) ),
    inference(cnf_transformation,[],[f1182]) ).

thf(f1182,plain,
    ! [X0: extended_ereal] :
      ( ( extended_MInfty = X0 )
      | ( extended_PInfty = X0 )
      | ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK41,X0)) = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK41])],[f910,f1181]) ).

thf(f1181,plain,
    ! [X0: extended_ereal] :
      ( ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 )
     => ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK41,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f910,plain,
    ! [X0: extended_ereal] :
      ( ( extended_MInfty = X0 )
      | ( extended_PInfty = X0 )
      | ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 ) ),
    inference(flattening,[],[f909]) ).

thf(f909,plain,
    ! [X0: extended_ereal] :
      ( ( extended_MInfty = X0 )
      | ( extended_PInfty = X0 )
      | ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 ) ),
    inference(ennf_transformation,[],[f873]) ).

thf(f873,plain,
    ! [X0: extended_ereal] :
      ( ! [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) != X0 )
     => ( ( extended_PInfty != X0 )
       => ( extended_MInfty = X0 ) ) ),
    inference(rectify,[],[f206]) ).

thf(f206,axiom,
    ! [X4: extended_ereal] :
      ( ! [X58: real] : ( vAPP(real,extended_ereal,extended_ereal2,X58) != X4 )
     => ( ( extended_PInfty != X4 )
       => ( extended_MInfty = X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_uminus__ereal_Ocases) ).

thf(f3209,plain,
    ( spl136_126
    | ~ spl136_31
    | ~ spl136_93 ),
    inference(avatar_split_clause,[],[f3009,f2980,f2628,f3207]) ).

thf(f3207,plain,
    ( spl136_126
  <=> ! [X0: $tType] : ( $true = uminus(sTfun(X0,$o)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_126])]) ).

thf(f2628,plain,
    ( spl136_31
  <=> ( uminus($o) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_31])]) ).

thf(f3009,plain,
    ( ! [X0: $tType] : ( $true = uminus(sTfun(X0,$o)) )
    | ~ spl136_31
    | ~ spl136_93 ),
    inference(trivial_inequality_removal,[],[f3004]) ).

thf(f3004,plain,
    ( ! [X0: $tType] :
        ( ( $true != $true )
        | ( $true = uminus(sTfun(X0,$o)) ) )
    | ~ spl136_31
    | ~ spl136_93 ),
    inference(superposition,[],[f2981,f2630]) ).

thf(f2630,plain,
    ( ( uminus($o) = $true )
    | ~ spl136_31 ),
    inference(avatar_component_clause,[],[f2628]) ).

thf(f3201,plain,
    spl136_125,
    inference(avatar_split_clause,[],[f2341,f3199]) ).

thf(f3199,plain,
    ( spl136_125
  <=> ! [X0: extended_ereal,X1: extended_ereal] :
        ( ( extended_PInfty = X0 )
        | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP8,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_125])]) ).

thf(f2341,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( extended_PInfty = X0 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP8,X1),X0) ) ),
    inference(forward_demodulation,[],[f1685,f1416]) ).

thf(f1685,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( extend1396239628finity(extended_ereal) = X0 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP8,X1),X0) ) ),
    inference(cnf_transformation,[],[f1261]) ).

thf(f1261,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( ( extend1396239628finity(extended_ereal) = X0 )
        & ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK75,X1)) = X1 ) )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP8,X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK75])],[f1259,f1260]) ).

thf(f1260,plain,
    ! [X1: extended_ereal] :
      ( ? [X2: real] : ( vAPP(real,extended_ereal,extended_ereal2,X2) = X1 )
     => ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK75,X1)) = X1 ) ),
    introduced(choice_axiom,[]) ).

thf(f1259,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( ( extend1396239628finity(extended_ereal) = X0 )
        & ? [X2: real] : ( vAPP(real,extended_ereal,extended_ereal2,X2) = X1 ) )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP8,X1),X0) ) ),
    inference(rectify,[],[f1258]) ).

thf(f1258,plain,
    ! [X1: extended_ereal,X0: extended_ereal] :
      ( ( ( extend1396239628finity(extended_ereal) = X1 )
        & ? [X4: real] : ( vAPP(real,extended_ereal,extended_ereal2,X4) = X0 ) )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP8,X0),X1) ) ),
    inference(nnf_transformation,[],[f1145]) ).

thf(f1145,plain,
    ! [X1: extended_ereal,X0: extended_ereal] :
      ( ( ( extend1396239628finity(extended_ereal) = X1 )
        & ? [X4: real] : ( vAPP(real,extended_ereal,extended_ereal2,X4) = X0 ) )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP8,X0),X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f3197,plain,
    spl136_124,
    inference(avatar_split_clause,[],[f2340,f3195]) ).

thf(f3195,plain,
    ( spl136_124
  <=> ! [X0: extended_ereal,X1: extended_ereal] :
        ( ( extended_MInfty = X0 )
        | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP9,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_124])]) ).

thf(f2340,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( extended_MInfty = X0 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP9,X1),X0) ) ),
    inference(forward_demodulation,[],[f2339,f1419]) ).

thf(f2339,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty) = X0 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP9,X1),X0) ) ),
    inference(forward_demodulation,[],[f1683,f1416]) ).

thf(f1683,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP9,X1),X0) ) ),
    inference(cnf_transformation,[],[f1257]) ).

thf(f1257,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
        & ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK74,X1)) = X1 ) )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP9,X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK74])],[f1255,f1256]) ).

thf(f1256,plain,
    ! [X1: extended_ereal] :
      ( ? [X2: real] : ( vAPP(real,extended_ereal,extended_ereal2,X2) = X1 )
     => ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK74,X1)) = X1 ) ),
    introduced(choice_axiom,[]) ).

thf(f1255,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
        & ? [X2: real] : ( vAPP(real,extended_ereal,extended_ereal2,X2) = X1 ) )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP9,X1),X0) ) ),
    inference(rectify,[],[f1254]) ).

thf(f1254,plain,
    ! [X1: extended_ereal,X0: extended_ereal] :
      ( ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X1 )
        & ? [X5: real] : ( vAPP(real,extended_ereal,extended_ereal2,X5) = X0 ) )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP9,X0),X1) ) ),
    inference(nnf_transformation,[],[f1146]) ).

thf(f1146,plain,
    ! [X1: extended_ereal,X0: extended_ereal] :
      ( ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X1 )
        & ? [X5: real] : ( vAPP(real,extended_ereal,extended_ereal2,X5) = X0 ) )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP9,X0),X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f3193,plain,
    spl136_123,
    inference(avatar_split_clause,[],[f2338,f3191]) ).

thf(f3191,plain,
    ( spl136_123
  <=> ! [X0: extended_ereal,X1: extended_ereal] :
        ( ( extended_PInfty = X1 )
        | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP10,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_123])]) ).

thf(f2338,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( extended_PInfty = X1 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP10,X1),X0) ) ),
    inference(forward_demodulation,[],[f1680,f1416]) ).

thf(f1680,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( extend1396239628finity(extended_ereal) = X1 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP10,X1),X0) ) ),
    inference(cnf_transformation,[],[f1253]) ).

thf(f1253,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK73,X0)) = X0 )
        & ( extend1396239628finity(extended_ereal) = X1 ) )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP10,X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK73])],[f1251,f1252]) ).

thf(f1252,plain,
    ! [X0: extended_ereal] :
      ( ? [X2: real] : ( vAPP(real,extended_ereal,extended_ereal2,X2) = X0 )
     => ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK73,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1251,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( ? [X2: real] : ( vAPP(real,extended_ereal,extended_ereal2,X2) = X0 )
        & ( extend1396239628finity(extended_ereal) = X1 ) )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP10,X1),X0) ) ),
    inference(rectify,[],[f1250]) ).

thf(f1250,plain,
    ! [X1: extended_ereal,X0: extended_ereal] :
      ( ( ? [X6: real] : ( vAPP(real,extended_ereal,extended_ereal2,X6) = X1 )
        & ( extend1396239628finity(extended_ereal) = X0 ) )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP10,X0),X1) ) ),
    inference(nnf_transformation,[],[f1147]) ).

thf(f1147,plain,
    ! [X1: extended_ereal,X0: extended_ereal] :
      ( ( ? [X6: real] : ( vAPP(real,extended_ereal,extended_ereal2,X6) = X1 )
        & ( extend1396239628finity(extended_ereal) = X0 ) )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP10,X0),X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f3189,plain,
    spl136_122,
    inference(avatar_split_clause,[],[f2337,f3187]) ).

thf(f3187,plain,
    ( spl136_122
  <=> ! [X0: extended_ereal,X1: extended_ereal] :
        ( ( extended_PInfty = X1 )
        | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP11,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_122])]) ).

thf(f2337,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( extended_PInfty = X1 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP11,X1),X0) ) ),
    inference(forward_demodulation,[],[f1678,f1416]) ).

thf(f1678,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( extend1396239628finity(extended_ereal) = X1 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP11,X1),X0) ) ),
    inference(cnf_transformation,[],[f1249]) ).

thf(f1249,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( ( extend1396239628finity(extended_ereal) = X0 )
        & ( extend1396239628finity(extended_ereal) = X1 ) )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP11,X1),X0) ) ),
    inference(rectify,[],[f1248]) ).

thf(f1248,plain,
    ! [X1: extended_ereal,X0: extended_ereal] :
      ( ( ( extend1396239628finity(extended_ereal) = X1 )
        & ( extend1396239628finity(extended_ereal) = X0 ) )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP11,X0),X1) ) ),
    inference(nnf_transformation,[],[f1148]) ).

thf(f1148,plain,
    ! [X1: extended_ereal,X0: extended_ereal] :
      ( ( ( extend1396239628finity(extended_ereal) = X1 )
        & ( extend1396239628finity(extended_ereal) = X0 ) )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP11,X0),X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f3185,plain,
    spl136_121,
    inference(avatar_split_clause,[],[f2336,f3183]) ).

thf(f3183,plain,
    ( spl136_121
  <=> ! [X0: extended_ereal,X1: extended_ereal] :
        ( ( extended_PInfty = X0 )
        | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP11,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_121])]) ).

thf(f2336,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( extended_PInfty = X0 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP11,X1),X0) ) ),
    inference(forward_demodulation,[],[f1679,f1416]) ).

thf(f1679,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( extend1396239628finity(extended_ereal) = X0 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP11,X1),X0) ) ),
    inference(cnf_transformation,[],[f1249]) ).

thf(f3181,plain,
    spl136_120,
    inference(avatar_split_clause,[],[f2335,f3179]) ).

thf(f3179,plain,
    ( spl136_120
  <=> ! [X0: extended_ereal,X1: extended_ereal] :
        ( ( extended_PInfty = X1 )
        | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP12,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_120])]) ).

thf(f2335,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( extended_PInfty = X1 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP12,X1),X0) ) ),
    inference(forward_demodulation,[],[f1676,f1416]) ).

thf(f1676,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( extend1396239628finity(extended_ereal) = X1 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP12,X1),X0) ) ),
    inference(cnf_transformation,[],[f1247]) ).

thf(f1247,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
        & ( extend1396239628finity(extended_ereal) = X1 ) )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP12,X1),X0) ) ),
    inference(rectify,[],[f1246]) ).

thf(f1246,plain,
    ! [X1: extended_ereal,X0: extended_ereal] :
      ( ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X1 )
        & ( extend1396239628finity(extended_ereal) = X0 ) )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP12,X0),X1) ) ),
    inference(nnf_transformation,[],[f1149]) ).

thf(f1149,plain,
    ! [X1: extended_ereal,X0: extended_ereal] :
      ( ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X1 )
        & ( extend1396239628finity(extended_ereal) = X0 ) )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP12,X0),X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f3177,plain,
    spl136_119,
    inference(avatar_split_clause,[],[f2334,f3175]) ).

thf(f3175,plain,
    ( spl136_119
  <=> ! [X0: extended_ereal,X1: extended_ereal] :
        ( ( extended_MInfty = X0 )
        | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP12,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_119])]) ).

thf(f2334,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( extended_MInfty = X0 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP12,X1),X0) ) ),
    inference(forward_demodulation,[],[f2333,f1419]) ).

thf(f2333,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty) = X0 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP12,X1),X0) ) ),
    inference(forward_demodulation,[],[f1677,f1416]) ).

thf(f1677,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP12,X1),X0) ) ),
    inference(cnf_transformation,[],[f1247]) ).

thf(f3173,plain,
    ( spl136_118
    | ~ spl136_32
    | ~ spl136_93 ),
    inference(avatar_split_clause,[],[f3008,f2980,f2633,f3171]) ).

thf(f3171,plain,
    ( spl136_118
  <=> ! [X0: $tType] : ( $true = uminus(sTfun(X0,extended_ereal)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_118])]) ).

thf(f2633,plain,
    ( spl136_32
  <=> ( uminus(extended_ereal) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_32])]) ).

