E---3.5.1.THM-CRf.s

%------------------------------------------------------------------------------
% File     : E---3.5.1
% Problem  : ITP011^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Sep 30 08:04:01 AM UTC 2026

% Result   : Theorem 4.27s 0.85s
% Output   : CNFRefutation 4.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   62 (  20 unt;   0 typ;   0 def)
%            Number of atoms       :  428 ( 113 equ;   0 cnn)
%            Maximal formula atoms :  128 (   6 avg)
%            Number of connectives : 5627 ( 161   ~; 228   |; 123   &;5077   @)
%                                         (  29 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   58 (  13 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   28 (  25 usr;  11 con; 0-5 aty)
%            Number of variables   :  189 (   0   ^; 187   !;   2   ?; 189   :)

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

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

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

thf(decl_23,type,
    tyop_2Emin_2Ebool: d ).

thf(decl_24,type,
    tyop_2Emin_2Efun: d > d > d ).

thf(decl_25,type,
    tyop_2Eoption_2Eoption: d > d ).

thf(decl_26,type,
    s: d > u > du ).

thf(decl_27,type,
    app_2E2: du > du > u ).

thf(decl_43,type,
    c_2Eoption_2EIS__NONE_2E1: du > u ).

thf(decl_45,type,
    c_2Eoption_2EIS__SOME_2E1: du > u ).

thf(decl_46,type,
    c_2Eoption_2ENONE_2E0: u ).

thf(decl_48,type,
    c_2Eoption_2EOPTION__JOIN_2E1: du > u ).

thf(decl_50,type,
    c_2Eoption_2EOPTION__MAP_2E2: du > du > u ).

thf(decl_52,type,
    c_2Eoption_2EOPTREL_2E3: du > du > du > u ).

thf(decl_53,type,
    c_2Eoption_2ESOME_2E0: u ).

thf(decl_54,type,
    c_2Eoption_2ESOME_2E1: du > u ).

thf(decl_57,type,
    c_2Eoption_2ETHE_2E1: du > u ).

thf(decl_61,type,
    c_2Eoption_2Eoption__CASE_2E3: du > du > du > u ).

thf(decl_68,type,
    mono_2Ec_2Ebool_2EF: $o ).

thf(decl_69,type,
    mono_2Ec_2Ebool_2ET: $o ).

thf(decl_72,type,
    i_mono_2Etyop_2Emin_2Ebool: $o > u ).

thf(decl_75,type,
    j_mono_2Etyop_2Emin_2Ebool: du > $o ).

thf(decl_78,type,
    esk1_0: d ).

thf(decl_79,type,
    esk2_0: u ).

thf(decl_80,type,
    esk3_0: u ).

thf(decl_81,type,
    esk4_0: u ).

thf(decl_83,type,
    esk6_5: d > d > u > u > u > u ).

thf(decl_84,type,
    esk7_5: d > d > u > u > u > u ).

thf(thm_2Equotient__option_2EOPTION__REL__def,conjecture,
    ! [X1: d,X55: u,X13: u,X56: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X56 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      <=> mono_2Ec_2Ebool_2ET )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X56 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X13 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      <=> mono_2Ec_2Ebool_2EF )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X56 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X55 ) ) ) ) ) )
      <=> mono_2Ec_2Ebool_2EF )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X56 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X13 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X55 ) ) ) ) ) )
      <=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X56 ) @ ( s @ X1 @ X13 ) ) ) @ ( s @ X1 @ X55 ) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.0hrxiejLMR/E---3.1_3612620.p',thm_2Equotient__option_2EOPTION__REL__def) ).

thf(thm_2Eoption_2Eoption__CLAUSES,axiom,
    ! [X1: d,X2: d,X3: u,X26: u,X27: u] :
      ( ! [X28: u,X29: u] :
          ( ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X28 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X29 ) ) ) )
        <=> ( ( s @ X1 @ X28 )
            = ( s @ X1 @ X29 ) ) )
      & ! [X30: u] :
          ( ( s @ X1 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X30 ) ) ) ) )
          = ( s @ X1 @ X30 ) )
      & ! [X31: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 )
         != ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X31 ) ) ) )
      & ! [X32: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X32 ) ) )
         != ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) )
      & ! [X33: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X33 ) ) ) ) ) )
        <=> mono_2Ec_2Ebool_2ET )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      <=> mono_2Ec_2Ebool_2EF )
      & ! [X34: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X34 ) ) ) )
        <=> ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X34 )
            = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) )
      & ! [X35: u] :
          ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X35 ) ) ) )
        <=> ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X35 )
            = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) )
      & ! [X36: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X36 ) ) ) )
         => ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X36 ) ) ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X36 ) ) )
      & ! [X37: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X37 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X37 ) )
      & ! [X38: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X38 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X38 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X38 ) )
      & ! [X39: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X39 ) ) ) )
         => ( ( s @ X2 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X39 ) @ ( s @ X2 @ X27 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X3 ) ) )
            = ( s @ X2 @ X27 ) ) )
      & ! [X40: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X40 ) ) ) )
         => ( ( s @ X2 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X40 ) @ ( s @ X2 @ X27 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X3 ) ) )
            = ( s @ X2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X3 ) @ ( s @ X1 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X40 ) ) ) ) ) ) )
      & ! [X41: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X41 ) ) ) )
         => ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X41 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X26 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X41 ) ) )
      & ! [X42: u,X43: u] :
          ( ( s @ X2 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ X2 @ X42 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X43 ) ) )
          = ( s @ X2 @ X42 ) )
      & ! [X44: u,X45: u,X46: u] :
          ( ( s @ X2 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X44 ) ) ) @ ( s @ X2 @ X45 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X46 ) ) )
          = ( s @ X2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X46 ) @ ( s @ X1 @ X44 ) ) ) )
      & ! [X47: u,X48: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X47 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X48 ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X47 ) @ ( s @ X1 @ X48 ) ) ) ) ) )
      & ! [X49: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X49 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) )
      & ! [X50: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X50 ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X50 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.0hrxiejLMR/E---3.1_3612620.p',thm_2Eoption_2Eoption__CLAUSES) ).

