%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SET600^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n028.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 15:17:42 EDT 2023

% Result   : Theorem 0.17s 0.37s
% Output   : Proof 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   47
% Syntax   : Number of formulae    :   60 (  25 unt;   6 typ;   2 def)
%            Number of atoms       :  132 (  23 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  130 (  52   ~;  17   |;   0   &;  31   @)
%                                         (  14 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  20 usr;  19 con; 0-2 aty)
%            Number of variables   :   35 (  22   ^;  13   !;   0   ?;  35   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_a,type,
    a: $tType ).

thf(ty_eigen__0,type,
    eigen__0: a > $o ).

thf(ty_eigen__5,type,
    eigen__5: a ).

thf(ty_eigen__3,type,
    eigen__3: a ).

thf(ty_eigen__1,type,
    eigen__1: a > $o ).

thf(ty_eigen__2,type,
    eigen__2: a ).

thf(h0,assumption,
    ! [X1: a > $o,X2: a] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__0 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__3,definition,
    ( eigen__3
    = ( eps__0
      @ ^ [X1: a] :
          ~ ~ ( eigen__1 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__3])]) ).

thf(eigendef_eigen__2,definition,
    ( eigen__2
    = ( eps__0
      @ ^ [X1: a] :
          ~ ~ ( eigen__0 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__2])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( ~ ( eigen__0 @ eigen__5 )
     => ( eigen__1 @ eigen__5 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( ^ [X1: a] :
            ( ~ ( eigen__0 @ X1 )
           => ( eigen__1 @ X1 ) ) )
      = ( ^ [X1: a] : $false ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: a] :
        ~ ( ~ ( eigen__0 @ X1 )
         => ( eigen__1 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: a] :
        ~ ( eigen__0 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( eigen__1 @ eigen__5 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: a] :
        ~ ( eigen__1 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( eigen__1 @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( eigen__0 @ eigen__5 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( eigen__0
      = ( ^ [X1: a] : $false ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( sP9
     => ( eigen__1
       != ( ^ [X1: a] : $false ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( eigen__0 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( ~ sP11
     => ( eigen__1 @ eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( eigen__1
      = ( ^ [X1: a] : $false ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( ~ ( eigen__0 @ eigen__3 )
     => sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(cBOOL_PROP_59_pme,conjecture,
    ! [X1: a > $o,X2: a > $o] :
      ( ( ( ^ [X3: a] :
              ( ~ ( X1 @ X3 )
             => ( X2 @ X3 ) ) )
        = ( ^ [X3: a] : $false ) )
      = ( ~ ( ( X1
              = ( ^ [X3: a] : $false ) )
           => ( X2
             != ( ^ [X3: a] : $false ) ) ) ) ) ).

thf(h1,negated_conjecture,
    ~ ! [X1: a > $o,X2: a > $o] :
        ( ( ( ^ [X3: a] :
                ( ~ ( X1 @ X3 )
               => ( X2 @ X3 ) ) )
          = ( ^ [X3: a] : $false ) )
        = ( ~ ( ( X1
                = ( ^ [X3: a] : $false ) )
             => ( X2
               != ( ^ [X3: a] : $false ) ) ) ) ),
    inference(assume_negation,[status(cth)],[cBOOL_PROP_59_pme]) ).

thf(h2,assumption,
    ~ ! [X1: a > $o] :
        ( ( ( ^ [X2: a] :
                ( ~ ( eigen__0 @ X2 )
               => ( X1 @ X2 ) ) )
          = ( ^ [X2: a] : $false ) )
        = ( ~ ( sP9
             => ( X1
               != ( ^ [X2: a] : $false ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ( sP2 != ~ sP10 ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ sP10,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP10,
    introduced(assumption,[]) ).

thf(1,plain,
    ( sP14
    | ~ sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP3
    | ~ sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP12
    | ~ sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP3
    | ~ sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP6
    | sP7 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).

thf(6,plain,
    ( sP4
    | sP11 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).

thf(7,plain,
    ( ~ sP2
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP13
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP9
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP10
    | ~ sP9
    | ~ sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,h4,h5]) ).

thf(h8,assumption,
    ~ ! [X1: a] :
        ( ( ~ ( eigen__0 @ X1 )
         => ( eigen__1 @ X1 ) )
        = $false ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h10,assumption,
    sP9,
    introduced(assumption,[]) ).

thf(h11,assumption,
    sP13,
    introduced(assumption,[]) ).

thf(12,plain,
    ( ~ sP6
    | ~ sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP4
    | ~ sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP1
    | sP8
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP9
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP13
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h10,h11,h9,h8,h6,h7,h3,h2,h1,h0])],[12,13,14,15,16,h9,h10,h11]) ).

thf(18,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h9,h8,h6,h7,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h7,17,h10,h11]) ).

thf(19,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h8,h6,h7,h3,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__5)],[h8,18,h9]) ).

thf(20,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h6,h7,h3,h2,h1,h0]),tab_fe(discharge,[h8])],[h6,19,h8]) ).

thf(21,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h3,h2,h1,h0]),tab_be(discharge,[h4,h5]),tab_be(discharge,[h6,h7])],[h3,11,20,h4,h5,h6,h7]) ).

thf(22,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,21,h3]) ).

thf(23,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,22,h2]) ).

thf(24,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[23,h0]) ).

thf(0,theorem,
    ! [X1: a > $o,X2: a > $o] :
      ( ( ( ^ [X3: a] :
              ( ~ ( X1 @ X3 )
             => ( X2 @ X3 ) ) )
        = ( ^ [X3: a] : $false ) )
      = ( ~ ( ( X1
              = ( ^ [X3: a] : $false ) )
           => ( X2
             != ( ^ [X3: a] : $false ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h1])],[23,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SET600^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.10/0.31  % Computer : n028.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Sat Aug 26 09:55:22 EDT 2023
% 0.10/0.31  % CPUTime  : 
% 0.17/0.37  % SZS status Theorem
% 0.17/0.37  % Mode: cade22grackle2xfee4
% 0.17/0.37  % Steps: 55
% 0.17/0.37  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------