TSTP Solution File: ITP015^1 by E---3.1.00

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%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP015^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n004.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 : Sat May  4 08:06:27 EDT 2024

% Result   : Theorem 0.37s 0.56s
% Output   : CNFRefutation 0.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   56 (  18 unt;  26 typ;   0 def)
%            Number of atoms       :  107 (  37 equ;   0 cnn)
%            Maximal formula atoms :   19 (   3 avg)
%            Number of connectives :  761 (  30   ~;  29   |;  23   &; 670   @)
%                                         (   8 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Number of types       :    6 (   5 usr)
%            Number of type conns  :   20 (  20   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   24 (  21 usr;   9 con; 0-3 aty)
%            Number of variables   :   51 (   0   ^  51   !;   0   ?;  51   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_sort1,type,
    d: $tType ).

thf(decl_sort2,type,
    u: $tType ).

thf(decl_sort3,type,
    du: $tType ).

thf(decl_sort4,type,
    mono_2Etyop_2Einteger_2Eint: $tType ).

thf(decl_sort5,type,
    mono_2Etyop_2Enum_2Enum: $tType ).

thf(decl_23,type,
    tyop_2Efcp_2Ecart: d > d > d ).

thf(decl_24,type,
    tyop_2Einteger_2Eint: d ).

thf(decl_25,type,
    tyop_2Emin_2Ebool: d ).

thf(decl_27,type,
    tyop_2Enum_2Enum: d ).

thf(decl_28,type,
    s: d > u > du ).

thf(decl_47,type,
    c_2Ebool_2ECOND_2E3: du > du > du > u ).

thf(decl_59,type,
    c_2Einteger__word_2Ei2w_2E1: du > u ).

thf(decl_67,type,
    c_2Ewords_2En2w_2E1: du > u ).

thf(decl_70,type,
    c_2Ewords_2Eword__2comp_2E1: du > u ).

thf(decl_85,type,
    mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).

thf(decl_86,type,
    mono_2Ec_2Eprim__rec_2E_3C: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).

thf(decl_88,type,
    mono_2Ec_2Ebool_2EF: $o ).

thf(decl_90,type,
    mono_2Ec_2Einteger_2ENum: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ).

thf(decl_91,type,
    mono_2Ec_2Ebool_2ET: $o ).

thf(decl_93,type,
    mono_2Ec_2Einteger_2Eint__lt: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).

thf(decl_94,type,
    mono_2Ec_2Einteger_2Eint__neg: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).

thf(decl_95,type,
    mono_2Ec_2Einteger_2Eint__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).

thf(decl_97,type,
    i_mono_2Etyop_2Emin_2Ebool: $o > u ).

thf(decl_109,type,
    i_mono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Einteger_2Eint > u ).

thf(decl_110,type,
    i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).

thf(decl_125,type,
    esk1_0: d ).

thf(thm_2Ebool_2Ebool__case__thm,axiom,
    ! [X1: d] :
      ( ! [X82: u,X83: u] :
          ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) @ ( s @ X1 @ X82 ) @ ( s @ X1 @ X83 ) ) )
          = ( s @ X1 @ X82 ) )
      & ! [X84: u,X85: u] :
          ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ X1 @ X84 ) @ ( s @ X1 @ X85 ) ) )
          = ( s @ X1 @ X85 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.yrIqfEXtiq/E---3.1_14254.p',thm_2Ebool_2Ebool__case__thm) ).

thf(thm_2Einteger_2EINT__LT__CALCULATE,axiom,
    ! [X86: mono_2Etyop_2Enum_2Enum,X87: mono_2Etyop_2Enum_2Enum] :
      ( ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X86 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X87 ) )
      <=> ( mono_2Ec_2Eprim__rec_2E_3C @ X86 @ X87 ) )
      & ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X86 ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X87 ) ) )
      <=> ( mono_2Ec_2Eprim__rec_2E_3C @ X87 @ X86 ) )
      & ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X86 ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X87 ) )
      <=> ( ( X86 != mono_2Ec_2Enum_2E0 )
          | ( X87 != mono_2Ec_2Enum_2E0 ) ) )
      & ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X86 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X87 ) ) )
      <=> mono_2Ec_2Ebool_2EF ) ),
    file('/export/starexec/sandbox2/tmp/tmp.yrIqfEXtiq/E---3.1_14254.p',thm_2Einteger_2EINT__LT__CALCULATE) ).