thf(thm_2Ebool_2EAND__CLAUSES,axiom,
    ! [X25: $o] :
      ( ( ( mono_2Ec_2Ebool_2ET
          & X25 )
      <=> X25 )
      & ( ( X25
          & mono_2Ec_2Ebool_2ET )
      <=> X25 )
      & ( ( mono_2Ec_2Ebool_2EF
          & X25 )
      <=> mono_2Ec_2Ebool_2EF )
      & ( ( X25
          & mono_2Ec_2Ebool_2EF )
      <=> mono_2Ec_2Ebool_2EF )
      & ( ( X25
          & X25 )
      <=> X25 ) ),
    file('/export/starexec/sandbox/tmp/tmp.0hrxiejLMR/E---3.1_3612620.p',thm_2Ebool_2EAND__CLAUSES) ).

thf(thm_2Eoption_2EOPTREL__def,axiom,
    ! [X1: d,X2: d,X51: u,X13: u,X52: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X51 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X13 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X52 ) ) ) )
    <=> ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X13 )
            = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) )
          & ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X52 )
            = ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) )
        | ? [X53: u,X54: u] :
            ( ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X13 )
              = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X53 ) ) ) )
            & ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X52 )
              = ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X54 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X51 ) @ ( s @ X1 @ X53 ) ) ) @ ( s @ X2 @ X54 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.0hrxiejLMR/E---3.1_3612620.p',thm_2Eoption_2EOPTREL__def) ).

thf(thm_2Ebool_2EFALSITY,axiom,
    ! [X25: $o] :
      ( mono_2Ec_2Ebool_2EF
     => X25 ),
    file('/export/starexec/sandbox/tmp/tmp.0hrxiejLMR/E---3.1_3612620.p',thm_2Ebool_2EFALSITY) ).

thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
    ! [X1: d,X16: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X16 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ X1 @ X16 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.0hrxiejLMR/E---3.1_3612620.p',arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a) ).

thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X11: u] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ X11 ) ) ) )
      = ( s @ tyop_2Emin_2Ebool @ X11 ) ),
    file('/export/starexec/sandbox/tmp/tmp.0hrxiejLMR/E---3.1_3612620.p',ij_2Emono_2Etyop_2Emin_2Ebool) ).

thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X9: $o] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X9 ) ) )
    <=> X9 ),
    file('/export/starexec/sandbox/tmp/tmp.0hrxiejLMR/E---3.1_3612620.p',ji_2Emono_2Etyop_2Emin_2Ebool) ).

thf(c_0_8,negated_conjecture,
    ~ ! [X1: d,X55: u,X13: u,X56: u] :
        ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X56 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
        <=> mono_2Ec_2Ebool_2ET )
        & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X56 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X13 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
        <=> mono_2Ec_2Ebool_2EF )
        & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X56 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X55 ) ) ) ) ) )
        <=> mono_2Ec_2Ebool_2EF )
        & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X56 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X13 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X55 ) ) ) ) ) )
        <=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X56 ) @ ( s @ X1 @ X13 ) ) ) @ ( s @ X1 @ X55 ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[thm_2Equotient__option_2EOPTION__REL__def]) ).

