%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEV171^5 : 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 : n032.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 19:32:50 EDT 2023

% Result   : Theorem 140.92s 141.17s
% Output   : Proof 140.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   35 (  10 unt;   4 typ;   3 def)
%            Number of atoms       :   68 (  24 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  118 (  27   ~;  11   |;   0   &;  59   @)
%                                         (  11 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   53 (  53   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  15 usr;  16 con; 0-2 aty)
%            Number of variables   :   46 (  26   ^;  20   !;   0   ?;  46   :)

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

thf(ty_eigen__151,type,
    eigen__151: a ).

thf(ty_eigen__155,type,
    eigen__155: a ).

thf(ty_eigen__77,type,
    eigen__77: a ).

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

thf(eigendef_eigen__151,definition,
    ( eigen__151
    = ( eps__0
      @ ^ [X1: a] :
          ~ ! [X2: a] :
              ( ( ( ^ [X3: a > a > a] : ( X3 @ X1 @ X1 ) )
                = ( ^ [X3: a > a > a] : ( X3 @ X2 @ X2 ) ) )
             => ( X1 = X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__151])]) ).

thf(eigendef_eigen__77,definition,
    ( eigen__77
    = ( eps__0
      @ ^ [X1: a] :
          ~ ~ ! [X2: a] :
                ( ( ^ [X3: a > a > a] : ( X3 @ X1 @ X1 ) )
               != ( ^ [X3: a > a > a] : ( X3 @ X1 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__77])]) ).

thf(eigendef_eigen__155,definition,
    ( eigen__155
    = ( eps__0
      @ ^ [X1: a] :
          ~ ( ( ( ^ [X2: a > a > a] : ( X2 @ eigen__151 @ eigen__151 ) )
              = ( ^ [X2: a > a > a] : ( X2 @ X1 @ X1 ) ) )
           => ( eigen__151 = X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__155])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( eigen__151 = eigen__155 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: a] :
        ( ( ( ^ [X2: a > a > a] : ( X2 @ eigen__151 @ eigen__151 ) )
          = ( ^ [X2: a > a > a] : ( X2 @ X1 @ X1 ) ) )
       => ( eigen__151 = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ! [X1: a,X2: a] :
          ( ( ( ^ [X3: a > a > a] : ( X3 @ X1 @ X1 ) )
            = ( ^ [X3: a > a > a] : ( X3 @ X2 @ X2 ) ) )
         => ( X1 = X2 ) )
     => ~ ! [X1: a] :
            ~ ! [X2: a] :
                ( ( ^ [X3: a > a > a] : ( X3 @ X1 @ X1 ) )
               != ( ^ [X3: a > a > a] : ( X3 @ X1 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: a,X2: a] :
        ( ( ( ^ [X3: a > a > a] : ( X3 @ X1 @ X1 ) )
          = ( ^ [X3: a > a > a] : ( X3 @ X2 @ X2 ) ) )
       => ( X1 = X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: a] :
        ~ ! [X2: a] :
            ( ( ^ [X3: a > a > a] : ( X3 @ X1 @ X1 ) )
           != ( ^ [X3: a > a > a] : ( X3 @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: a > a > a] :
        ( ( X1 @ eigen__151 @ eigen__151 )
        = ( X1 @ eigen__155 @ eigen__155 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: a] :
        ( ( ^ [X2: a > a > a] : ( X2 @ eigen__77 @ eigen__77 ) )
       != ( ^ [X2: a > a > a] : ( X2 @ eigen__77 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( ( ^ [X1: a > a > a] : ( X1 @ eigen__151 @ eigen__151 ) )
        = ( ^ [X1: a > a > a] : ( X1 @ eigen__155 @ eigen__155 ) ) )
     => sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: a > ( a > a > a ) > a] :
        ( ! [X2: a,X3: a] :
            ( ( ( X1 @ X2 )
              = ( X1 @ X3 ) )
           => ( X2 = X3 ) )
       => ~ ! [X2: a] :
              ~ ! [X3: a] :
                  ( ( X1 @ X2 )
                 != ( ^ [X4: a > a > a] : ( X4 @ X2 @ X3 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( ( ^ [X1: a > a > a] : ( X1 @ eigen__151 @ eigen__151 ) )
      = ( ^ [X1: a > a > a] : ( X1 @ eigen__155 @ eigen__155 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(cTHM33_pme,conjecture,
    ~ sP10 ).

thf(h1,negated_conjecture,
    sP10,
    inference(assume_negation,[status(cth)],[cTHM33_pme]) ).

thf(1,plain,
    ( ~ sP6
    | sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP11
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP8
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP8
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP2
    | ~ sP8 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__155]) ).

thf(6,plain,
    ( sP4
    | ~ sP2 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__151]) ).

thf(7,plain,
    ( ~ sP7
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP5
    | sP7 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__77]) ).

thf(9,plain,
    ( ~ sP3
    | ~ sP4
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP10
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ~ sP9,
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h1]) ).

thf(13,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[12,h0]) ).

thf(0,theorem,
    ~ sP10,
    inference(contra,[status(thm),contra(discharge,[h1])],[12,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SEV171^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.10/0.30  % Computer : n032.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Thu Aug 24 03:14:26 EDT 2023
% 0.10/0.30  % CPUTime  : 
% 140.92/141.17  % SZS status Theorem
% 140.92/141.17  % Mode: cade22grackle2x01b3
% 140.92/141.17  % Steps: 8148455
% 140.92/141.17  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------