thf(thm_2Einteger__word_2Ei2w__def,axiom,
    ! [X1: d,X88: mono_2Etyop_2Einteger_2Eint] :
      ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ X88 ) ) ) )
      = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Einteger_2Eint__lt @ X88 @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ X88 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ X88 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.yrIqfEXtiq/E---3.1_14254.p',thm_2Einteger__word_2Ei2w__def) ).

thf(thm_2Ebool_2EFALSITY,axiom,
    ! [X75: $o] :
      ( mono_2Ec_2Ebool_2EF
     => X75 ),
    file('/export/starexec/sandbox2/tmp/tmp.yrIqfEXtiq/E---3.1_14254.p',thm_2Ebool_2EFALSITY) ).

thf(thm_2Einteger__word_2Ei2w__0,conjecture,
    ! [X1: d] :
      ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.yrIqfEXtiq/E---3.1_14254.p',thm_2Einteger__word_2Ei2w__0) ).

thf(thm_2Einteger_2ENUM__OF__INT,axiom,
    ! [X86: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__of__num @ X86 ) )
      = X86 ),
    file('/export/starexec/sandbox2/tmp/tmp.yrIqfEXtiq/E---3.1_14254.p',thm_2Einteger_2ENUM__OF__INT) ).

thf(thm_2Einteger_2EINT__NEG__0,axiom,
    ( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
    = ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.yrIqfEXtiq/E---3.1_14254.p',thm_2Einteger_2EINT__NEG__0) ).

thf(c_0_7,axiom,
    ! [X1: d] :
      ( ! [X82: u,X83: u] :
          ( ( ~ mono_2Ec_2Ebool_2ET
            | ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ X1 @ X82 ) @ ( s @ X1 @ X83 ) ) )
              = ( s @ X1 @ X82 ) ) )
          & ( mono_2Ec_2Ebool_2ET
            | ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ X1 @ X82 ) @ ( s @ X1 @ X83 ) ) )
              = ( s @ X1 @ X82 ) ) ) )
      & ! [X84: u,X85: u] :
          ( ( ~ mono_2Ec_2Ebool_2EF
            | ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ X1 @ X84 ) @ ( s @ X1 @ X85 ) ) )
              = ( s @ X1 @ X85 ) ) )
          & ( mono_2Ec_2Ebool_2EF
            | ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ X1 @ X84 ) @ ( s @ X1 @ X85 ) ) )
              = ( s @ X1 @ X85 ) ) ) ) ),
    inference(fool_unroll,[status(thm)],[thm_2Ebool_2Ebool__case__thm]) ).

thf(c_0_8,plain,
    ! [X86: mono_2Etyop_2Enum_2Enum,X87: mono_2Etyop_2Enum_2Enum] :
      ( ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X86 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X87 ) )
      <=> ( mono_2Ec_2Eprim__rec_2E_3C @ X86 @ X87 ) )
      & ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X86 ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X87 ) ) )
      <=> ( mono_2Ec_2Eprim__rec_2E_3C @ X87 @ X86 ) )
      & ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X86 ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X87 ) )
      <=> ( ( X86 != mono_2Ec_2Enum_2E0 )
          | ( X87 != mono_2Ec_2Enum_2E0 ) ) )
      & ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X86 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X87 ) ) )
      <=> mono_2Ec_2Ebool_2EF ) ),
    inference(fof_simplification,[status(thm)],[thm_2Einteger_2EINT__LT__CALCULATE]) ).

thf(c_0_9,axiom,
    ! [X1: d,X88: mono_2Etyop_2Einteger_2Eint] :
      ( ( ~ ( mono_2Ec_2Einteger_2Eint__lt @ X88 @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
        | ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ X88 ) ) ) )
          = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ X88 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ X88 ) ) ) ) ) ) ) ) )
      & ( ( mono_2Ec_2Einteger_2Eint__lt @ X88 @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
        | ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ X88 ) ) ) )
          = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ X88 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ X88 ) ) ) ) ) ) ) ) ) ),
    inference(fool_unroll,[status(thm)],[thm_2Einteger__word_2Ei2w__def]) ).