thf(c_0_9,plain,
    ! [X1: d,X2: d,X3: u,X26: u,X27: u] :
      ( ! [X28: u,X29: u] :
          ( ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X28 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X29 ) ) ) )
        <=> ( ( s @ X1 @ X28 )
            = ( s @ X1 @ X29 ) ) )
      & ! [X30: u] :
          ( ( s @ X1 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X30 ) ) ) ) )
          = ( s @ X1 @ X30 ) )
      & ! [X31: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 )
         != ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X31 ) ) ) )
      & ! [X32: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X32 ) ) )
         != ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) )
      & ! [X33: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X33 ) ) ) ) ) )
        <=> mono_2Ec_2Ebool_2ET )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      <=> mono_2Ec_2Ebool_2EF )
      & ! [X34: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X34 ) ) ) )
        <=> ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X34 )
            = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) )
      & ! [X35: u] :
          ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X35 ) ) ) )
        <=> ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X35 )
            = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) )
      & ! [X36: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X36 ) ) ) )
         => ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X36 ) ) ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X36 ) ) )
      & ! [X37: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X37 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X37 ) )
      & ! [X38: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X38 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X38 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X38 ) )
      & ! [X39: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X39 ) ) ) )
         => ( ( s @ X2 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X39 ) @ ( s @ X2 @ X27 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X3 ) ) )
            = ( s @ X2 @ X27 ) ) )
      & ! [X40: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X40 ) ) ) )
         => ( ( s @ X2 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X40 ) @ ( s @ X2 @ X27 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X3 ) ) )
            = ( s @ X2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X3 ) @ ( s @ X1 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X40 ) ) ) ) ) ) )
      & ! [X41: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X41 ) ) ) )
         => ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X41 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X26 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X41 ) ) )
      & ! [X42: u,X43: u] :
          ( ( s @ X2 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ X2 @ X42 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X43 ) ) )
          = ( s @ X2 @ X42 ) )
      & ! [X44: u,X45: u,X46: u] :
          ( ( s @ X2 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X44 ) ) ) @ ( s @ X2 @ X45 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X46 ) ) )
          = ( s @ X2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X46 ) @ ( s @ X1 @ X44 ) ) ) )
      & ! [X47: u,X48: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X47 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X48 ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X47 ) @ ( s @ X1 @ X48 ) ) ) ) ) )
      & ! [X49: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X49 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) )
      & ! [X50: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X50 ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X50 ) ) ),
    inference(fof_simplification,[status(thm)],[thm_2Eoption_2Eoption__CLAUSES]) ).

thf(c_0_10,negated_conjecture,
    ( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ~ mono_2Ec_2Ebool_2EF
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | ~ mono_2Ec_2Ebool_2EF
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | ~ mono_2Ec_2Ebool_2ET )
    & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ~ mono_2Ec_2Ebool_2EF
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | ~ mono_2Ec_2Ebool_2EF
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | ~ mono_2Ec_2Ebool_2ET )
    & ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | mono_2Ec_2Ebool_2EF
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | ~ mono_2Ec_2Ebool_2EF
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | ~ mono_2Ec_2Ebool_2ET )
    & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | mono_2Ec_2Ebool_2EF
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | ~ mono_2Ec_2Ebool_2EF
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | ~ mono_2Ec_2Ebool_2ET )
    & ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ~ mono_2Ec_2Ebool_2EF
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | mono_2Ec_2Ebool_2EF
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | ~ mono_2Ec_2Ebool_2ET )
    & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ~ mono_2Ec_2Ebool_2EF
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | mono_2Ec_2Ebool_2EF
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | ~ mono_2Ec_2Ebool_2ET )
    & ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | mono_2Ec_2Ebool_2EF
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | mono_2Ec_2Ebool_2EF
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | ~ mono_2Ec_2Ebool_2ET )
    & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | mono_2Ec_2Ebool_2EF
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | mono_2Ec_2Ebool_2EF
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | ~ mono_2Ec_2Ebool_2ET )
    & ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ~ mono_2Ec_2Ebool_2EF
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | ~ mono_2Ec_2Ebool_2EF
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | mono_2Ec_2Ebool_2ET )
    & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ~ mono_2Ec_2Ebool_2EF
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | ~ mono_2Ec_2Ebool_2EF
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | mono_2Ec_2Ebool_2ET )
    & ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | mono_2Ec_2Ebool_2EF
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | ~ mono_2Ec_2Ebool_2EF
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | mono_2Ec_2Ebool_2ET )
    & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | mono_2Ec_2Ebool_2EF
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | ~ mono_2Ec_2Ebool_2EF
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | mono_2Ec_2Ebool_2ET )
    & ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ~ mono_2Ec_2Ebool_2EF
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | mono_2Ec_2Ebool_2EF
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | mono_2Ec_2Ebool_2ET )
    & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ~ mono_2Ec_2Ebool_2EF
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | mono_2Ec_2Ebool_2EF
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | mono_2Ec_2Ebool_2ET )
    & ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | mono_2Ec_2Ebool_2EF
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | mono_2Ec_2Ebool_2EF
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | mono_2Ec_2Ebool_2ET )
    & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | mono_2Ec_2Ebool_2EF
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | mono_2Ec_2Ebool_2EF
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | mono_2Ec_2Ebool_2ET ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])]) ).

thf(c_0_11,plain,
    ! [X25: $o] :
      ( ( ( mono_2Ec_2Ebool_2ET
          & X25 )
      <=> X25 )
      & ( ( X25
          & mono_2Ec_2Ebool_2ET )
      <=> X25 )
      & ( ( mono_2Ec_2Ebool_2EF
          & X25 )
      <=> mono_2Ec_2Ebool_2EF )
      & ( ( X25
          & mono_2Ec_2Ebool_2EF )
      <=> mono_2Ec_2Ebool_2EF ) ),
    inference(fof_simplification,[status(thm)],[thm_2Ebool_2EAND__CLAUSES]) ).