thf(f3008,plain,
    ( ! [X0: $tType] : ( $true = uminus(sTfun(X0,extended_ereal)) )
    | ~ spl136_32
    | ~ spl136_93 ),
    inference(trivial_inequality_removal,[],[f3005]) ).

thf(f3005,plain,
    ( ! [X0: $tType] :
        ( ( $true != $true )
        | ( $true = uminus(sTfun(X0,extended_ereal)) ) )
    | ~ spl136_32
    | ~ spl136_93 ),
    inference(superposition,[],[f2981,f2635]) ).

thf(f2635,plain,
    ( ( uminus(extended_ereal) = $true )
    | ~ spl136_32 ),
    inference(avatar_component_clause,[],[f2633]) ).

thf(f3169,plain,
    spl136_117,
    inference(avatar_split_clause,[],[f2332,f3167]) ).

thf(f3167,plain,
    ( spl136_117
  <=> ! [X0: extended_ereal,X1: extended_ereal] :
        ( ( extended_MInfty = X1 )
        | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP13,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_117])]) ).

thf(f2332,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( extended_MInfty = X1 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP13,X1),X0) ) ),
    inference(forward_demodulation,[],[f2331,f1419]) ).

thf(f2331,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty) = X1 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP13,X1),X0) ) ),
    inference(forward_demodulation,[],[f1674,f1416]) ).

thf(f1674,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X1 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP13,X1),X0) ) ),
    inference(cnf_transformation,[],[f1245]) ).

thf(f1245,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK72,X0)) = X0 )
        & ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X1 ) )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP13,X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK72])],[f1243,f1244]) ).

thf(f1244,plain,
    ! [X0: extended_ereal] :
      ( ? [X2: real] : ( vAPP(real,extended_ereal,extended_ereal2,X2) = X0 )
     => ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK72,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f1243,plain,
    ! [X0: extended_ereal,X1: extended_ereal] :
      ( ( ? [X2: real] : ( vAPP(real,extended_ereal,extended_ereal2,X2) = X0 )
        & ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X1 ) )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP13,X1),X0) ) ),
    inference(rectify,[],[f1242]) ).

thf(f1242,plain,
    ! [X1: extended_ereal,X0: extended_ereal] :
      ( ( ? [X7: real] : ( vAPP(real,extended_ereal,extended_ereal2,X7) = X1 )
        & ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 ) )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP13,X0),X1) ) ),
    inference(nnf_transformation,[],[f1150]) ).

thf(f1150,plain,
    ! [X1: extended_ereal,X0: extended_ereal] :
      ( ( ? [X7: real] : ( vAPP(real,extended_ereal,extended_ereal2,X7) = X1 )
        & ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 ) )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP13,X0),X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f3165,plain,
    spl136_116,
    inference(avatar_split_clause,[],[f1448,f3163]) ).

thf(f3163,plain,
    ( spl136_116
  <=> ! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),zero_zero(extended_ereal)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_116])]) ).

thf(f1448,plain,
    ! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),zero_zero(extended_ereal)),X0) ),
    inference(cnf_transformation,[],[f857]) ).

thf(f857,plain,
    ! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),zero_zero(extended_ereal)),X0) ),
    inference(rectify,[],[f222]) ).

thf(f222,axiom,
    ! [X15: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),zero_zero(extended_ereal)),X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_ereal__divide__zero__left) ).

thf(f3159,plain,
    ~ spl136_115,
    inference(avatar_split_clause,[],[f2312,f3156]) ).

thf(f3156,plain,
    ( spl136_115
  <=> ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),extended_MInfty) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_115])]) ).

thf(f2312,plain,
    $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),extended_MInfty),
    inference(forward_demodulation,[],[f2311,f1419]) ).

thf(f2311,plain,
    $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty)),
    inference(forward_demodulation,[],[f1886,f1416]) ).

thf(f1886,plain,
    $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))),
    inference(equality_resolution,[],[f1607]) ).

thf(f1607,plain,
    ! [X0: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X0 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),X0) ) ),
    inference(cnf_transformation,[],[f1037]) ).

thf(f1037,plain,
    ! [X0: extended_ereal] :
      ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X0 )
      | ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),X0) ) ),
    inference(ennf_transformation,[],[f578]) ).

thf(f578,plain,
    ! [X0: extended_ereal] :
      ( ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),X0) )
     => ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X0 ) ),
    inference(fool_elimination,[],[f577]) ).

thf(f577,plain,
    ! [X0: extended_ereal] :
      ( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),X0)
     => ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X0 ) ),
    inference(rectify,[],[f133]) ).

thf(f133,axiom,
    ! [X4: extended_ereal] :
      ( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),X4)
     => ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_not__MInfty__nonneg) ).

thf(f3154,plain,
    spl136_114,
    inference(avatar_split_clause,[],[f2263,f3152]) ).

thf(f3152,plain,
    ( spl136_114
  <=> ! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),X0),extended_MInfty) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_114])]) ).

thf(f2263,plain,
    ! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),X0),extended_MInfty) ),
    inference(forward_demodulation,[],[f2262,f1419]) ).

thf(f2262,plain,
    ! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),X0),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty)) ),
    inference(forward_demodulation,[],[f1450,f1416]) ).

thf(f1450,plain,
    ! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),X0),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))) ),
    inference(cnf_transformation,[],[f859]) ).

thf(f859,plain,
    ! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),X0),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))) ),
    inference(rectify,[],[f230]) ).

thf(f230,axiom,
    ! [X4: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),X4),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_ereal__divide__Infty_I2_J) ).

thf(f3150,plain,
    spl136_113,
    inference(avatar_split_clause,[],[f2261,f3148]) ).

thf(f3148,plain,
    ( spl136_113
  <=> ! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),X0),extended_PInfty) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_113])]) ).

thf(f2261,plain,
    ! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),X0),extended_PInfty) ),
    inference(forward_demodulation,[],[f1447,f1416]) ).

thf(f1447,plain,
    ! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),X0),extend1396239628finity(extended_ereal)) ),
    inference(cnf_transformation,[],[f856]) ).

thf(f856,plain,
    ! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),X0),extend1396239628finity(extended_ereal)) ),
    inference(rectify,[],[f228]) ).

thf(f228,axiom,
    ! [X4: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),X4),extend1396239628finity(extended_ereal)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_ereal__divide__Infty_I1_J) ).

thf(f3146,plain,
    spl136_112,
    inference(avatar_split_clause,[],[f1617,f3144]) ).

thf(f3144,plain,
    ( spl136_112
  <=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_112])]) ).

thf(f1617,plain,
    ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat)),X0) ),
    inference(cnf_transformation,[],[f590]) ).

thf(f590,plain,
    ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat)),X0) ),
    inference(fool_elimination,[],[f589]) ).

thf(f589,plain,
    ! [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat)),X0),
    inference(rectify,[],[f147]) ).

thf(f147,axiom,
    ! [X36: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat)),X36),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_less__eq__nat_Osimps_I1_J) ).

thf(f3142,plain,
    spl136_111,
    inference(avatar_split_clause,[],[f1616,f3140]) ).

thf(f3140,plain,
    ( spl136_111
  <=> ! [X0: extended_enat] : ( $true = vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less_eq(extended_enat),zero_zero(extended_enat)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_111])]) ).

thf(f1616,plain,
    ! [X0: extended_enat] : ( $true = vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less_eq(extended_enat),zero_zero(extended_enat)),X0) ),
    inference(cnf_transformation,[],[f588]) ).

thf(f588,plain,
    ! [X0: extended_enat] : ( $true = vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less_eq(extended_enat),zero_zero(extended_enat)),X0) ),
    inference(fool_elimination,[],[f587]) ).

thf(f587,plain,
    ! [X0: extended_enat] : vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less_eq(extended_enat),zero_zero(extended_enat)),X0),
    inference(rectify,[],[f67]) ).

thf(f67,axiom,
    ! [X36: extended_enat] : vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less_eq(extended_enat),zero_zero(extended_enat)),X36),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_i0__lb) ).

thf(f3126,plain,
    spl136_110,
    inference(avatar_split_clause,[],[f2315,f3124]) ).

thf(f3124,plain,
    ( spl136_110
  <=> ! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),extended_MInfty),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_110])]) ).

thf(f2315,plain,
    ! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),extended_MInfty),X0) ),
    inference(forward_demodulation,[],[f2314,f1419]) ).

thf(f2314,plain,
    ! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty)),X0) ),
    inference(forward_demodulation,[],[f1623,f1416]) ).

thf(f1623,plain,
    ! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))),X0) ),
    inference(cnf_transformation,[],[f602]) ).

thf(f602,plain,
    ! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))),X0) ),
    inference(fool_elimination,[],[f601]) ).

thf(f601,plain,
    ! [X0: extended_ereal] : vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))),X0),
    inference(rectify,[],[f129]) ).

thf(f129,axiom,
    ! [X4: extended_ereal] : vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))),X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_ereal__less__eq_I2_J) ).

thf(f3122,plain,
    spl136_109,
    inference(avatar_split_clause,[],[f2313,f3120]) ).

thf(f3120,plain,
    ( spl136_109
  <=> ! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),extended_PInfty) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_109])]) ).

thf(f2313,plain,
    ! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),extended_PInfty) ),
    inference(forward_demodulation,[],[f1620,f1416]) ).

thf(f1620,plain,
    ! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),extend1396239628finity(extended_ereal)) ),
    inference(cnf_transformation,[],[f596]) ).

thf(f596,plain,
    ! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),extend1396239628finity(extended_ereal)) ),
    inference(fool_elimination,[],[f595]) ).

thf(f595,plain,
    ! [X0: extended_ereal] : vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),extend1396239628finity(extended_ereal)),
    inference(rectify,[],[f60]) ).

thf(f60,axiom,
    ! [X4: extended_ereal] : vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X4),extend1396239628finity(extended_ereal)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_ereal__less__eq_I1_J) ).

thf(f3118,plain,
    ( spl136_108
    | ~ spl136_34
    | ~ spl136_79 ),
    inference(avatar_split_clause,[],[f2929,f2895,f2643,f3115]) ).

thf(f3115,plain,
    ( spl136_108
  <=> ( $true = type(real) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_108])]) ).

thf(f2643,plain,
    ( spl136_34
  <=> ( real_V2090557954_space(real) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_34])]) ).

thf(f2895,plain,
    ( spl136_79
  <=> ! [X0: $tType] :
        ( ( type(X0) = $true )
        | ( real_V2090557954_space(X0) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_79])]) ).

thf(f2929,plain,
    ( ( $true = type(real) )
    | ~ spl136_34
    | ~ spl136_79 ),
    inference(trivial_inequality_removal,[],[f2926]) ).

thf(f2926,plain,
    ( ( $true != $true )
    | ( $true = type(real) )
    | ~ spl136_34
    | ~ spl136_79 ),
    inference(superposition,[],[f2896,f2645]) ).

thf(f2645,plain,
    ( ( real_V2090557954_space(real) = $true )
    | ~ spl136_34 ),
    inference(avatar_component_clause,[],[f2643]) ).

thf(f2896,plain,
    ( ! [X0: $tType] :
        ( ( real_V2090557954_space(X0) != $true )
        | ( type(X0) = $true ) )
    | ~ spl136_79 ),
    inference(avatar_component_clause,[],[f2895]) ).

thf(f3113,plain,
    spl136_107,
    inference(avatar_split_clause,[],[f1615,f3111]) ).

thf(f3111,plain,
    ( spl136_107
  <=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_107])]) ).

thf(f1615,plain,
    ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X0) ),
    inference(cnf_transformation,[],[f586]) ).

thf(f586,plain,
    ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X0) ),
    inference(fool_elimination,[],[f585]) ).

thf(f585,plain,
    ! [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X0),
    inference(rectify,[],[f134]) ).

thf(f134,axiom,
    ! [X36: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X36),X36),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_le__refl) ).

thf(f3109,plain,
    spl136_106,
    inference(avatar_split_clause,[],[f1566,f3107]) ).

thf(f3107,plain,
    ( spl136_106
  <=> ! [X0: $tType] :
        ( ( zero_zero(X0) = vAPP(X0,X0,abs_abs(X0),zero_zero(X0)) )
        | ( ordere142940540dd_abs(X0) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_106])]) ).

thf(f1566,plain,
    ! [X0: $tType] :
      ( ( zero_zero(X0) = vAPP(X0,X0,abs_abs(X0),zero_zero(X0)) )
      | ( ordere142940540dd_abs(X0) != $true ) ),
    inference(cnf_transformation,[],[f990]) ).

thf(f990,plain,
    ! [X0: $tType] :
      ( ( zero_zero(X0) = vAPP(X0,X0,abs_abs(X0),zero_zero(X0)) )
      | ( ordere142940540dd_abs(X0) != $true ) ),
    inference(ennf_transformation,[],[f506]) ).

thf(f506,plain,
    ! [X0: $tType] :
      ( ( ordere142940540dd_abs(X0) = $true )
     => ( zero_zero(X0) = vAPP(X0,X0,abs_abs(X0),zero_zero(X0)) ) ),
    inference(fool_elimination,[],[f505]) ).