thf(c_0_10,plain,
    ! [X195: d,X196: u,X197: u,X198: u,X199: u] :
      ( ( ~ mono_2Ec_2Ebool_2ET
        | ( ( s @ X195 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ X195 @ X196 ) @ ( s @ X195 @ X197 ) ) )
          = ( s @ X195 @ X196 ) ) )
      & ( mono_2Ec_2Ebool_2ET
        | ( ( s @ X195 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ X195 @ X196 ) @ ( s @ X195 @ X197 ) ) )
          = ( s @ X195 @ X196 ) ) )
      & ( ~ mono_2Ec_2Ebool_2EF
        | ( ( s @ X195 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ X195 @ X198 ) @ ( s @ X195 @ X199 ) ) )
          = ( s @ X195 @ X199 ) ) )
      & ( mono_2Ec_2Ebool_2EF
        | ( ( s @ X195 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ X195 @ X198 ) @ ( s @ X195 @ X199 ) ) )
          = ( s @ X195 @ X199 ) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_7])])]) ).

thf(c_0_11,plain,
    ! [X208: $o] :
      ( ~ mono_2Ec_2Ebool_2EF
      | X208 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Ebool_2EFALSITY])])]) ).

thf(c_0_12,plain,
    ! [X172: mono_2Etyop_2Enum_2Enum,X173: mono_2Etyop_2Enum_2Enum] :
      ( ( ~ ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X172 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X173 ) )
        | ( mono_2Ec_2Eprim__rec_2E_3C @ X172 @ X173 ) )
      & ( ~ ( mono_2Ec_2Eprim__rec_2E_3C @ X172 @ X173 )
        | ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X172 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X173 ) ) )
      & ( ~ ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X172 ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X173 ) ) )
        | ( mono_2Ec_2Eprim__rec_2E_3C @ X173 @ X172 ) )
      & ( ~ ( mono_2Ec_2Eprim__rec_2E_3C @ X173 @ X172 )
        | ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X172 ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X173 ) ) ) )
      & ( ~ ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X172 ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X173 ) )
        | ( X172 != mono_2Ec_2Enum_2E0 )
        | ( X173 != mono_2Ec_2Enum_2E0 ) )
      & ( ( X172 = mono_2Ec_2Enum_2E0 )
        | ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X172 ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X173 ) ) )
      & ( ( X173 = mono_2Ec_2Enum_2E0 )
        | ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X172 ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X173 ) ) )
      & ( ~ ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X172 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X173 ) ) )
        | mono_2Ec_2Ebool_2EF )
      & ( ~ mono_2Ec_2Ebool_2EF
        | ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X172 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X173 ) ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).

thf(c_0_13,plain,
    ! [X169: d,X170: mono_2Etyop_2Einteger_2Eint] :
      ( ( ~ ( mono_2Ec_2Einteger_2Eint__lt @ X170 @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
        | ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X169 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ X170 ) ) ) )
          = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X169 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X169 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X169 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ X170 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X169 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ X170 ) ) ) ) ) ) ) ) )
      & ( ( mono_2Ec_2Einteger_2Eint__lt @ X170 @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
        | ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X169 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ X170 ) ) ) )
          = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X169 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X169 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X169 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ X170 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X169 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ X170 ) ) ) ) ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_9])]) ).

thf(c_0_14,plain,
    ! [X1: d,X3: u,X4: u] :
      ( mono_2Ec_2Ebool_2EF
      | ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ~ $true ) ) @ ( s @ X1 @ X3 ) @ ( s @ X1 @ X4 ) ) )
        = ( s @ X1 @ X4 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_15,plain,
    ~ mono_2Ec_2Ebool_2EF,
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_11])])]) ).

thf(c_0_16,plain,
    ! [X26: mono_2Etyop_2Enum_2Enum,X32: mono_2Etyop_2Enum_2Enum] :
      ( mono_2Ec_2Ebool_2EF
      | ~ ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X26 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X32 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_17,negated_conjecture,
    ~ ! [X1: d] :
        ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ),
    inference(assume_negation,[status(cth)],[thm_2Einteger__word_2Ei2w__0]) ).

thf(c_0_18,plain,
    ! [X1: d,X25: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__lt @ X25 @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
      | ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ X25 ) ) ) )
        = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ~ $true ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ X25 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ X25 ) ) ) ) ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_19,plain,
    ! [X1: d,X3: u,X4: u] :
      ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ~ $true ) ) @ ( s @ X1 @ X3 ) @ ( s @ X1 @ X4 ) ) )
      = ( s @ X1 @ X4 ) ),
    inference(sr,[status(thm)],[c_0_14,c_0_15]) ).

thf(c_0_20,plain,
    ! [X179: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__of__num @ X179 ) )
      = X179 ),
    inference(variable_rename,[status(thm)],[thm_2Einteger_2ENUM__OF__INT]) ).