thf(c_0_12,plain,
    ! [X174: d,X175: d,X176: u,X177: u,X178: u,X181: d,X182: d,X183: u,X184: u,X185: u,X186: u,X187: u] :
      ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ X177 )
          = ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X174 @ ( esk6_5 @ X174 @ X175 @ X176 @ X177 @ X178 ) ) ) ) )
        | ( ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ X177 )
          = ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ c_2Eoption_2ENONE_2E0 ) )
        | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X174 @ ( tyop_2Emin_2Efun @ X175 @ tyop_2Emin_2Ebool ) ) @ X176 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ X177 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ X178 ) ) ) ) )
      & ( ( ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ X178 )
          = ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X175 @ ( esk7_5 @ X174 @ X175 @ X176 @ X177 @ X178 ) ) ) ) )
        | ( ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ X177 )
          = ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ c_2Eoption_2ENONE_2E0 ) )
        | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X174 @ ( tyop_2Emin_2Efun @ X175 @ tyop_2Emin_2Ebool ) ) @ X176 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ X177 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ X178 ) ) ) ) )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X175 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X174 @ ( tyop_2Emin_2Efun @ X175 @ tyop_2Emin_2Ebool ) ) @ X176 ) @ ( s @ X174 @ ( esk6_5 @ X174 @ X175 @ X176 @ X177 @ X178 ) ) ) ) @ ( s @ X175 @ ( esk7_5 @ X174 @ X175 @ X176 @ X177 @ X178 ) ) ) ) )
        | ( ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ X177 )
          = ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ c_2Eoption_2ENONE_2E0 ) )
        | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X174 @ ( tyop_2Emin_2Efun @ X175 @ tyop_2Emin_2Ebool ) ) @ X176 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ X177 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ X178 ) ) ) ) )
      & ( ( ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ X177 )
          = ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X174 @ ( esk6_5 @ X174 @ X175 @ X176 @ X177 @ X178 ) ) ) ) )
        | ( ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ X178 )
          = ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ c_2Eoption_2ENONE_2E0 ) )
        | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X174 @ ( tyop_2Emin_2Efun @ X175 @ tyop_2Emin_2Ebool ) ) @ X176 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ X177 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ X178 ) ) ) ) )
      & ( ( ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ X178 )
          = ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X175 @ ( esk7_5 @ X174 @ X175 @ X176 @ X177 @ X178 ) ) ) ) )
        | ( ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ X178 )
          = ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ c_2Eoption_2ENONE_2E0 ) )
        | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X174 @ ( tyop_2Emin_2Efun @ X175 @ tyop_2Emin_2Ebool ) ) @ X176 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ X177 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ X178 ) ) ) ) )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X175 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X174 @ ( tyop_2Emin_2Efun @ X175 @ tyop_2Emin_2Ebool ) ) @ X176 ) @ ( s @ X174 @ ( esk6_5 @ X174 @ X175 @ X176 @ X177 @ X178 ) ) ) ) @ ( s @ X175 @ ( esk7_5 @ X174 @ X175 @ X176 @ X177 @ X178 ) ) ) ) )
        | ( ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ X178 )
          = ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ c_2Eoption_2ENONE_2E0 ) )
        | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X174 @ ( tyop_2Emin_2Efun @ X175 @ tyop_2Emin_2Ebool ) ) @ X176 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ X177 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ X178 ) ) ) ) )
      & ( ( ( s @ ( tyop_2Eoption_2Eoption @ X181 ) @ X184 )
         != ( s @ ( tyop_2Eoption_2Eoption @ X181 ) @ c_2Eoption_2ENONE_2E0 ) )
        | ( ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X185 )
         != ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ c_2Eoption_2ENONE_2E0 ) )
        | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X181 @ ( tyop_2Emin_2Efun @ X182 @ tyop_2Emin_2Ebool ) ) @ X183 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X181 ) @ X184 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X185 ) ) ) ) )
      & ( ( ( s @ ( tyop_2Eoption_2Eoption @ X181 ) @ X184 )
         != ( s @ ( tyop_2Eoption_2Eoption @ X181 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X181 @ X186 ) ) ) )
        | ( ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X185 )
         != ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X182 @ X187 ) ) ) )
        | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X182 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X181 @ ( tyop_2Emin_2Efun @ X182 @ tyop_2Emin_2Ebool ) ) @ X183 ) @ ( s @ X181 @ X186 ) ) ) @ ( s @ X182 @ X187 ) ) ) )
        | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X181 @ ( tyop_2Emin_2Efun @ X182 @ tyop_2Emin_2Ebool ) ) @ X183 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X181 ) @ X184 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X185 ) ) ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Eoption_2EOPTREL__def])])])])])])]) ).