thf(f505,plain,
    ! [X0: $tType] :
      ( ordere142940540dd_abs(X0)
     => ( zero_zero(X0) = vAPP(X0,X0,abs_abs(X0),zero_zero(X0)) ) ),
    inference(rectify,[],[f214]) ).

thf(f214,axiom,
    ! [X0: $tType] :
      ( ordere142940540dd_abs(X0)
     => ( zero_zero(X0) = vAPP(X0,X0,abs_abs(X0),zero_zero(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_abs__zero) ).

thf(f3105,plain,
    spl136_105,
    inference(avatar_split_clause,[],[f1520,f3103]) ).

thf(f3103,plain,
    ( spl136_105
  <=> ! [X0: $tType] :
        ( ( zero_zero(X0) = vAPP(X0,X0,uminus_uminus(X0),zero_zero(X0)) )
        | ( group_add(X0) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_105])]) ).

thf(f1520,plain,
    ! [X0: $tType] :
      ( ( zero_zero(X0) = vAPP(X0,X0,uminus_uminus(X0),zero_zero(X0)) )
      | ( group_add(X0) != $true ) ),
    inference(cnf_transformation,[],[f955]) ).

thf(f955,plain,
    ! [X0: $tType] :
      ( ( zero_zero(X0) = vAPP(X0,X0,uminus_uminus(X0),zero_zero(X0)) )
      | ( group_add(X0) != $true ) ),
    inference(ennf_transformation,[],[f442]) ).

thf(f442,plain,
    ! [X0: $tType] :
      ( ( group_add(X0) = $true )
     => ( zero_zero(X0) = vAPP(X0,X0,uminus_uminus(X0),zero_zero(X0)) ) ),
    inference(fool_elimination,[],[f441]) ).

thf(f441,plain,
    ! [X0: $tType] :
      ( group_add(X0)
     => ( zero_zero(X0) = vAPP(X0,X0,uminus_uminus(X0),zero_zero(X0)) ) ),
    inference(rectify,[],[f93]) ).

thf(f93,axiom,
    ! [X0: $tType] :
      ( group_add(X0)
     => ( zero_zero(X0) = vAPP(X0,X0,uminus_uminus(X0),zero_zero(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_add_Oinverse__neutral) ).

thf(f3101,plain,
    spl136_104,
    inference(avatar_split_clause,[],[f1488,f3099]) ).

thf(f3099,plain,
    ( spl136_104
  <=> ! [X0: $tType] :
        ( ( zero_zero(X0) = vAPP(X0,X0,neg_numeral_dbl(X0),zero_zero(X0)) )
        | ( neg_numeral(X0) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_104])]) ).

thf(f1488,plain,
    ! [X0: $tType] :
      ( ( zero_zero(X0) = vAPP(X0,X0,neg_numeral_dbl(X0),zero_zero(X0)) )
      | ( neg_numeral(X0) != $true ) ),
    inference(cnf_transformation,[],[f922]) ).

thf(f922,plain,
    ! [X0: $tType] :
      ( ( zero_zero(X0) = vAPP(X0,X0,neg_numeral_dbl(X0),zero_zero(X0)) )
      | ( neg_numeral(X0) != $true ) ),
    inference(ennf_transformation,[],[f378]) ).

thf(f378,plain,
    ! [X0: $tType] :
      ( ( neg_numeral(X0) = $true )
     => ( zero_zero(X0) = vAPP(X0,X0,neg_numeral_dbl(X0),zero_zero(X0)) ) ),
    inference(fool_elimination,[],[f377]) ).

thf(f377,plain,
    ! [X0: $tType] :
      ( neg_numeral(X0)
     => ( zero_zero(X0) = vAPP(X0,X0,neg_numeral_dbl(X0),zero_zero(X0)) ) ),
    inference(rectify,[],[f164]) ).

thf(f164,axiom,
    ! [X0: $tType] :
      ( neg_numeral(X0)
     => ( zero_zero(X0) = vAPP(X0,X0,neg_numeral_dbl(X0),zero_zero(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_dbl__simps_I2_J) ).

thf(f3093,plain,
    spl136_103,
    inference(avatar_split_clause,[],[f1492,f3091]) ).

thf(f3091,plain,
    ( spl136_103
  <=> ! [X0: $tType,X1: num] :
        ( ( zero_zero(X0) != vAPP(num,X0,numeral_numeral(X0),X1) )
        | ( semiring_char_0(X0) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_103])]) ).

thf(f1492,plain,
    ! [X0: $tType,X1: num] :
      ( ( zero_zero(X0) != vAPP(num,X0,numeral_numeral(X0),X1) )
      | ( semiring_char_0(X0) != $true ) ),
    inference(cnf_transformation,[],[f926]) ).

thf(f926,plain,
    ! [X0: $tType] :
      ( ! [X1: num] : ( zero_zero(X0) != vAPP(num,X0,numeral_numeral(X0),X1) )
      | ( semiring_char_0(X0) != $true ) ),
    inference(ennf_transformation,[],[f386]) ).

thf(f386,plain,
    ! [X0: $tType] :
      ( ( semiring_char_0(X0) = $true )
     => ! [X1: num] : ( zero_zero(X0) != vAPP(num,X0,numeral_numeral(X0),X1) ) ),
    inference(fool_elimination,[],[f385]) ).

thf(f385,plain,
    ! [X0: $tType] :
      ( semiring_char_0(X0)
     => ! [X1: num] : ( zero_zero(X0) != vAPP(num,X0,numeral_numeral(X0),X1) ) ),
    inference(rectify,[],[f72]) ).

thf(f72,axiom,
    ! [X0: $tType] :
      ( semiring_char_0(X0)
     => ! [X36: num] : ( vAPP(num,X0,numeral_numeral(X0),X36) != zero_zero(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_zero__neq__numeral) ).

thf(f3089,plain,
    spl136_102,
    inference(avatar_split_clause,[],[f1446,f3087]) ).

thf(f3087,plain,
    ( spl136_102
  <=> ! [X0: extended_ereal] : ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_102])]) ).

thf(f1446,plain,
    ! [X0: extended_ereal] : ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X0)) = X0 ),
    inference(cnf_transformation,[],[f855]) ).

thf(f855,plain,
    ! [X0: extended_ereal] : ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X0)) = X0 ),
    inference(rectify,[],[f154]) ).

thf(f154,axiom,
    ! [X15: extended_ereal] : ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X15)) = X15 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_ereal__uminus__uminus) ).

thf(f3084,plain,
    spl136_101,
    inference(avatar_split_clause,[],[f1444,f3082]) ).

thf(f3082,plain,
    ( spl136_101
  <=> ! [X0: real] : ( zero_zero(nat) = vAPP(extended_ereal,nat,extended_size_ereal,vAPP(real,extended_ereal,extended_ereal2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_101])]) ).

thf(f1444,plain,
    ! [X0: real] : ( zero_zero(nat) = vAPP(extended_ereal,nat,extended_size_ereal,vAPP(real,extended_ereal,extended_ereal2,X0)) ),
    inference(cnf_transformation,[],[f853]) ).

thf(f853,plain,
    ! [X0: real] : ( zero_zero(nat) = vAPP(extended_ereal,nat,extended_size_ereal,vAPP(real,extended_ereal,extended_ereal2,X0)) ),
    inference(rectify,[],[f199]) ).

thf(f199,axiom,
    ! [X52: real] : ( zero_zero(nat) = vAPP(extended_ereal,nat,extended_size_ereal,vAPP(real,extended_ereal,extended_ereal2,X52)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_ereal_Osize__gen_I1_J) ).

thf(f3076,plain,
    spl136_100,
    inference(avatar_split_clause,[],[f1443,f3074]) ).

thf(f3074,plain,
    ( spl136_100
  <=> ! [X0: real] : ( vAPP(extended_ereal,real,extend1716541707_ereal,vAPP(real,extended_ereal,extended_ereal2,X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_100])]) ).

thf(f1443,plain,
    ! [X0: real] : ( vAPP(extended_ereal,real,extend1716541707_ereal,vAPP(real,extended_ereal,extended_ereal2,X0)) = X0 ),
    inference(cnf_transformation,[],[f852]) ).

thf(f852,plain,
    ! [X0: real] : ( vAPP(extended_ereal,real,extend1716541707_ereal,vAPP(real,extended_ereal,extended_ereal2,X0)) = X0 ),
    inference(rectify,[],[f175]) ).

thf(f175,axiom,
    ! [X41: real] : ( vAPP(extended_ereal,real,extend1716541707_ereal,vAPP(real,extended_ereal,extended_ereal2,X41)) = X41 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_real__of__ereal_Osimps_I1_J) ).

thf(f3072,plain,
    spl136_99,
    inference(avatar_split_clause,[],[f1442,f3070]) ).

thf(f3070,plain,
    ( spl136_99
  <=> ! [X0: nat] : ( vAPP(extended_enat,nat,extended_the_enat,vAPP(nat,extended_enat,extended_enat2,X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_99])]) ).

thf(f1442,plain,
    ! [X0: nat] : ( vAPP(extended_enat,nat,extended_the_enat,vAPP(nat,extended_enat,extended_enat2,X0)) = X0 ),
    inference(cnf_transformation,[],[f851]) ).

thf(f851,plain,
    ! [X0: nat] : ( vAPP(extended_enat,nat,extended_the_enat,vAPP(nat,extended_enat,extended_enat2,X0)) = X0 ),
    inference(rectify,[],[f149]) ).

thf(f149,axiom,
    ! [X36: nat] : ( vAPP(extended_enat,nat,extended_the_enat,vAPP(nat,extended_enat,extended_enat2,X36)) = X36 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_the__enat_Osimps) ).

thf(f3002,plain,
    spl136_98,
    inference(avatar_split_clause,[],[f1711,f3000]) ).

thf(f3000,plain,
    ( spl136_98
  <=> ! [X1: $tType,X0: $tType] :
        ( ( $true = order(sTfun(X0,X1)) )
        | ( $true != order(X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_98])]) ).

thf(f1711,plain,
    ! [X1: $tType,X0: $tType] :
      ( ( $true = order(sTfun(X0,X1)) )
      | ( $true != order(X1) ) ),
    inference(cnf_transformation,[],[f1097]) ).

thf(f1097,plain,
    ! [X0: $tType,X1: $tType] :
      ( ( $true = order(sTfun(X0,X1)) )
      | ( $true != order(X1) ) ),
    inference(ennf_transformation,[],[f684]) ).

thf(f684,plain,
    ! [X0: $tType,X1: $tType] :
      ( ( $true = order(X1) )
     => ( $true = order(sTfun(X0,X1)) ) ),
    inference(fool_elimination,[],[f683]) ).

thf(f683,plain,
    ! [X0: $tType,X1: $tType] :
      ( order(X1)
     => order(sTfun(X0,X1)) ),
    inference(rectify,[],[f258]) ).

thf(f258,axiom,
    ! [X73: $tType,X74: $tType] :
      ( order(X74)
     => order(sTfun(X73,X74)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).

thf(f2998,plain,
    spl136_97,
    inference(avatar_split_clause,[],[f1710,f2996]) ).

thf(f2996,plain,
    ( spl136_97
  <=> ! [X1: $tType,X0: $tType] :
        ( ( $true = ord(sTfun(X0,X1)) )
        | ( $true != ord(X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_97])]) ).

thf(f1710,plain,
    ! [X1: $tType,X0: $tType] :
      ( ( $true = ord(sTfun(X0,X1)) )
      | ( $true != ord(X1) ) ),
    inference(cnf_transformation,[],[f1096]) ).

thf(f1096,plain,
    ! [X0: $tType,X1: $tType] :
      ( ( $true = ord(sTfun(X0,X1)) )
      | ( $true != ord(X1) ) ),
    inference(ennf_transformation,[],[f682]) ).

thf(f682,plain,
    ! [X0: $tType,X1: $tType] :
      ( ( $true = ord(X1) )
     => ( $true = ord(sTfun(X0,X1)) ) ),
    inference(fool_elimination,[],[f681]) ).

thf(f681,plain,
    ! [X0: $tType,X1: $tType] :
      ( ord(X1)
     => ord(sTfun(X0,X1)) ),
    inference(rectify,[],[f259]) ).

thf(f259,axiom,
    ! [X73: $tType,X74: $tType] :
      ( ord(X74)
     => ord(sTfun(X73,X74)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).

thf(f2994,plain,
    spl136_96,
    inference(avatar_split_clause,[],[f1705,f2992]) ).

thf(f2992,plain,
    ( spl136_96
  <=> ! [X1: $tType,X0: $tType] :
        ( ( $true = preorder(sTfun(X0,X1)) )
        | ( $true != preorder(X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_96])]) ).

thf(f1705,plain,
    ! [X1: $tType,X0: $tType] :
      ( ( $true = preorder(sTfun(X0,X1)) )
      | ( $true != preorder(X1) ) ),
    inference(cnf_transformation,[],[f1091]) ).