thf(c_0_21,plain,
    ! [X26: mono_2Etyop_2Enum_2Enum,X32: mono_2Etyop_2Enum_2Enum] :
      ~ ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X26 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X32 ) ) ),
    inference(sr,[status(thm)],[c_0_16,c_0_15]) ).

thf(c_0_22,plain,
    ( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
    = ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ),
    inference(split_conjunct,[status(thm)],[thm_2Einteger_2EINT__NEG__0]) ).

thf(c_0_23,negated_conjecture,
    ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ esk1_0 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) )
   != ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ esk1_0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).

thf(c_0_24,plain,
    ! [X1: d,X25: mono_2Etyop_2Einteger_2Eint] :
      ( ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ X25 ) ) ) ) )
        = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ X25 ) ) ) ) )
      | ( mono_2Ec_2Einteger_2Eint__lt @ X25 @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(rw,[status(thm)],[c_0_18,c_0_19]) ).

thf(c_0_25,plain,
    ! [X26: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__of__num @ X26 ) )
      = X26 ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_26,plain,
    ! [X26: mono_2Etyop_2Enum_2Enum] :
      ~ ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X26 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

thf(c_0_27,negated_conjecture,
    ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ esk1_0 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) )
   != ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ esk1_0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

thf(c_0_28,plain,
    ! [X1: d,X26: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ X26 ) ) ) ) )
      = ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X26 ) ) ) ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).