thf(c_0_13,plain,
    ! [X194: d,X195: d,X196: u,X197: u,X198: u,X199: u,X200: u,X201: u,X202: u,X203: u,X204: u,X205: u,X206: u,X207: u,X208: u,X209: u,X210: u,X211: u,X212: u,X213: u,X214: u,X215: u,X216: u,X217: u,X218: u,X219: u,X220: u,X221: u] :
      ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ X199 ) ) )
         != ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ X200 ) ) ) )
        | ( ( s @ X194 @ X199 )
          = ( s @ X194 @ X200 ) ) )
      & ( ( ( s @ X194 @ X199 )
         != ( s @ X194 @ X200 ) )
        | ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ X199 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ X200 ) ) ) ) )
      & ( ( s @ X194 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ X201 ) ) ) ) )
        = ( s @ X194 @ X201 ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ c_2Eoption_2ENONE_2E0 )
       != ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ X202 ) ) ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ X203 ) ) )
       != ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ c_2Eoption_2ENONE_2E0 ) )
      & ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ X204 ) ) ) ) ) )
        | mono_2Ec_2Ebool_2ET )
      & ( ~ mono_2Ec_2Ebool_2ET
        | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ X204 ) ) ) ) ) ) )
      & ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
        | mono_2Ec_2Ebool_2EF )
      & ( ~ mono_2Ec_2Ebool_2EF
        | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) )
      & ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X205 ) ) ) )
        | ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X205 )
          = ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ c_2Eoption_2ENONE_2E0 ) ) )
      & ( ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X205 )
         != ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ c_2Eoption_2ENONE_2E0 ) )
        | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X205 ) ) ) ) )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X206 ) ) ) )
        | ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X206 )
          = ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ c_2Eoption_2ENONE_2E0 ) ) )
      & ( ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X206 )
         != ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ c_2Eoption_2ENONE_2E0 ) )
        | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X206 ) ) ) ) )
      & ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X207 ) ) ) )
        | ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X207 ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X207 ) ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X208 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X194 @ ( tyop_2Eoption_2Eoption @ X194 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X208 ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X209 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X209 ) @ ( s @ ( tyop_2Emin_2Efun @ X194 @ ( tyop_2Eoption_2Eoption @ X194 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X209 ) )
      & ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X210 ) ) ) )
        | ( ( s @ X195 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X210 ) @ ( s @ X195 @ X198 ) @ ( s @ ( tyop_2Emin_2Efun @ X194 @ X195 ) @ X196 ) ) )
          = ( s @ X195 @ X198 ) ) )
      & ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X211 ) ) ) )
        | ( ( s @ X195 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X211 ) @ ( s @ X195 @ X198 ) @ ( s @ ( tyop_2Emin_2Efun @ X194 @ X195 ) @ X196 ) ) )
          = ( s @ X195 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X194 @ X195 ) @ X196 ) @ ( s @ X194 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X211 ) ) ) ) ) ) )
      & ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X212 ) ) ) )
        | ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X212 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X197 ) @ ( s @ ( tyop_2Emin_2Efun @ X194 @ ( tyop_2Eoption_2Eoption @ X194 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X212 ) ) )
      & ( ( s @ X195 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ X195 @ X213 ) @ ( s @ ( tyop_2Emin_2Efun @ X194 @ X195 ) @ X214 ) ) )
        = ( s @ X195 @ X213 ) )
      & ( ( s @ X195 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ X215 ) ) ) @ ( s @ X195 @ X216 ) @ ( s @ ( tyop_2Emin_2Efun @ X194 @ X195 ) @ X217 ) ) )
        = ( s @ X195 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X194 @ X195 ) @ X217 ) @ ( s @ X194 @ X215 ) ) ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ X195 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X194 @ X195 ) @ X218 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ X219 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ X195 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X195 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X194 @ X195 ) @ X218 ) @ ( s @ X194 @ X219 ) ) ) ) ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ X195 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X194 @ X195 ) @ X220 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ c_2Eoption_2ENONE_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ X195 ) @ c_2Eoption_2ENONE_2E0 ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X194 ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ c_2Eoption_2ENONE_2E0 ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X194 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X221 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X221 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).

thf(c_0_14,negated_conjecture,
    ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
    | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
    | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
    | mono_2Ec_2Ebool_2EF
    | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
    | mono_2Ec_2Ebool_2EF
    | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
    | ~ mono_2Ec_2Ebool_2ET ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_15,plain,
    ! [X223: $o] :
      ( ( ~ mono_2Ec_2Ebool_2ET
        | ~ X223
        | X223 )
      & ( mono_2Ec_2Ebool_2ET
        | ~ X223 )
      & ( X223
        | ~ X223 )
      & ( ~ X223
        | ~ mono_2Ec_2Ebool_2ET
        | X223 )
      & ( X223
        | ~ X223 )
      & ( mono_2Ec_2Ebool_2ET
        | ~ X223 )
      & ( ~ mono_2Ec_2Ebool_2EF
        | ~ X223
        | mono_2Ec_2Ebool_2EF )
      & ( mono_2Ec_2Ebool_2EF
        | ~ mono_2Ec_2Ebool_2EF )
      & ( X223
        | ~ mono_2Ec_2Ebool_2EF )
      & ( ~ X223
        | ~ mono_2Ec_2Ebool_2EF
        | mono_2Ec_2Ebool_2EF )
      & ( X223
        | ~ mono_2Ec_2Ebool_2EF )
      & ( mono_2Ec_2Ebool_2EF
        | ~ mono_2Ec_2Ebool_2EF ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).

thf(c_0_16,plain,
    ! [X222: $o] :
      ( ~ mono_2Ec_2Ebool_2EF
      | X222 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Ebool_2EFALSITY])])]) ).

thf(c_0_17,plain,
    ! [X1: d,X5: u,X4: u,X3: u,X2: d] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X4 ) ) ) )
      | ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 )
       != ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) )
      | ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X4 )
       != ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_18,plain,
    ! [X1: d,X2: d,X4: u,X3: u,X5: u] :
      ( ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 )
        = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ ( esk6_5 @ X1 @ X2 @ X4 @ X3 @ X5 ) ) ) ) )
      | ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X5 )
        = ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X5 ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_19,plain,
    ! [X3: u,X2: d,X1: d] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_20,plain,
    ! [X1: d,X3: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 )
     != ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X3 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_21,plain,
    ! [X188: d,X189: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ X188 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X188 @ X189 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ X188 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X188 @ ( tyop_2Eoption_2Eoption @ X188 ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ X188 @ X189 ) ) ) ),
    inference(variable_rename,[status(thm)],[arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a]) ).