thf(f1091,plain,
    ! [X0: $tType,X1: $tType] :
      ( ( $true = preorder(sTfun(X0,X1)) )
      | ( $true != preorder(X1) ) ),
    inference(ennf_transformation,[],[f672]) ).

thf(f672,plain,
    ! [X0: $tType,X1: $tType] :
      ( ( $true = preorder(X1) )
     => ( $true = preorder(sTfun(X0,X1)) ) ),
    inference(fool_elimination,[],[f671]) ).

thf(f671,plain,
    ! [X0: $tType,X1: $tType] :
      ( preorder(X1)
     => preorder(sTfun(X0,X1)) ),
    inference(rectify,[],[f257]) ).

thf(f257,axiom,
    ! [X73: $tType,X74: $tType] :
      ( preorder(X74)
     => preorder(sTfun(X73,X74)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).

thf(f2990,plain,
    spl136_95,
    inference(avatar_split_clause,[],[f1704,f2988]) ).

thf(f1704,plain,
    ! [X1: $tType,X0: $tType] :
      ( ( $true = topolo503727757_space(sTfun(X0,X1)) )
      | ( $true != topolo503727757_space(X1) ) ),
    inference(cnf_transformation,[],[f1090]) ).

thf(f1090,plain,
    ! [X0: $tType,X1: $tType] :
      ( ( $true = topolo503727757_space(sTfun(X0,X1)) )
      | ( $true != topolo503727757_space(X1) ) ),
    inference(ennf_transformation,[],[f670]) ).

thf(f670,plain,
    ! [X0: $tType,X1: $tType] :
      ( ( $true = topolo503727757_space(X1) )
     => ( $true = topolo503727757_space(sTfun(X0,X1)) ) ),
    inference(fool_elimination,[],[f669]) ).

thf(f669,plain,
    ! [X0: $tType,X1: $tType] :
      ( topolo503727757_space(X1)
     => topolo503727757_space(sTfun(X0,X1)) ),
    inference(rectify,[],[f255]) ).

thf(f255,axiom,
    ! [X73: $tType,X74: $tType] :
      ( topolo503727757_space(X74)
     => topolo503727757_space(sTfun(X73,X74)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Topological__Spaces_Otopological__space) ).

thf(f2986,plain,
    spl136_94,
    inference(avatar_split_clause,[],[f1703,f2984]) ).

thf(f1703,plain,
    ! [X1: $tType,X0: $tType] :
      ( ( $true = boolean_algebra(sTfun(X0,X1)) )
      | ( $true != boolean_algebra(X1) ) ),
    inference(cnf_transformation,[],[f1089]) ).

thf(f1089,plain,
    ! [X0: $tType,X1: $tType] :
      ( ( $true = boolean_algebra(sTfun(X0,X1)) )
      | ( $true != boolean_algebra(X1) ) ),
    inference(ennf_transformation,[],[f668]) ).

thf(f668,plain,
    ! [X0: $tType,X1: $tType] :
      ( ( $true = boolean_algebra(X1) )
     => ( $true = boolean_algebra(sTfun(X0,X1)) ) ),
    inference(fool_elimination,[],[f667]) ).

thf(f667,plain,
    ! [X0: $tType,X1: $tType] :
      ( boolean_algebra(X1)
     => boolean_algebra(sTfun(X0,X1)) ),
    inference(rectify,[],[f256]) ).

thf(f256,axiom,
    ! [X73: $tType,X74: $tType] :
      ( boolean_algebra(X74)
     => boolean_algebra(sTfun(X73,X74)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Oboolean__algebra) ).

thf(f2982,plain,
    spl136_93,
    inference(avatar_split_clause,[],[f1702,f2980]) ).

thf(f1702,plain,
    ! [X1: $tType,X0: $tType] :
      ( ( $true = uminus(sTfun(X0,X1)) )
      | ( $true != uminus(X1) ) ),
    inference(cnf_transformation,[],[f1088]) ).

thf(f1088,plain,
    ! [X0: $tType,X1: $tType] :
      ( ( $true = uminus(sTfun(X0,X1)) )
      | ( $true != uminus(X1) ) ),
    inference(ennf_transformation,[],[f666]) ).

thf(f666,plain,
    ! [X0: $tType,X1: $tType] :
      ( ( $true = uminus(X1) )
     => ( $true = uminus(sTfun(X0,X1)) ) ),
    inference(fool_elimination,[],[f665]) ).

thf(f665,plain,
    ! [X0: $tType,X1: $tType] :
      ( uminus(X1)
     => uminus(sTfun(X0,X1)) ),
    inference(rectify,[],[f260]) ).

thf(f260,axiom,
    ! [X73: $tType,X74: $tType] :
      ( uminus(X74)
     => uminus(sTfun(X73,X74)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Groups_Ouminus) ).

thf(f2978,plain,
    spl136_92,
    inference(avatar_split_clause,[],[f1431,f2975]) ).

thf(f2975,plain,
    ( spl136_92
  <=> ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),zero_zero(extended_ereal)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_92])]) ).

thf(f1431,plain,
    zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),zero_zero(extended_ereal)),
    inference(cnf_transformation,[],[f84]) ).

thf(f84,axiom,
    zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),zero_zero(extended_ereal)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_ereal__uminus__zero) ).

thf(f2973,plain,
    spl136_91,
    inference(avatar_split_clause,[],[f1430,f2970]) ).

thf(f2970,plain,
    ( spl136_91
  <=> ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),zero_zero(extended_ereal)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_91])]) ).

thf(f1430,plain,
    zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),zero_zero(extended_ereal)),
    inference(cnf_transformation,[],[f220]) ).

thf(f220,axiom,
    zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),zero_zero(extended_ereal)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_abs__ereal__zero) ).

thf(f2968,plain,
    ( spl136_90
    | ~ spl136_3
    | ~ spl136_80 ),
    inference(avatar_split_clause,[],[f2936,f2899,f2488,f2965]) ).

thf(f2965,plain,
    ( spl136_90
  <=> ( $true = topolo503727757_space(a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_90])]) ).

thf(f2488,plain,
    ( spl136_3
  <=> ( real_V2090557954_space(a) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_3])]) ).

thf(f2899,plain,
    ( spl136_80
  <=> ! [X0: $tType] :
        ( ( topolo503727757_space(X0) = $true )
        | ( real_V2090557954_space(X0) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_80])]) ).

thf(f2936,plain,
    ( ( $true = topolo503727757_space(a) )
    | ~ spl136_3
    | ~ spl136_80 ),
    inference(trivial_inequality_removal,[],[f2931]) ).

thf(f2931,plain,
    ( ( $true != $true )
    | ( $true = topolo503727757_space(a) )
    | ~ spl136_3
    | ~ spl136_80 ),
    inference(superposition,[],[f2900,f2490]) ).

thf(f2490,plain,
    ( ( real_V2090557954_space(a) = $true )
    | ~ spl136_3 ),
    inference(avatar_component_clause,[],[f2488]) ).

thf(f2900,plain,
    ( ! [X0: $tType] :
        ( ( real_V2090557954_space(X0) != $true )
        | ( topolo503727757_space(X0) = $true ) )
    | ~ spl136_80 ),
    inference(avatar_component_clause,[],[f2899]) ).

thf(f2961,plain,
    spl136_89,
    inference(avatar_split_clause,[],[f1426,f2958]) ).

thf(f2958,plain,
    ( spl136_89
  <=> ( zero_zero(extended_ereal) = vAPP(real,extended_ereal,extended_ereal2,zero_zero(real)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_89])]) ).

thf(f1426,plain,
    zero_zero(extended_ereal) = vAPP(real,extended_ereal,extended_ereal2,zero_zero(real)),
    inference(cnf_transformation,[],[f178]) ).

thf(f178,axiom,
    zero_zero(extended_ereal) = vAPP(real,extended_ereal,extended_ereal2,zero_zero(real)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_zero__ereal__def) ).

thf(f2956,plain,
    spl136_88,
    inference(avatar_split_clause,[],[f1425,f2953]) ).

thf(f2953,plain,
    ( spl136_88
  <=> ( zero_zero(extended_ereal) = vAPP(extended_enat,extended_ereal,extend1771934483f_enat,zero_zero(extended_enat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_88])]) ).

thf(f1425,plain,
    zero_zero(extended_ereal) = vAPP(extended_enat,extended_ereal,extend1771934483f_enat,zero_zero(extended_enat)),
    inference(cnf_transformation,[],[f54]) ).

thf(f54,axiom,
    zero_zero(extended_ereal) = vAPP(extended_enat,extended_ereal,extend1771934483f_enat,zero_zero(extended_enat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_ereal__of__enat__zero) ).

thf(f2951,plain,
    spl136_87,
    inference(avatar_split_clause,[],[f1423,f2948]) ).

thf(f2948,plain,
    ( spl136_87
  <=> ( zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,zero_zero(extended_ereal)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_87])]) ).

thf(f1423,plain,
    zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,zero_zero(extended_ereal)),
    inference(cnf_transformation,[],[f102]) ).

thf(f102,axiom,
    zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,zero_zero(extended_ereal)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_real__of__ereal__0) ).

thf(f2946,plain,
    spl136_86,
    inference(avatar_split_clause,[],[f1422,f2943]) ).

thf(f2943,plain,
    ( spl136_86
  <=> ( zero_zero(extended_enat) = vAPP(nat,extended_enat,extended_enat2,zero_zero(nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_86])]) ).

thf(f1422,plain,
    zero_zero(extended_enat) = vAPP(nat,extended_enat,extended_enat2,zero_zero(nat)),
    inference(cnf_transformation,[],[f115]) ).

thf(f115,axiom,
    zero_zero(extended_enat) = vAPP(nat,extended_enat,extended_enat2,zero_zero(nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_zero__enat__def) ).

thf(f2941,plain,
    ( spl136_85
    | ~ spl136_3
    | ~ spl136_79 ),
    inference(avatar_split_clause,[],[f2930,f2895,f2488,f2938]) ).

thf(f2938,plain,
    ( spl136_85
  <=> ( $true = type(a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_85])]) ).

thf(f2930,plain,
    ( ( $true = type(a) )
    | ~ spl136_3
    | ~ spl136_79 ),
    inference(trivial_inequality_removal,[],[f2925]) ).

thf(f2925,plain,
    ( ( $true != $true )
    | ( $true = type(a) )
    | ~ spl136_3
    | ~ spl136_79 ),
    inference(superposition,[],[f2896,f2490]) ).

thf(f2924,plain,
    spl136_84,
    inference(avatar_split_clause,[],[f2253,f2921]) ).

thf(f2921,plain,
    ( spl136_84
  <=> ( extended_PInfty = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),extended_MInfty) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_84])]) ).

thf(f2253,plain,
    extended_PInfty = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),extended_MInfty),
    inference(forward_demodulation,[],[f2252,f1419]) ).

thf(f2252,plain,
    extended_PInfty = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty)),
    inference(forward_demodulation,[],[f1434,f1416]) ).

thf(f1434,plain,
    extend1396239628finity(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))),
    inference(cnf_transformation,[],[f233]) ).

thf(f233,axiom,
    extend1396239628finity(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_abs__ereal_Osimps_I2_J) ).

thf(f2919,plain,
    spl136_83,
    inference(avatar_split_clause,[],[f2251,f2916]) ).

thf(f2916,plain,
    ( spl136_83
  <=> ( zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,extended_MInfty) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_83])]) ).

thf(f2251,plain,
    zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,extended_MInfty),
    inference(forward_demodulation,[],[f2250,f1419]) ).

thf(f2250,plain,
    zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty)),
    inference(forward_demodulation,[],[f1433,f1416]) ).

thf(f1433,plain,
    zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))),
    inference(cnf_transformation,[],[f104]) ).

thf(f104,axiom,
    zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_real__of__ereal_Osimps_I3_J) ).

thf(f2911,plain,
    spl136_82,
    inference(avatar_split_clause,[],[f2249,f2908]) ).

thf(f2908,plain,
    ( spl136_82
  <=> ( extended_PInfty = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),extended_PInfty) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_82])]) ).

thf(f2249,plain,
    extended_PInfty = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),extended_PInfty),
    inference(forward_demodulation,[],[f1432,f1416]) ).

thf(f1432,plain,
    extend1396239628finity(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),extend1396239628finity(extended_ereal)),
    inference(cnf_transformation,[],[f245]) ).

thf(f245,axiom,
    extend1396239628finity(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),extend1396239628finity(extended_ereal)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_abs__ereal_Osimps_I3_J) ).

thf(f2906,plain,
    spl136_81,
    inference(avatar_split_clause,[],[f2243,f2903]) ).

thf(f2903,plain,
    ( spl136_81
  <=> ( zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,extended_PInfty) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_81])]) ).

thf(f2243,plain,
    zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,extended_PInfty),
    inference(forward_demodulation,[],[f1424,f1416]) ).