thf(c_0_29,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.15  % Problem    : ITP015^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.15/0.16  % Command    : run_E %s %d THM
% 0.16/0.37  % Computer : n004.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Fri May  3 12:45:18 EDT 2024
% 0.16/0.37  % CPUTime    : 
% 0.23/0.52  Running higher-order theorem proving
% 0.23/0.52  Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.yrIqfEXtiq/E---3.1_14254.p
% 0.37/0.56  # Version: 3.1.0-ho
% 0.37/0.56  # partial match(1): HSLSSLSMSSSNSFA
% 0.37/0.56  # Preprocessing class: HSLMSLSMSSSNSFA.
% 0.37/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.56  # Starting additional_ho_4 with 1500s (5) cores
% 0.37/0.56  # Starting pre_casc_8 with 300s (1) cores
% 0.37/0.56  # Starting pre_casc_5 with 300s (1) cores
% 0.37/0.56  # Starting pre_casc_6 with 300s (1) cores
% 0.37/0.56  # pre_casc_5 with pid 14335 completed with status 0
% 0.37/0.56  # Result found by pre_casc_5
% 0.37/0.56  # partial match(1): HSLSSLSMSSSNSFA
% 0.37/0.56  # Preprocessing class: HSLMSLSMSSSNSFA.
% 0.37/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.56  # Starting additional_ho_4 with 1500s (5) cores
% 0.37/0.56  # Starting pre_casc_8 with 300s (1) cores
% 0.37/0.56  # Starting pre_casc_5 with 300s (1) cores
% 0.37/0.56  # SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 0.37/0.56  # Search class: HGHSM-FFMS31-DSFFFSBN
% 0.37/0.56  # partial match(2): HGHSM-FFMM31-DSFFFFBN
% 0.37/0.56  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.37/0.56  # Starting sh5 with 163s (1) cores
% 0.37/0.56  # sh5 with pid 14337 completed with status 0
% 0.37/0.56  # Result found by sh5
% 0.37/0.56  # partial match(1): HSLSSLSMSSSNSFA
% 0.37/0.56  # Preprocessing class: HSLMSLSMSSSNSFA.
% 0.37/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.56  # Starting additional_ho_4 with 1500s (5) cores
% 0.37/0.56  # Starting pre_casc_8 with 300s (1) cores
% 0.37/0.56  # Starting pre_casc_5 with 300s (1) cores
% 0.37/0.56  # SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 0.37/0.56  # Search class: HGHSM-FFMS31-DSFFFSBN
% 0.37/0.56  # partial match(2): HGHSM-FFMM31-DSFFFFBN
% 0.37/0.56  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.37/0.56  # Starting sh5 with 163s (1) cores
% 0.37/0.56  # Preprocessing time       : 0.003 s
% 0.37/0.56  # Presaturation interreduction done
% 0.37/0.56  
% 0.37/0.56  # Proof found!
% 0.37/0.56  # SZS status Theorem
% 0.37/0.56  # SZS output start CNFRefutation
% See solution above
% 0.37/0.56  # Parsed axioms                        : 194
% 0.37/0.56  # Removed by relevancy pruning/SinE    : 156
% 0.37/0.56  # Initial clauses                      : 64
% 0.37/0.56  # Removed in clause preprocessing      : 9
% 0.37/0.56  # Initial clauses in saturation        : 55
% 0.37/0.56  # Processed clauses                    : 112
% 0.37/0.56  # ...of these trivial                  : 5
% 0.37/0.56  # ...subsumed                          : 16
% 0.37/0.56  # ...remaining for further processing  : 91
% 0.37/0.56  # Other redundant clauses eliminated   : 2
% 0.37/0.56  # Clauses deleted for lack of memory   : 0
% 0.37/0.56  # Backward-subsumed                    : 1
% 0.37/0.56  # Backward-rewritten                   : 1
% 0.37/0.56  # Generated clauses                    : 122
% 0.37/0.56  # ...of the previous two non-redundant : 43
% 0.37/0.56  # ...aggressively subsumed             : 0
% 0.37/0.56  # Contextual simplify-reflections      : 0
% 0.37/0.56  # Paramodulations                      : 95
% 0.37/0.56  # Factorizations                       : 2
% 0.37/0.56  # NegExts                              : 0
% 0.37/0.56  # Equation resolutions                 : 2
% 0.37/0.56  # Disequality decompositions           : 0
% 0.37/0.56  # Total rewrite steps                  : 69
% 0.37/0.56  # ...of those cached                   : 21
% 0.37/0.56  # Propositional unsat checks           : 0
% 0.37/0.56  #    Propositional check models        : 0
% 0.37/0.56  #    Propositional check unsatisfiable : 0
% 0.37/0.56  #    Propositional clauses             : 0
% 0.37/0.56  #    Propositional clauses after purity: 0
% 0.37/0.56  #    Propositional unsat core size     : 0
% 0.37/0.56  #    Propositional preprocessing time  : 0.000
% 0.37/0.56  #    Propositional encoding time       : 0.000
% 0.37/0.56  #    Propositional solver time         : 0.000
% 0.37/0.56  #    Success case prop preproc time    : 0.000
% 0.37/0.56  #    Success case prop encoding time   : 0.000
% 0.37/0.56  #    Success case prop solver time     : 0.000
% 0.37/0.56  # Current number of processed clauses  : 39
% 0.37/0.56  #    Positive orientable unit clauses  : 17
% 0.37/0.56  #    Positive unorientable unit clauses: 0
% 0.37/0.56  #    Negative unit clauses             : 5
% 0.37/0.56  #    Non-unit-clauses                  : 17
% 0.37/0.56  # Current number of unprocessed clauses: 34
% 0.37/0.56  # ...number of literals in the above   : 55
% 0.37/0.56  # Current number of archived formulas  : 0
% 0.37/0.56  # Current number of archived clauses   : 51
% 0.37/0.56  # Clause-clause subsumption calls (NU) : 63
% 0.37/0.56  # Rec. Clause-clause subsumption calls : 58
% 0.37/0.56  # Non-unit clause-clause subsumptions  : 8
% 0.37/0.56  # Unit Clause-clause subsumption calls : 11
% 0.37/0.56  # Rewrite failures with RHS unbound    : 0
% 0.37/0.56  # BW rewrite match attempts            : 16
% 0.37/0.56  # BW rewrite match successes           : 1
% 0.37/0.56  # Condensation attempts                : 112
% 0.37/0.56  # Condensation successes               : 0
% 0.37/0.56  # Termbank termtop insertions          : 11053
% 0.37/0.56  # Search garbage collected termcells   : 1276
% 0.37/0.56  
% 0.37/0.56  # -------------------------------------------------
% 0.37/0.56  # User time                : 0.015 s
% 0.37/0.56  # System time              : 0.003 s
% 0.37/0.56  # Total time               : 0.018 s
% 0.37/0.56  # Maximum resident set size: 2304 pages
% 0.37/0.56  
% 0.37/0.56  # -------------------------------------------------
% 0.37/0.56  # User time                : 0.020 s
% 0.37/0.56  # System time              : 0.007 s
% 0.37/0.56  # Total time               : 0.026 s
% 0.37/0.56  # Maximum resident set size: 1984 pages
% 0.37/0.56  % E---3.1 exiting
% 0.37/0.56  % E exiting
%------------------------------------------------------------------------------