thf(c_0_22,plain,
    ! [X2: d,X1: d,X5: u,X4: u,X3: u] :
      ( ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 )
        = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ ( esk7_5 @ X2 @ X1 @ X4 @ X5 @ X3 ) ) ) ) )
      | ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X5 )
        = ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_23,negated_conjecture,
    ( mono_2Ec_2Ebool_2EF
    | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
    | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
    | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
    | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
    | ~ mono_2Ec_2Ebool_2ET
    | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ),
    inference(cn,[status(thm)],[c_0_14]) ).

thf(c_0_24,plain,
    mono_2Ec_2Ebool_2ET,
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_15])])]) ).

thf(c_0_25,plain,
    ~ mono_2Ec_2Ebool_2EF,
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_16])])]) ).

thf(c_0_26,plain,
    ! [X3: u,X4: u,X2: d,X1: d] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      | ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X4 )
       != ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) ),
    inference(er,[status(thm)],[c_0_17]) ).

thf(c_0_27,plain,
    ! [X1: d,X2: d,X4: u,X3: u] :
      ( ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 )
        = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 ) ) ) ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).

thf(c_0_28,plain,
    ! [X1: d,X3: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X3 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ X1 @ X3 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

thf(c_0_29,plain,
    ! [X1: d,X4: u,X3: u,X2: d] :
      ( ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 )
        = ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_19]),c_0_20]) ).

thf(c_0_30,negated_conjecture,
    ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
    | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
    | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
    | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
    | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]),c_0_25]) ).

thf(c_0_31,plain,
    ! [X1: d,X3: u,X2: d] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ),
    inference(er,[status(thm)],[c_0_26]) ).

thf(c_0_32,plain,
    ! [X1: d,X2: d,X3: u,X4: u] :
      ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X4 ) ) ) ) ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_20]) ).

thf(c_0_33,plain,
    ! [X1: d,X4: u,X3: u,X2: d] :
      ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_28]),c_0_20]) ).

thf(c_0_34,negated_conjecture,
    ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
    | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]),c_0_32]),c_0_33]) ).

thf(c_0_35,plain,
    ! [X2: d,X1: d,X4: u,X3: u,X5: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ X2 @ ( esk6_5 @ X2 @ X1 @ X3 @ X4 @ X5 ) ) ) ) @ ( s @ X1 @ ( esk7_5 @ X2 @ X1 @ X3 @ X4 @ X5 ) ) ) ) )
      | ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X4 )
        = ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X5 ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_36,plain,
    ! [X1: d,X3: u] :
      ( ( s @ X1 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X3 ) ) ) ) )
      = ( s @ X1 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_37,negated_conjecture,
    ( ( ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ ( esk7_5 @ esk1_0 @ esk1_0 @ esk4_0 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) )
    | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_34]),c_0_20]) ).

thf(c_0_38,axiom,
    ! [X11: u] :
      ( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ X11 ) )
        | ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) )
          = ( s @ tyop_2Emin_2Ebool @ X11 ) ) )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ X11 ) )
        | ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) )
          = ( s @ tyop_2Emin_2Ebool @ X11 ) ) ) ),
    inference(fool_unroll,[status(thm)],[ij_2Emono_2Etyop_2Emin_2Ebool]) ).

thf(c_0_39,negated_conjecture,
    ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ ( esk6_5 @ esk1_0 @ esk1_0 @ esk4_0 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) ) @ ( s @ esk1_0 @ ( esk7_5 @ esk1_0 @ esk1_0 @ esk4_0 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) ) )
    | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_34]),c_0_20]) ).

thf(c_0_40,negated_conjecture,
    ( ( ( s @ esk1_0 @ ( esk7_5 @ esk1_0 @ esk1_0 @ esk4_0 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) )
      = ( s @ esk1_0 @ esk2_0 ) )
    | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_36]) ).

thf(c_0_41,negated_conjecture,
    ( ( ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ ( esk6_5 @ esk1_0 @ esk1_0 @ esk4_0 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) )
    | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_34]),c_0_20]) ).

thf(c_0_42,negated_conjecture,
    ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
    | mono_2Ec_2Ebool_2EF
    | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
    | mono_2Ec_2Ebool_2EF
    | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
    | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
    | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
    | ~ mono_2Ec_2Ebool_2ET ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_43,plain,
    ! [X158: u] :
      ( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ X158 ) )
        | ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) )
          = ( s @ tyop_2Emin_2Ebool @ X158 ) ) )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ X158 ) )
        | ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) )
          = ( s @ tyop_2Emin_2Ebool @ X158 ) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_38])]) ).

thf(c_0_44,negated_conjecture,
    ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ ( esk6_5 @ esk1_0 @ esk1_0 @ esk4_0 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
    | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

thf(c_0_45,negated_conjecture,
    ( ( ( s @ esk1_0 @ ( esk6_5 @ esk1_0 @ esk1_0 @ esk4_0 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) )
      = ( s @ esk1_0 @ esk3_0 ) )
    | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_41]),c_0_36]) ).