thf(f1424,plain,
    zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,extend1396239628finity(extended_ereal)),
    inference(cnf_transformation,[],[f109]) ).

thf(f109,axiom,
    zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,extend1396239628finity(extended_ereal)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_real__of__ereal_Osimps_I2_J) ).

thf(f2901,plain,
    spl136_80,
    inference(avatar_split_clause,[],[f1519,f2899]) ).

thf(f1519,plain,
    ! [X0: $tType] :
      ( ( topolo503727757_space(X0) = $true )
      | ( real_V2090557954_space(X0) != $true ) ),
    inference(cnf_transformation,[],[f954]) ).

thf(f954,plain,
    ! [X0: $tType] :
      ( ( topolo503727757_space(X0) = $true )
      | ( real_V2090557954_space(X0) != $true ) ),
    inference(ennf_transformation,[],[f440]) ).

thf(f440,plain,
    ! [X0: $tType] :
      ( ( real_V2090557954_space(X0) = $true )
     => ( topolo503727757_space(X0) = $true ) ),
    inference(fool_elimination,[],[f439]) ).

thf(f439,plain,
    ! [X0: $tType] :
      ( real_V2090557954_space(X0)
     => topolo503727757_space(X0) ),
    inference(rectify,[],[f254]) ).

thf(f254,axiom,
    ! [X0: $tType] :
      ( real_V2090557954_space(X0)
     => topolo503727757_space(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Real__Vector__Spaces_Ometric__space___Topological__Spaces_Otopological__space) ).

thf(f2897,plain,
    spl136_79,
    inference(avatar_split_clause,[],[f1518,f2895]) ).

thf(f1518,plain,
    ! [X0: $tType] :
      ( ( type(X0) = $true )
      | ( real_V2090557954_space(X0) != $true ) ),
    inference(cnf_transformation,[],[f953]) ).

thf(f953,plain,
    ! [X0: $tType] :
      ( ( type(X0) = $true )
      | ( real_V2090557954_space(X0) != $true ) ),
    inference(ennf_transformation,[],[f438]) ).

thf(f438,plain,
    ! [X0: $tType] :
      ( ( real_V2090557954_space(X0) = $true )
     => ( type(X0) = $true ) ),
    inference(fool_elimination,[],[f437]) ).

thf(f437,plain,
    ! [X0: $tType] :
      ( real_V2090557954_space(X0)
     => type(X0) ),
    inference(rectify,[],[f253]) ).

thf(f253,axiom,
    ! [X0: $tType] :
      ( real_V2090557954_space(X0)
     => type(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Real__Vector__Spaces_Ometric__space___HOL_Otype) ).

thf(f2893,plain,
    spl136_78,
    inference(avatar_split_clause,[],[f1421,f2890]) ).

thf(f2890,plain,
    ( spl136_78
  <=> ( zero_zero(nat) = vAPP(extended_ereal,nat,extended_size_ereal,extended_PInfty) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_78])]) ).

thf(f1421,plain,
    zero_zero(nat) = vAPP(extended_ereal,nat,extended_size_ereal,extended_PInfty),
    inference(cnf_transformation,[],[f202]) ).

thf(f202,axiom,
    zero_zero(nat) = vAPP(extended_ereal,nat,extended_size_ereal,extended_PInfty),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_ereal_Osize__gen_I2_J) ).

thf(f2888,plain,
    spl136_77,
    inference(avatar_split_clause,[],[f1420,f2885]) ).

thf(f2885,plain,
    ( spl136_77
  <=> ( zero_zero(nat) = vAPP(extended_ereal,nat,extended_size_ereal,extended_MInfty) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_77])]) ).

thf(f1420,plain,
    zero_zero(nat) = vAPP(extended_ereal,nat,extended_size_ereal,extended_MInfty),
    inference(cnf_transformation,[],[f198]) ).

thf(f198,axiom,
    zero_zero(nat) = vAPP(extended_ereal,nat,extended_size_ereal,extended_MInfty),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_ereal_Osize__gen_I3_J) ).

thf(f2883,plain,
    spl136_76,
    inference(avatar_split_clause,[],[f1419,f2880]) ).

thf(f2880,plain,
    ( spl136_76
  <=> ( extended_MInfty = vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_76])]) ).

thf(f2878,plain,
    spl136_75,
    inference(avatar_split_clause,[],[f1418,f2875]) ).

thf(f2875,plain,
    ( spl136_75
  <=> ( extended_PInfty = vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_MInfty) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_75])]) ).

thf(f1418,plain,
    extended_PInfty = vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_MInfty),
    inference(cnf_transformation,[],[f210]) ).

thf(f210,axiom,
    extended_PInfty = vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_MInfty),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_uminus__ereal_Osimps_I3_J) ).

thf(f2873,plain,
    ( spl136_74
    | spl136_70
    | ~ spl136_71 ),
    inference(avatar_split_clause,[],[f2842,f2828,f2823,f2870]) ).

thf(f2828,plain,
    ( spl136_71
  <=> ! [X0: $o] :
        ( ( $true = X0 )
        | ( $false = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_71])]) ).

thf(f2842,plain,
    ( ( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)) = $false )
    | spl136_70
    | ~ spl136_71 ),
    inference(trivial_inequality_removal,[],[f2840]) ).

thf(f2840,plain,
    ( ( $true != $true )
    | ( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)) = $false )
    | spl136_70
    | ~ spl136_71 ),
    inference(superposition,[],[f2825,f2829]) ).

thf(f2829,plain,
    ( ! [X0: $o] :
        ( ( $true = X0 )
        | ( $false = X0 ) )
    | ~ spl136_71 ),
    inference(avatar_component_clause,[],[f2828]) ).

thf(f2868,plain,
    spl136_73,
    inference(avatar_split_clause,[],[f1440,f2866]) ).

thf(f2866,plain,
    ( spl136_73
  <=> ! [X0: real] : ( extended_PInfty != vAPP(real,extended_ereal,extended_ereal2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_73])]) ).

thf(f1440,plain,
    ! [X0: real] : ( extended_PInfty != vAPP(real,extended_ereal,extended_ereal2,X0) ),
    inference(cnf_transformation,[],[f849]) ).

thf(f849,plain,
    ! [X0: real] : ( extended_PInfty != vAPP(real,extended_ereal,extended_ereal2,X0) ),
    inference(rectify,[],[f201]) ).

thf(f201,axiom,
    ! [X52: real] : ( vAPP(real,extended_ereal,extended_ereal2,X52) != extended_PInfty ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_ereal_Odistinct_I1_J) ).

thf(f2864,plain,
    spl136_72,
    inference(avatar_split_clause,[],[f1439,f2862]) ).

thf(f2862,plain,
    ( spl136_72
  <=> ! [X0: real] : ( extended_MInfty != vAPP(real,extended_ereal,extended_ereal2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_72])]) ).

thf(f1439,plain,
    ! [X0: real] : ( extended_MInfty != vAPP(real,extended_ereal,extended_ereal2,X0) ),
    inference(cnf_transformation,[],[f848]) ).

thf(f848,plain,
    ! [X0: real] : ( extended_MInfty != vAPP(real,extended_ereal,extended_ereal2,X0) ),
    inference(rectify,[],[f174]) ).

thf(f174,axiom,
    ! [X52: real] : ( extended_MInfty != vAPP(real,extended_ereal,extended_ereal2,X52) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_ereal_Odistinct_I3_J) ).

thf(f2830,plain,
    spl136_71,
    inference(avatar_split_clause,[],[f328,f2828]) ).

thf(f328,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( $false = X0 ) ),
    introduced(fool_axiom,[]) ).

thf(f2826,plain,
    ~ spl136_70,
    inference(avatar_split_clause,[],[f1413,f2823]) ).

thf(f1413,plain,
    vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)) != $true,
    inference(cnf_transformation,[],[f847]) ).

thf(f847,plain,
    vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)) != $true,
    inference(flattening,[],[f330]) ).

thf(f330,plain,
    vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)) != $true,
    inference(fool_elimination,[],[f329]) ).

thf(f329,plain,
    ~ vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)),
    inference(rectify,[],[f326]) ).

thf(f326,negated_conjecture,
    ~ vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)),
    inference(negated_conjecture,[],[f325]) ).

thf(f325,conjecture,
    vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(f2821,plain,
    ~ spl136_69,
    inference(avatar_split_clause,[],[f2246,f2818]) ).

thf(f2818,plain,
    ( spl136_69
  <=> ( zero_zero(extended_ereal) = extended_MInfty ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_69])]) ).

thf(f2246,plain,
    zero_zero(extended_ereal) != extended_MInfty,
    inference(forward_demodulation,[],[f2245,f1419]) ).

thf(f2245,plain,
    zero_zero(extended_ereal) != vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty),
    inference(forward_demodulation,[],[f1428,f1416]) ).

thf(f1428,plain,
    zero_zero(extended_ereal) != vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)),
    inference(cnf_transformation,[],[f127]) ).

thf(f127,axiom,
    zero_zero(extended_ereal) != vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_Infty__neq__0_I3_J) ).

thf(f2816,plain,
    ~ spl136_68,
    inference(avatar_split_clause,[],[f2242,f2813]) ).

thf(f2813,plain,
    ( spl136_68
  <=> ( zero_zero(extended_ereal) = extended_PInfty ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_68])]) ).

thf(f2242,plain,
    zero_zero(extended_ereal) != extended_PInfty,
    inference(forward_demodulation,[],[f1417,f1416]) ).

thf(f1417,plain,
    zero_zero(extended_ereal) != extend1396239628finity(extended_ereal),
    inference(cnf_transformation,[],[f56]) ).

thf(f56,axiom,
    zero_zero(extended_ereal) != extend1396239628finity(extended_ereal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Infty__neq__0_I1_J) ).

thf(f2811,plain,
    spl136_67,
    inference(avatar_split_clause,[],[f1880,f2808]) ).

thf(f2808,plain,
    ( spl136_67
  <=> ( order(extended_ereal) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_67])]) ).

thf(f1880,plain,
    order(extended_ereal) = $true,
    inference(cnf_transformation,[],[f844]) ).

thf(f844,plain,
    order(extended_ereal) = $true,
    inference(fool_elimination,[],[f843]) ).

thf(f843,plain,
    order(extended_ereal),
    inference(rectify,[],[f319]) ).

thf(f319,axiom,
    order(extended_ereal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Orderings_Oorder_43) ).

thf(f2806,plain,
    spl136_66,
    inference(avatar_split_clause,[],[f1879,f2803]) ).

thf(f2803,plain,
    ( spl136_66
  <=> ( order($o) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_66])]) ).

thf(f1879,plain,
    order($o) = $true,
    inference(cnf_transformation,[],[f842]) ).

thf(f842,plain,
    order($o) = $true,
    inference(fool_elimination,[],[f841]) ).

thf(f841,plain,
    order($o),
    inference(rectify,[],[f281]) ).

thf(f281,axiom,
    order($o),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_14) ).

thf(f2801,plain,
    spl136_65,
    inference(avatar_split_clause,[],[f1878,f2798]) ).

thf(f2798,plain,
    ( spl136_65
  <=> ( order(real) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_65])]) ).

thf(f1878,plain,
    order(real) = $true,
    inference(cnf_transformation,[],[f840]) ).

thf(f840,plain,
    order(real) = $true,
    inference(fool_elimination,[],[f839]) ).

thf(f839,plain,
    order(real),
    inference(rectify,[],[f297]) ).

thf(f297,axiom,
    order(real),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Oorder_23) ).

thf(f2796,plain,
    spl136_64,
    inference(avatar_split_clause,[],[f1877,f2793]) ).

thf(f2793,plain,
    ( spl136_64
  <=> ( order(nat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_64])]) ).

thf(f1877,plain,
    order(nat) = $true,
    inference(cnf_transformation,[],[f838]) ).

thf(f838,plain,
    order(nat) = $true,
    inference(fool_elimination,[],[f837]) ).

thf(f837,plain,
    order(nat),
    inference(rectify,[],[f268]) ).

thf(f268,axiom,
    order(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_3) ).

thf(f2791,plain,
    spl136_63,
    inference(avatar_split_clause,[],[f1876,f2788]) ).

thf(f2788,plain,
    ( spl136_63
  <=> ( order(extended_enat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_63])]) ).

thf(f1876,plain,
    order(extended_enat) = $true,
    inference(cnf_transformation,[],[f836]) ).

thf(f836,plain,
    order(extended_enat) = $true,
    inference(fool_elimination,[],[f835]) ).

thf(f835,plain,
    order(extended_enat),
    inference(rectify,[],[f311]) ).

thf(f311,axiom,
    order(extended_enat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Oorder_35) ).

thf(f2786,plain,
    spl136_62,
    inference(avatar_split_clause,[],[f1875,f2783]) ).

thf(f2783,plain,
    ( spl136_62
  <=> ( order(num) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_62])]) ).

thf(f1875,plain,
    order(num) = $true,
    inference(cnf_transformation,[],[f834]) ).

thf(f834,plain,
    order(num) = $true,
    inference(fool_elimination,[],[f833]) ).

thf(f833,plain,
    order(num),
    inference(rectify,[],[f274]) ).

thf(f274,axiom,
    order(num),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Oorder_7) ).

thf(f2781,plain,
    spl136_61,
    inference(avatar_split_clause,[],[f1874,f2778]) ).

thf(f2778,plain,
    ( spl136_61
  <=> ( ord(extended_ereal) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_61])]) ).

thf(f1874,plain,
    ord(extended_ereal) = $true,
    inference(cnf_transformation,[],[f832]) ).

thf(f832,plain,
    ord(extended_ereal) = $true,
    inference(fool_elimination,[],[f831]) ).

thf(f831,plain,
    ord(extended_ereal),
    inference(rectify,[],[f320]) ).

thf(f320,axiom,
    ord(extended_ereal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Orderings_Oord_44) ).

thf(f2776,plain,
    spl136_60,
    inference(avatar_split_clause,[],[f1873,f2773]) ).

thf(f2773,plain,
    ( spl136_60
  <=> ( ord($o) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_60])]) ).

thf(f1873,plain,
    ord($o) = $true,
    inference(cnf_transformation,[],[f830]) ).

thf(f830,plain,
    ord($o) = $true,
    inference(fool_elimination,[],[f829]) ).

thf(f829,plain,
    ord($o),
    inference(rectify,[],[f282]) ).

thf(f282,axiom,
    ord($o),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_15) ).

thf(f2771,plain,
    spl136_59,
    inference(avatar_split_clause,[],[f1872,f2768]) ).

thf(f2768,plain,
    ( spl136_59
  <=> ( ord(real) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_59])]) ).

thf(f1872,plain,
    ord(real) = $true,
    inference(cnf_transformation,[],[f828]) ).

thf(f828,plain,
    ord(real) = $true,
    inference(fool_elimination,[],[f827]) ).

thf(f827,plain,
    ord(real),
    inference(rectify,[],[f300]) ).

thf(f300,axiom,
    ord(real),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Oord_24) ).

thf(f2766,plain,
    spl136_58,
    inference(avatar_split_clause,[],[f1871,f2763]) ).

thf(f2763,plain,
    ( spl136_58
  <=> ( ord(nat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_58])]) ).

thf(f1871,plain,
    ord(nat) = $true,
    inference(cnf_transformation,[],[f826]) ).

thf(f826,plain,
    ord(nat) = $true,
    inference(fool_elimination,[],[f825]) ).

thf(f825,plain,
    ord(nat),
    inference(rectify,[],[f269]) ).

thf(f269,axiom,
    ord(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_4) ).

thf(f2761,plain,
    spl136_57,
    inference(avatar_split_clause,[],[f1870,f2758]) ).

thf(f2758,plain,
    ( spl136_57
  <=> ( ord(extended_enat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_57])]) ).

thf(f1870,plain,
    ord(extended_enat) = $true,
    inference(cnf_transformation,[],[f824]) ).

thf(f824,plain,
    ord(extended_enat) = $true,
    inference(fool_elimination,[],[f823]) ).

thf(f823,plain,
    ord(extended_enat),
    inference(rectify,[],[f312]) ).

thf(f312,axiom,
    ord(extended_enat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Oord_36) ).

thf(f2756,plain,
    spl136_56,
    inference(avatar_split_clause,[],[f1869,f2753]) ).

thf(f2753,plain,
    ( spl136_56
  <=> ( ord(num) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_56])]) ).

thf(f1869,plain,
    ord(num) = $true,
    inference(cnf_transformation,[],[f822]) ).

thf(f822,plain,
    ord(num) = $true,
    inference(fool_elimination,[],[f821]) ).

thf(f821,plain,
    ord(num),
    inference(rectify,[],[f275]) ).

thf(f275,axiom,
    ord(num),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Oord_8) ).

thf(f2751,plain,
    spl136_55,
    inference(avatar_split_clause,[],[f1868,f2748]) ).

thf(f2748,plain,
    ( spl136_55
  <=> ( ordere142940540dd_abs(real) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_55])]) ).

thf(f1868,plain,
    ordere142940540dd_abs(real) = $true,
    inference(cnf_transformation,[],[f820]) ).

thf(f820,plain,
    ordere142940540dd_abs(real) = $true,
    inference(fool_elimination,[],[f819]) ).

thf(f819,plain,
    ordere142940540dd_abs(real),
    inference(rectify,[],[f288]) ).

thf(f288,axiom,
    ordere142940540dd_abs(real),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__group__add__abs) ).

thf(f2746,plain,
    spl136_54,
    inference(avatar_split_clause,[],[f1867,f2743]) ).

thf(f2743,plain,
    ( spl136_54
  <=> ( linorder(extended_ereal) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_54])]) ).

thf(f1867,plain,
    linorder(extended_ereal) = $true,
    inference(cnf_transformation,[],[f818]) ).

thf(f818,plain,
    linorder(extended_ereal) = $true,
    inference(fool_elimination,[],[f817]) ).

thf(f817,plain,
    linorder(extended_ereal),
    inference(rectify,[],[f318]) ).

thf(f318,axiom,
    linorder(extended_ereal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Orderings_Olinorder_42) ).

thf(f2741,plain,
    spl136_53,
    inference(avatar_split_clause,[],[f1866,f2738]) ).

thf(f2738,plain,
    ( spl136_53
  <=> ( linorder($o) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_53])]) ).

thf(f1866,plain,
    linorder($o) = $true,
    inference(cnf_transformation,[],[f816]) ).

thf(f816,plain,
    linorder($o) = $true,
    inference(fool_elimination,[],[f815]) ).

thf(f815,plain,
    linorder($o),
    inference(rectify,[],[f280]) ).

thf(f280,axiom,
    linorder($o),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_13) ).

thf(f2736,plain,
    spl136_52,
    inference(avatar_split_clause,[],[f1865,f2733]) ).

thf(f2733,plain,
    ( spl136_52
  <=> ( linorder(real) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_52])]) ).

thf(f1865,plain,
    linorder(real) = $true,
    inference(cnf_transformation,[],[f814]) ).

thf(f814,plain,
    linorder(real) = $true,
    inference(fool_elimination,[],[f813]) ).

thf(f813,plain,
    linorder(real),
    inference(rectify,[],[f295]) ).

thf(f295,axiom,
    linorder(real),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Olinorder_22) ).

thf(f2731,plain,
    spl136_51,
    inference(avatar_split_clause,[],[f1864,f2728]) ).

thf(f2728,plain,
    ( spl136_51
  <=> ( linorder(nat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_51])]) ).

thf(f1864,plain,
    linorder(nat) = $true,
    inference(cnf_transformation,[],[f812]) ).

thf(f812,plain,
    linorder(nat) = $true,
    inference(fool_elimination,[],[f811]) ).

thf(f811,plain,
    linorder(nat),
    inference(rectify,[],[f267]) ).

thf(f267,axiom,
    linorder(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).

thf(f2726,plain,
    spl136_50,
    inference(avatar_split_clause,[],[f1863,f2723]) ).

thf(f2723,plain,
    ( spl136_50
  <=> ( linorder(extended_enat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_50])]) ).

thf(f1863,plain,
    linorder(extended_enat) = $true,
    inference(cnf_transformation,[],[f810]) ).

thf(f810,plain,
    linorder(extended_enat) = $true,
    inference(fool_elimination,[],[f809]) ).

thf(f809,plain,
    linorder(extended_enat),
    inference(rectify,[],[f310]) ).

thf(f310,axiom,
    linorder(extended_enat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Olinorder_34) ).

thf(f2721,plain,
    spl136_49,
    inference(avatar_split_clause,[],[f1862,f2718]) ).

thf(f2718,plain,
    ( spl136_49
  <=> ( linorder(num) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_49])]) ).

thf(f1862,plain,
    linorder(num) = $true,
    inference(cnf_transformation,[],[f808]) ).

thf(f808,plain,
    linorder(num) = $true,
    inference(fool_elimination,[],[f807]) ).

thf(f807,plain,
    linorder(num),
    inference(rectify,[],[f273]) ).

thf(f273,axiom,
    linorder(num),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Olinorder_6) ).

thf(f2716,plain,
    spl136_48,
    inference(avatar_split_clause,[],[f1861,f2713]) ).

thf(f2713,plain,
    ( spl136_48
  <=> ( preorder(extended_ereal) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_48])]) ).

thf(f1861,plain,
    preorder(extended_ereal) = $true,
    inference(cnf_transformation,[],[f806]) ).

thf(f806,plain,
    preorder(extended_ereal) = $true,
    inference(fool_elimination,[],[f805]) ).

thf(f805,plain,
    preorder(extended_ereal),
    inference(rectify,[],[f317]) ).

thf(f317,axiom,
    preorder(extended_ereal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Orderings_Opreorder_41) ).

thf(f2711,plain,
    spl136_47,
    inference(avatar_split_clause,[],[f1860,f2708]) ).

thf(f2708,plain,
    ( spl136_47
  <=> ( preorder($o) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_47])]) ).

thf(f1860,plain,
    preorder($o) = $true,
    inference(cnf_transformation,[],[f804]) ).

thf(f804,plain,
    preorder($o) = $true,
    inference(fool_elimination,[],[f803]) ).

thf(f803,plain,
    preorder($o),
    inference(rectify,[],[f279]) ).

thf(f279,axiom,
    preorder($o),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_12) ).

thf(f2706,plain,
    spl136_46,
    inference(avatar_split_clause,[],[f1859,f2703]) ).

thf(f2703,plain,
    ( spl136_46
  <=> ( preorder(real) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_46])]) ).

thf(f1859,plain,
    preorder(real) = $true,
    inference(cnf_transformation,[],[f802]) ).

thf(f802,plain,
    preorder(real) = $true,
    inference(fool_elimination,[],[f801]) ).

thf(f801,plain,
    preorder(real),
    inference(rectify,[],[f294]) ).

thf(f294,axiom,
    preorder(real),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Opreorder_21) ).

thf(f2701,plain,
    spl136_45,
    inference(avatar_split_clause,[],[f1858,f2698]) ).

thf(f2698,plain,
    ( spl136_45
  <=> ( preorder(nat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_45])]) ).

thf(f1858,plain,
    preorder(nat) = $true,
    inference(cnf_transformation,[],[f800]) ).

thf(f800,plain,
    preorder(nat) = $true,
    inference(fool_elimination,[],[f799]) ).

thf(f799,plain,
    preorder(nat),
    inference(rectify,[],[f266]) ).

thf(f266,axiom,
    preorder(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_2) ).

thf(f2696,plain,
    spl136_44,
    inference(avatar_split_clause,[],[f1857,f2693]) ).

thf(f2693,plain,
    ( spl136_44
  <=> ( preorder(extended_enat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_44])]) ).

thf(f1857,plain,
    preorder(extended_enat) = $true,
    inference(cnf_transformation,[],[f798]) ).

thf(f798,plain,
    preorder(extended_enat) = $true,
    inference(fool_elimination,[],[f797]) ).

thf(f797,plain,
    preorder(extended_enat),
    inference(rectify,[],[f309]) ).

thf(f309,axiom,
    preorder(extended_enat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Opreorder_33) ).

thf(f2691,plain,
    spl136_43,
    inference(avatar_split_clause,[],[f1856,f2688]) ).

thf(f2688,plain,
    ( spl136_43
  <=> ( preorder(num) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_43])]) ).

thf(f1856,plain,
    preorder(num) = $true,
    inference(cnf_transformation,[],[f796]) ).

thf(f796,plain,
    preorder(num) = $true,
    inference(fool_elimination,[],[f795]) ).

thf(f795,plain,
    preorder(num),
    inference(rectify,[],[f272]) ).

thf(f272,axiom,
    preorder(num),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Opreorder_5) ).

thf(f2686,plain,
    spl136_42,
    inference(avatar_split_clause,[],[f1855,f2683]) ).

thf(f1855,plain,
    topolo503727757_space(extended_ereal) = $true,
    inference(cnf_transformation,[],[f794]) ).

thf(f794,plain,
    topolo503727757_space(extended_ereal) = $true,
    inference(fool_elimination,[],[f793]) ).

thf(f793,plain,
    topolo503727757_space(extended_ereal),
    inference(rectify,[],[f315]) ).

thf(f315,axiom,
    topolo503727757_space(extended_ereal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Topological__Spaces_Otopological__space_39) ).

thf(f2681,plain,
    spl136_41,
    inference(avatar_split_clause,[],[f1854,f2678]) ).

thf(f2678,plain,
    ( spl136_41
  <=> ( topolo503727757_space($o) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_41])]) ).

thf(f1854,plain,
    topolo503727757_space($o) = $true,
    inference(cnf_transformation,[],[f792]) ).

thf(f792,plain,
    topolo503727757_space($o) = $true,
    inference(fool_elimination,[],[f791]) ).