thf(c_0_46,negated_conjecture,
    ( mono_2Ec_2Ebool_2EF
    | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
    | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
    | ~ mono_2Ec_2Ebool_2ET
    | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
    | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
    | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) ) ),
    inference(cn,[status(thm)],[c_0_42]) ).

thf(c_0_47,plain,
    ! [X3: u] :
      ( ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) )
        = ( s @ tyop_2Emin_2Ebool @ X3 ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ X3 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

thf(c_0_48,negated_conjecture,
    j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

thf(c_0_49,plain,
    ! [X159: $o] :
      ( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X159 ) ) )
        | X159 )
      & ( ~ X159
        | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X159 ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ji_2Emono_2Etyop_2Emin_2Ebool])])]) ).

thf(c_0_50,negated_conjecture,
    ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
    | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
    | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
    | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
    | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_24])]),c_0_25]) ).

thf(c_0_51,plain,
    ! [X1: d,X2: d,X5: u,X4: u,X3: u,X7: u,X6: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X7 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X5 ) ) ) )
      | ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 )
       != ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X4 ) ) ) )
      | ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X5 )
       != ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X6 ) ) ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X7 ) @ ( s @ X1 @ X4 ) ) ) @ ( s @ X2 @ X6 ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_52,negated_conjecture,
    ( ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) )
    = ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) ),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

thf(c_0_53,plain,
    j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_49])])]) ).

thf(c_0_54,negated_conjecture,
    ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
    | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_31])]),c_0_32]),c_0_33]) ).

thf(c_0_55,negated_conjecture,
    ! [X4: u,X3: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ X4 ) ) ) )
      | ( ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ X4 )
       != ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) )
      | ( ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ X3 )
       != ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53])]) ).

thf(c_0_56,negated_conjecture,
    ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_48])]) ).

thf(c_0_57,plain,
    ! [X3: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ X3 ) )
      | ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ~ $true ) )
        = ( s @ tyop_2Emin_2Ebool @ X3 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

thf(c_0_58,negated_conjecture,
    ! [X3: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
      | ( ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ X3 )
       != ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) ) ),
    inference(er,[status(thm)],[c_0_55]) ).

thf(c_0_59,negated_conjecture,
    ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) )
    = ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ~ $true ) ) ),
    inference(spm,[status(thm)],[c_0_56,c_0_57]) ).

thf(c_0_60,plain,
    ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ~ $true ) ) ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_49])])]) ).

thf(c_0_61,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_58]),c_0_59]),c_0_60]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : ITP011^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04  % Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17  % Computer : n008.cluster.edu
% 0.09/0.17  % Model    : x86_64 x86_64
% 0.09/0.17  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17  % Memory   : 8046.5625MB
% 0.09/0.17  % OS       : Linux 6.8.0-71-generic
% 0.09/0.17  % CPULimit : 300
% 0.09/0.17  % WCLimit  : 300
% 0.09/0.17  % DateTime : Tue Sep 29 19:26:39 UTC 2026
% 0.09/0.17  % CPUTime  : 
% 0.09/0.17  Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22  Running higher-order theorem proving
% 0.09/0.25  Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.0hrxiejLMR/E---3.1_3612620.p
% 4.27/0.85  % Version: 3.5.1-ho
% 4.27/0.85  % Preprocessing class: HSLSSLSMSSSNSFA.
% 4.27/0.85  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.27/0.85  % Starting additional_ho_4 with 1500s (5) cores
% 4.27/0.85  % Starting pre_casc_8 with 300s (1) cores
% 4.27/0.85  % Starting pre_casc_5 with 300s (1) cores
% 4.27/0.85  % Starting pre_casc_6 with 300s (1) cores
% 4.27/0.85  % additional_ho_4 with pid 3612642 completed with status 0
% 4.27/0.85  % Result found by additional_ho_4
% 4.27/0.85  % Preprocessing class: HSLSSLSMSSSNSFA.
% 4.27/0.85  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.27/0.85  % Starting additional_ho_4 with 1500s (5) cores
% 4.27/0.85  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4.0,,6,20000,1.0))
% 4.27/0.85  % SinE strategy is GSinE(CountFormulas,hypos,4.0,,6,20000,1.0)
% 4.27/0.85  % Search class: HGHSM-FFLM32-DSFFFFBN
% 4.27/0.85  % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 4.27/0.85  % Starting SubtermCWHack with 151s (1) cores
% 4.27/0.85  % Starting lpo8_s with 901s (1) cores
% 4.27/0.85  % Starting pre_casc_8 with 151s (1) cores
% 4.27/0.85  % Starting additional_ho_4 with 151s (1) cores
% 4.27/0.85  % Starting pre_casc_6 with 146s (1) cores
% 4.27/0.85  % additional_ho_4 with pid 3612656 completed with status 0
% 4.27/0.85  % Result found by additional_ho_4
% 4.27/0.85  % Preprocessing class: HSLSSLSMSSSNSFA.
% 4.27/0.85  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.27/0.85  % Starting additional_ho_4 with 1500s (5) cores
% 4.27/0.85  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4.0,,6,20000,1.0))
% 4.27/0.85  % SinE strategy is GSinE(CountFormulas,hypos,4.0,,6,20000,1.0)
% 4.27/0.85  % Search class: HGHSM-FFLM32-DSFFFFBN
% 4.27/0.85  % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 4.27/0.85  % Starting SubtermCWHack with 151s (1) cores
% 4.27/0.85  % Starting lpo8_s with 901s (1) cores
% 4.27/0.85  % Starting pre_casc_8 with 151s (1) cores
% 4.27/0.85  % Starting additional_ho_4 with 151s (1) cores
% 4.27/0.85  % Preprocessing time       : 0.004 s
% 4.27/0.85  % Presaturation interreduction done
% 4.27/0.85  
% 4.27/0.85  % Proof found!
% 4.27/0.85  % SZS status Theorem
% 4.27/0.85  % SZS output start CNFRefutation
% See solution above
% 4.27/0.85  % Parsed axioms                        : 106
% 4.27/0.85  % Removed by relevancy pruning/SinE    : 75
% 4.27/0.85  % Initial clauses                      : 125
% 4.27/0.85  % Removed in clause preprocessing      : 34
% 4.27/0.85  % Initial clauses in saturation        : 91
% 4.27/0.85  % Processed clauses                    : 2818
% 4.27/0.85  % ...of these trivial                  : 37
% 4.27/0.85  % ...subsumed                          : 2389
% 4.27/0.85  % ...remaining for further processing  : 392
% 4.27/0.85  % Other redundant clauses eliminated   : 0
% 4.27/0.85  % Clauses deleted for lack of memory   : 0
% 4.27/0.85  % Backward-subsumed                    : 18
% 4.27/0.85  % Backward-rewritten                   : 41
% 4.27/0.85  % Generated clauses                    : 14835
% 4.27/0.85  % ...of the previous two non-redundant : 10909
% 4.27/0.85  % ...aggressively subsumed             : 0
% 4.27/0.85  % Contextual simplify-reflections      : 1
% 4.27/0.85  % Paramodulations                      : 14535
% 4.27/0.85  % Factorizations                       : 57
% 4.27/0.85  % NegExts                              : 40
% 4.27/0.85  % Equation resolutions                 : 43
% 4.27/0.85  % Disequality decompositions           : 0
% 4.27/0.85  % Total rewrite steps                  : 4897
% 4.27/0.85  % ...of those cached                   : 3670
% 4.27/0.85  % Propositional unsat checks           : 0
% 4.27/0.85  %    Propositional check models        : 0
% 4.27/0.85  %    Propositional check unsatisfiable : 0
% 4.27/0.85  %    Propositional clauses             : 0
% 4.27/0.85  %    Propositional clauses after purity: 0
% 4.27/0.85  %    Propositional unsat core size     : 0
% 4.27/0.85  %    Propositional preprocessing time  : 0.000
% 4.27/0.85  %    Propositional encoding time       : 0.000
% 4.27/0.85  %    Propositional solver time         : 0.000
% 4.27/0.85  %    Success case prop preproc time    : 0.000
% 4.27/0.85  %    Success case prop encoding time   : 0.000
% 4.27/0.85  %    Success case prop solver time     : 0.000
% 4.27/0.85  % Current number of processed clauses  : 245
% 4.27/0.85  %    Positive orientable unit clauses  : 41
% 4.27/0.85  %    Positive unorientable unit clauses: 3
% 4.27/0.85  %    Negative unit clauses             : 11
% 4.27/0.85  %    Non-unit-clauses                  : 190
% 4.27/0.85  % Current number of unprocessed clauses: 8022
% 4.27/0.85  % ...number of literals in the above   : 32388
% 4.27/0.85  % Current number of archived formulas  : 0
% 4.27/0.85  % Current number of archived clauses   : 147
% 4.27/0.85  % Clause-clause subsumption calls (NU) : 17129
% 4.27/0.85  % Rec. Clause-clause subsumption calls : 7040
% 4.27/0.85  % Non-unit clause-clause subsumptions  : 1488
% 4.27/0.85  % Unit Clause-clause subsumption calls : 134
% 4.27/0.85  % Rewrite failures with RHS unbound    : 0
% 4.27/0.85  % BW rewrite match attempts            : 291
% 4.27/0.85  % BW rewrite match successes           : 21
% 4.27/0.85  % Condensation attempts                : 0
% 4.27/0.85  % Condensation successes               : 0
% 4.27/0.85  % Termbank termtop insertions          : 426782
% 4.27/0.85  % Search garbage collected termcells   : 1993
% 4.27/0.85  
% 4.27/0.85  % -------------------------------------------------
% 4.27/0.85  % User time                : 0.556 s
% 4.27/0.85  % System time              : 0.015 s
% 4.27/0.85  % Total time               : 0.571 s
% 4.27/0.85  % Maximum resident set size: 4056 pages
% 4.27/0.85  
% 4.27/0.85  % -------------------------------------------------
% 4.27/0.85  % User time                : 2.648 s
% 4.27/0.85  % System time              : 0.083 s
% 4.27/0.85  % Total time               : 2.731 s
% 4.27/0.85  % Maximum resident set size: 5120 pages
% 4.27/0.85  % E exiting
%------------------------------------------------------------------------------