thf(f791,plain,
    topolo503727757_space($o),
    inference(rectify,[],[f276]) ).

thf(f276,axiom,
    topolo503727757_space($o),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Otopological__space_9) ).

thf(f2676,plain,
    spl136_40,
    inference(avatar_split_clause,[],[f1853,f2673]) ).

thf(f1853,plain,
    topolo503727757_space(real) = $true,
    inference(cnf_transformation,[],[f790]) ).

thf(f790,plain,
    topolo503727757_space(real) = $true,
    inference(fool_elimination,[],[f789]) ).

thf(f789,plain,
    topolo503727757_space(real),
    inference(rectify,[],[f284]) ).

thf(f284,axiom,
    topolo503727757_space(real),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Topological__Spaces_Otopological__space_17) ).

thf(f2671,plain,
    spl136_39,
    inference(avatar_split_clause,[],[f1852,f2668]) ).

thf(f2668,plain,
    ( spl136_39
  <=> ( linordered_idom(real) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_39])]) ).

thf(f1852,plain,
    linordered_idom(real) = $true,
    inference(cnf_transformation,[],[f788]) ).

thf(f788,plain,
    linordered_idom(real) = $true,
    inference(fool_elimination,[],[f787]) ).

thf(f787,plain,
    linordered_idom(real),
    inference(rectify,[],[f292]) ).

thf(f292,axiom,
    linordered_idom(real),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__idom) ).

thf(f2666,plain,
    spl136_38,
    inference(avatar_split_clause,[],[f1851,f2663]) ).

thf(f1851,plain,
    topolo503727757_space(nat) = $true,
    inference(cnf_transformation,[],[f786]) ).

thf(f786,plain,
    topolo503727757_space(nat) = $true,
    inference(fool_elimination,[],[f785]) ).

thf(f785,plain,
    topolo503727757_space(nat),
    inference(rectify,[],[f262]) ).

thf(f262,axiom,
    topolo503727757_space(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Topological__Spaces_Otopological__space_1) ).

thf(f2661,plain,
    spl136_37,
    inference(avatar_split_clause,[],[f1850,f2658]) ).

thf(f1850,plain,
    topolo503727757_space(extended_enat) = $true,
    inference(cnf_transformation,[],[f784]) ).

thf(f784,plain,
    topolo503727757_space(extended_enat) = $true,
    inference(fool_elimination,[],[f783]) ).

thf(f783,plain,
    topolo503727757_space(extended_enat),
    inference(rectify,[],[f305]) ).

thf(f305,axiom,
    topolo503727757_space(extended_enat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Topological__Spaces_Otopological__space_29) ).

thf(f2656,plain,
    spl136_36,
    inference(avatar_split_clause,[],[f1849,f2653]) ).

thf(f1849,plain,
    boolean_algebra($o) = $true,
    inference(cnf_transformation,[],[f782]) ).

thf(f782,plain,
    boolean_algebra($o) = $true,
    inference(fool_elimination,[],[f781]) ).

thf(f781,plain,
    boolean_algebra($o),
    inference(rectify,[],[f278]) ).

thf(f278,axiom,
    boolean_algebra($o),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Oboolean__algebra_11) ).

thf(f2651,plain,
    spl136_35,
    inference(avatar_split_clause,[],[f1848,f2648]) ).

thf(f2648,plain,
    ( spl136_35
  <=> ( group_add(real) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_35])]) ).

thf(f1848,plain,
    group_add(real) = $true,
    inference(cnf_transformation,[],[f780]) ).

thf(f780,plain,
    group_add(real) = $true,
    inference(fool_elimination,[],[f779]) ).

thf(f779,plain,
    group_add(real),
    inference(rectify,[],[f296]) ).

thf(f296,axiom,
    group_add(real),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ogroup__add) ).

thf(f2646,plain,
    spl136_34,
    inference(avatar_split_clause,[],[f1847,f2643]) ).

thf(f1847,plain,
    real_V2090557954_space(real) = $true,
    inference(cnf_transformation,[],[f778]) ).

thf(f778,plain,
    real_V2090557954_space(real) = $true,
    inference(fool_elimination,[],[f777]) ).

thf(f777,plain,
    real_V2090557954_space(real),
    inference(rectify,[],[f287]) ).

thf(f287,axiom,
    real_V2090557954_space(real),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Real__Vector__Spaces_Ometric__space) ).

thf(f2641,plain,
    spl136_33,
    inference(avatar_split_clause,[],[f1846,f2638]) ).

thf(f2638,plain,
    ( spl136_33
  <=> ( ordered_ab_group_add(real) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_33])]) ).

thf(f1846,plain,
    ordered_ab_group_add(real) = $true,
    inference(cnf_transformation,[],[f776]) ).

thf(f776,plain,
    ordered_ab_group_add(real) = $true,
    inference(fool_elimination,[],[f775]) ).

thf(f775,plain,
    ordered_ab_group_add(real),
    inference(rectify,[],[f290]) ).

thf(f290,axiom,
    ordered_ab_group_add(real),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__group__add) ).

thf(f2636,plain,
    spl136_32,
    inference(avatar_split_clause,[],[f1845,f2633]) ).

thf(f1845,plain,
    uminus(extended_ereal) = $true,
    inference(cnf_transformation,[],[f774]) ).

thf(f774,plain,
    uminus(extended_ereal) = $true,
    inference(fool_elimination,[],[f773]) ).

thf(f773,plain,
    uminus(extended_ereal),
    inference(rectify,[],[f321]) ).

thf(f321,axiom,
    uminus(extended_ereal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Groups_Ouminus_45) ).

thf(f2631,plain,
    spl136_31,
    inference(avatar_split_clause,[],[f1844,f2628]) ).

thf(f1844,plain,
    uminus($o) = $true,
    inference(cnf_transformation,[],[f772]) ).

thf(f772,plain,
    uminus($o) = $true,
    inference(fool_elimination,[],[f771]) ).

thf(f771,plain,
    uminus($o),
    inference(rectify,[],[f283]) ).

thf(f283,axiom,
    uminus($o),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Groups_Ouminus_16) ).

thf(f2626,plain,
    spl136_30,
    inference(avatar_split_clause,[],[f1843,f2623]) ).

thf(f2623,plain,
    ( spl136_30
  <=> ( linord1659791738miring(real) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_30])]) ).

thf(f1843,plain,
    linord1659791738miring(real) = $true,
    inference(cnf_transformation,[],[f770]) ).

thf(f770,plain,
    linord1659791738miring(real) = $true,
    inference(fool_elimination,[],[f769]) ).

thf(f769,plain,
    linord1659791738miring(real),
    inference(rectify,[],[f286]) ).

thf(f286,axiom,
    linord1659791738miring(real),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_19) ).

thf(f2621,plain,
    spl136_29,
    inference(avatar_split_clause,[],[f1842,f2618]) ).

thf(f1842,plain,
    uminus(real) = $true,
    inference(cnf_transformation,[],[f768]) ).

thf(f768,plain,
    uminus(real) = $true,
    inference(fool_elimination,[],[f767]) ).

thf(f767,plain,
    uminus(real),
    inference(rectify,[],[f301]) ).

thf(f301,axiom,
    uminus(real),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ouminus_25) ).

thf(f2616,plain,
    spl136_28,
    inference(avatar_split_clause,[],[f1841,f2613]) ).

thf(f2613,plain,
    ( spl136_28
  <=> ( linord1659791738miring(nat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_28])]) ).

thf(f1841,plain,
    linord1659791738miring(nat) = $true,
    inference(cnf_transformation,[],[f766]) ).

thf(f766,plain,
    linord1659791738miring(nat) = $true,
    inference(fool_elimination,[],[f765]) ).

thf(f765,plain,
    linord1659791738miring(nat),
    inference(rectify,[],[f264]) ).

thf(f264,axiom,
    linord1659791738miring(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring) ).

thf(f2611,plain,
    spl136_27,
    inference(avatar_split_clause,[],[f1840,f2608]) ).

thf(f2608,plain,
    ( spl136_27
  <=> ( linord1659791738miring(extended_enat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_27])]) ).

thf(f1840,plain,
    linord1659791738miring(extended_enat) = $true,
    inference(cnf_transformation,[],[f764]) ).

thf(f764,plain,
    linord1659791738miring(extended_enat) = $true,
    inference(fool_elimination,[],[f763]) ).

thf(f763,plain,
    linord1659791738miring(extended_enat),
    inference(rectify,[],[f307]) ).

thf(f307,axiom,
    linord1659791738miring(extended_enat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Olinordered__nonzero__semiring_31) ).

thf(f2606,plain,
    spl136_26,
    inference(avatar_split_clause,[],[f1839,f2603]) ).

thf(f2603,plain,
    ( spl136_26
  <=> ( topolo259154727pology(extended_ereal) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_26])]) ).

thf(f1839,plain,
    topolo259154727pology(extended_ereal) = $true,
    inference(cnf_transformation,[],[f762]) ).

thf(f762,plain,
    topolo259154727pology(extended_ereal) = $true,
    inference(fool_elimination,[],[f761]) ).

thf(f761,plain,
    topolo259154727pology(extended_ereal),
    inference(rectify,[],[f316]) ).

thf(f316,axiom,
    topolo259154727pology(extended_ereal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Topological__Spaces_Oorder__topology_40) ).

thf(f2601,plain,
    spl136_25,
    inference(avatar_split_clause,[],[f1838,f2598]) ).

thf(f2598,plain,
    ( spl136_25
  <=> ( topolo259154727pology($o) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_25])]) ).

thf(f1838,plain,
    topolo259154727pology($o) = $true,
    inference(cnf_transformation,[],[f760]) ).

thf(f760,plain,
    topolo259154727pology($o) = $true,
    inference(fool_elimination,[],[f759]) ).

thf(f759,plain,
    topolo259154727pology($o),
    inference(rectify,[],[f277]) ).

thf(f277,axiom,
    topolo259154727pology($o),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Oorder__topology_10) ).

thf(f2596,plain,
    spl136_24,
    inference(avatar_split_clause,[],[f1837,f2593]) ).

thf(f2593,plain,
    ( spl136_24
  <=> ( topolo259154727pology(real) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_24])]) ).

thf(f1837,plain,
    topolo259154727pology(real) = $true,
    inference(cnf_transformation,[],[f758]) ).

thf(f758,plain,
    topolo259154727pology(real) = $true,
    inference(fool_elimination,[],[f757]) ).

thf(f757,plain,
    topolo259154727pology(real),
    inference(rectify,[],[f285]) ).

thf(f285,axiom,
    topolo259154727pology(real),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Topological__Spaces_Oorder__topology_18) ).

thf(f2591,plain,
    spl136_23,
    inference(avatar_split_clause,[],[f1836,f2588]) ).

thf(f2588,plain,
    ( spl136_23
  <=> ( topolo259154727pology(nat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_23])]) ).

thf(f1836,plain,
    topolo259154727pology(nat) = $true,
    inference(cnf_transformation,[],[f756]) ).

thf(f756,plain,
    topolo259154727pology(nat) = $true,
    inference(fool_elimination,[],[f755]) ).

thf(f755,plain,
    topolo259154727pology(nat),
    inference(rectify,[],[f263]) ).

thf(f263,axiom,
    topolo259154727pology(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Topological__Spaces_Oorder__topology) ).

thf(f2586,plain,
    spl136_22,
    inference(avatar_split_clause,[],[f1835,f2583]) ).

thf(f2583,plain,
    ( spl136_22
  <=> ( topolo259154727pology(extended_enat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_22])]) ).

thf(f1835,plain,
    topolo259154727pology(extended_enat) = $true,
    inference(cnf_transformation,[],[f754]) ).

thf(f754,plain,
    topolo259154727pology(extended_enat) = $true,
    inference(fool_elimination,[],[f753]) ).

thf(f753,plain,
    topolo259154727pology(extended_enat),
    inference(rectify,[],[f306]) ).

thf(f306,axiom,
    topolo259154727pology(extended_enat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Topological__Spaces_Oorder__topology_30) ).

thf(f2581,plain,
    spl136_21,
    inference(avatar_split_clause,[],[f1834,f2578]) ).

thf(f2578,plain,
    ( spl136_21
  <=> ( zero(extended_ereal) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_21])]) ).

thf(f1834,plain,
    zero(extended_ereal) = $true,
    inference(cnf_transformation,[],[f752]) ).

thf(f752,plain,
    zero(extended_ereal) = $true,
    inference(fool_elimination,[],[f751]) ).

thf(f751,plain,
    zero(extended_ereal),
    inference(rectify,[],[f323]) ).

thf(f323,axiom,
    zero(extended_ereal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Groups_Ozero_47) ).

thf(f2576,plain,
    spl136_20,
    inference(avatar_split_clause,[],[f1833,f2573]) ).

thf(f2573,plain,
    ( spl136_20
  <=> ( ring_char_0(real) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_20])]) ).

thf(f1833,plain,
    ring_char_0(real) = $true,
    inference(cnf_transformation,[],[f750]) ).

thf(f750,plain,
    ring_char_0(real) = $true,
    inference(fool_elimination,[],[f749]) ).

thf(f749,plain,
    ring_char_0(real),
    inference(rectify,[],[f299]) ).

thf(f299,axiom,
    ring_char_0(real),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Nat_Oring__char__0) ).

thf(f2571,plain,
    spl136_19,
    inference(avatar_split_clause,[],[f1832,f2568]) ).

thf(f2568,plain,
    ( spl136_19
  <=> ( semiring_char_0(real) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_19])]) ).

thf(f1832,plain,
    semiring_char_0(real) = $true,
    inference(cnf_transformation,[],[f748]) ).

thf(f748,plain,
    semiring_char_0(real) = $true,
    inference(fool_elimination,[],[f747]) ).

thf(f747,plain,
    semiring_char_0(real),
    inference(rectify,[],[f293]) ).

thf(f293,axiom,
    semiring_char_0(real),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Nat_Osemiring__char__0_20) ).

thf(f2566,plain,
    spl136_18,
    inference(avatar_split_clause,[],[f1831,f2563]) ).

thf(f2563,plain,
    ( spl136_18
  <=> ( zero(real) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_18])]) ).

thf(f1831,plain,
    zero(real) = $true,
    inference(cnf_transformation,[],[f746]) ).

thf(f746,plain,
    zero(real) = $true,
    inference(fool_elimination,[],[f745]) ).

thf(f745,plain,
    zero(real),
    inference(rectify,[],[f303]) ).

thf(f303,axiom,
    zero(real),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ozero_27) ).

thf(f2561,plain,
    spl136_17,
    inference(avatar_split_clause,[],[f1830,f2558]) ).

thf(f2558,plain,
    ( spl136_17
  <=> ( linord219039673up_add(real) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_17])]) ).

thf(f1830,plain,
    linord219039673up_add(real) = $true,
    inference(cnf_transformation,[],[f744]) ).

thf(f744,plain,
    linord219039673up_add(real) = $true,
    inference(fool_elimination,[],[f743]) ).

thf(f743,plain,
    linord219039673up_add(real),
    inference(rectify,[],[f289]) ).

thf(f289,axiom,
    linord219039673up_add(real),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Olinordered__ab__group__add) ).

thf(f2556,plain,
    spl136_16,
    inference(avatar_split_clause,[],[f1829,f2553]) ).

thf(f2553,plain,
    ( spl136_16
  <=> ( zero(nat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_16])]) ).

thf(f1829,plain,
    zero(nat) = $true,
    inference(cnf_transformation,[],[f742]) ).

thf(f742,plain,
    zero(nat) = $true,
    inference(fool_elimination,[],[f741]) ).

thf(f741,plain,
    zero(nat),
    inference(rectify,[],[f271]) ).

thf(f271,axiom,
    zero(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero) ).

thf(f2551,plain,
    spl136_15,
    inference(avatar_split_clause,[],[f1828,f2548]) ).

thf(f2548,plain,
    ( spl136_15
  <=> ( semiring_char_0(nat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_15])]) ).

thf(f1828,plain,
    semiring_char_0(nat) = $true,
    inference(cnf_transformation,[],[f740]) ).

thf(f740,plain,
    semiring_char_0(nat) = $true,
    inference(fool_elimination,[],[f739]) ).

thf(f739,plain,
    semiring_char_0(nat),
    inference(rectify,[],[f265]) ).

thf(f265,axiom,
    semiring_char_0(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osemiring__char__0) ).

thf(f2546,plain,
    spl136_14,
    inference(avatar_split_clause,[],[f1827,f2543]) ).

thf(f2543,plain,
    ( spl136_14
  <=> ( semiring_char_0(extended_enat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_14])]) ).

thf(f1827,plain,
    semiring_char_0(extended_enat) = $true,
    inference(cnf_transformation,[],[f738]) ).

thf(f738,plain,
    semiring_char_0(extended_enat) = $true,
    inference(fool_elimination,[],[f737]) ).

thf(f737,plain,
    semiring_char_0(extended_enat),
    inference(rectify,[],[f308]) ).

thf(f308,axiom,
    semiring_char_0(extended_enat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Nat_Osemiring__char__0_32) ).

thf(f2541,plain,
    spl136_13,
    inference(avatar_split_clause,[],[f1826,f2538]) ).

thf(f2538,plain,
    ( spl136_13
  <=> ( zero(extended_enat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_13])]) ).

thf(f1826,plain,
    zero(extended_enat) = $true,
    inference(cnf_transformation,[],[f736]) ).

thf(f736,plain,
    zero(extended_enat) = $true,
    inference(fool_elimination,[],[f735]) ).

thf(f735,plain,
    zero(extended_enat),
    inference(rectify,[],[f314]) ).

thf(f314,axiom,
    zero(extended_enat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ozero_38) ).

thf(f2536,plain,
    spl136_12,
    inference(avatar_split_clause,[],[f1825,f2533]) ).

thf(f2533,plain,
    ( spl136_12
  <=> ( numeral(extended_ereal) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_12])]) ).

thf(f1825,plain,
    numeral(extended_ereal) = $true,
    inference(cnf_transformation,[],[f734]) ).

thf(f734,plain,
    numeral(extended_ereal) = $true,
    inference(fool_elimination,[],[f733]) ).

thf(f733,plain,
    numeral(extended_ereal),
    inference(rectify,[],[f322]) ).

thf(f322,axiom,
    numeral(extended_ereal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Num_Onumeral_46) ).

thf(f2531,plain,
    spl136_11,
    inference(avatar_split_clause,[],[f1824,f2528]) ).

thf(f2528,plain,
    ( spl136_11
  <=> ( numeral(real) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_11])]) ).

thf(f1824,plain,
    numeral(real) = $true,
    inference(cnf_transformation,[],[f732]) ).

thf(f732,plain,
    numeral(real) = $true,
    inference(fool_elimination,[],[f731]) ).

thf(f731,plain,
    numeral(real),
    inference(rectify,[],[f302]) ).

thf(f302,axiom,
    numeral(real),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Num_Onumeral_26) ).

thf(f2526,plain,
    spl136_10,
    inference(avatar_split_clause,[],[f1823,f2523]) ).

thf(f2523,plain,
    ( spl136_10
  <=> ( numeral(nat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_10])]) ).

thf(f1823,plain,
    numeral(nat) = $true,
    inference(cnf_transformation,[],[f730]) ).

thf(f730,plain,
    numeral(nat) = $true,
    inference(fool_elimination,[],[f729]) ).

thf(f729,plain,
    numeral(nat),
    inference(rectify,[],[f270]) ).

thf(f270,axiom,
    numeral(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Num_Onumeral) ).

thf(f2521,plain,
    spl136_9,
    inference(avatar_split_clause,[],[f1822,f2518]) ).

thf(f2518,plain,
    ( spl136_9
  <=> ( canoni770627133id_add(nat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_9])]) ).

thf(f1822,plain,
    canoni770627133id_add(nat) = $true,
    inference(cnf_transformation,[],[f728]) ).

thf(f728,plain,
    canoni770627133id_add(nat) = $true,
    inference(fool_elimination,[],[f727]) ).

thf(f727,plain,
    canoni770627133id_add(nat),
    inference(rectify,[],[f261]) ).

thf(f261,axiom,
    canoni770627133id_add(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).

thf(f2516,plain,
    spl136_8,
    inference(avatar_split_clause,[],[f1821,f2513]) ).

thf(f2513,plain,
    ( spl136_8
  <=> ( canoni770627133id_add(extended_enat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_8])]) ).

thf(f1821,plain,
    canoni770627133id_add(extended_enat) = $true,
    inference(cnf_transformation,[],[f726]) ).

thf(f726,plain,
    canoni770627133id_add(extended_enat) = $true,
    inference(fool_elimination,[],[f725]) ).

thf(f725,plain,
    canoni770627133id_add(extended_enat),
    inference(rectify,[],[f304]) ).

thf(f304,axiom,
    canoni770627133id_add(extended_enat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add_28) ).

thf(f2511,plain,
    spl136_7,
    inference(avatar_split_clause,[],[f1820,f2508]) ).

thf(f2508,plain,
    ( spl136_7
  <=> ( numeral(extended_enat) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_7])]) ).

thf(f1820,plain,
    numeral(extended_enat) = $true,
    inference(cnf_transformation,[],[f724]) ).

thf(f724,plain,
    numeral(extended_enat) = $true,
    inference(fool_elimination,[],[f723]) ).

thf(f723,plain,
    numeral(extended_enat),
    inference(rectify,[],[f313]) ).

thf(f313,axiom,
    numeral(extended_enat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Num_Onumeral_37) ).

thf(f2506,plain,
    spl136_6,
    inference(avatar_split_clause,[],[f1819,f2503]) ).

thf(f2503,plain,
    ( spl136_6
  <=> ( neg_numeral(real) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_6])]) ).

thf(f1819,plain,
    neg_numeral(real) = $true,
    inference(cnf_transformation,[],[f722]) ).

thf(f722,plain,
    neg_numeral(real) = $true,
    inference(fool_elimination,[],[f721]) ).

thf(f721,plain,
    neg_numeral(real),
    inference(rectify,[],[f298]) ).

thf(f298,axiom,
    neg_numeral(real),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Num_Oneg__numeral) ).

thf(f2501,plain,
    spl136_5,
    inference(avatar_split_clause,[],[f1818,f2498]) ).

thf(f2498,plain,
    ( spl136_5
  <=> ( linordered_field(real) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_5])]) ).

thf(f1818,plain,
    linordered_field(real) = $true,
    inference(cnf_transformation,[],[f720]) ).

thf(f720,plain,
    linordered_field(real) = $true,
    inference(fool_elimination,[],[f719]) ).

thf(f719,plain,
    linordered_field(real),
    inference(rectify,[],[f291]) ).

thf(f291,axiom,
    linordered_field(real),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Fields_Olinordered__field) ).

thf(f2496,plain,
    spl136_4,
    inference(avatar_split_clause,[],[f1416,f2493]) ).

thf(f2493,plain,
    ( spl136_4
  <=> ( extend1396239628finity(extended_ereal) = extended_PInfty ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_4])]) ).

thf(f2491,plain,
    spl136_3,
    inference(avatar_split_clause,[],[f1414,f2488]) ).

thf(f1414,plain,
    real_V2090557954_space(a) = $true,
    inference(cnf_transformation,[],[f332]) ).

thf(f332,plain,
    real_V2090557954_space(a) = $true,
    inference(fool_elimination,[],[f331]) ).

thf(f331,plain,
    real_V2090557954_space(a),
    inference(rectify,[],[f324]) ).

thf(f324,axiom,
    real_V2090557954_space(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).

thf(f2486,plain,
    ~ spl136_2,
    inference(avatar_split_clause,[],[f1415,f2483]) ).

thf(f2483,plain,
    ( spl136_2
  <=> ( extended_MInfty = extended_PInfty ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_2])]) ).

thf(f1415,plain,
    extended_MInfty != extended_PInfty,
    inference(cnf_transformation,[],[f204]) ).

thf(f204,axiom,
    extended_MInfty != extended_PInfty,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_ereal_Odistinct_I5_J) ).

thf(f2481,plain,
    ~ spl136_1,
    inference(avatar_split_clause,[],[f327,f2478]) ).

thf(f2478,plain,
    ( spl136_1
  <=> ( $true = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl136_1])]) ).

thf(f327,plain,
    $true != $false,
    introduced(fool_axiom,[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem    : ITP114^2 : TPTP v8.2.0. Released v7.5.0.
% 0.02/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sat May 18 17:28:52 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.35  % (27737)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.38  % (27739)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.38  % (27741)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.38  % (27744)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)
% 0.20/0.38  % (27743)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)
% 0.20/0.38  % (27742)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)
% 0.20/0.38  % (27738)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.39  % (27740)WARNING: value z3 for option sas not known
% 0.20/0.39  % (27740)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)
% 0.20/0.41  % (27744)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.42  % Exception at run slice level
% 0.20/0.42  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.44  % (27745)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.47  % (27745)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.47  % Exception at run slice level
% 0.20/0.47  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.49  % (27746)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)
% 0.20/0.49  % (27742)First to succeed.
% 0.20/0.51  % (27742)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-27737"
% 0.20/0.51  % (27742)Refutation found. Thanks to Tanya!
% 0.20/0.51  % SZS status Theorem for theBenchmark
% 0.20/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52  % (27742)------------------------------
% 0.20/0.52  % (27742)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.52  % (27742)Termination reason: Refutation
% 0.20/0.52  
% 0.20/0.52  % (27742)Memory used [KB]: 2787
% 0.20/0.52  % (27742)Time elapsed: 0.124 s
% 0.20/0.52  % (27742)Instructions burned: 253 (million)
% 0.20/0.52  % (27737)Success in time 0.162 s
%------------------------------------------------------------------------------