%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO030^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n026.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 : Fri Sep  1 04:44:46 EDT 2023

% Result   : Theorem 0.19s 0.36s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   21 (  10 unt;   1 typ;   2 def)
%            Number of atoms       :   38 (   2 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   59 (  20   ~;   8   |;   0   &;  17   @)
%                                         (   6 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;  10 con; 0-2 aty)
%            Number of variables   :   15 (   5   ^;  10   !;   0   ?;  15   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
    eigen__2: $o ).

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

thf(eigendef_eigen__2,definition,
    ( eigen__2
    = ( eps__0
      @ ^ [X1: $o] :
          ~ ~ ! [X2: $o > $o] :
                ( ( X2 @ ~ X1 )
               => ( X2 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__2])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $o > $o] :
        ( ( X1 @ ~ eigen__2 )
       => ( X1 @ eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> eigen__2 ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

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

thf(sP4,plain,
    ( sP4
  <=> ( sP2
     => ~ sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

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

thf(sP6,plain,
    ( sP6
  <=> ( ~ sP2
     => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(def_leibeq,definition,
    ( leibeq
    = ( ^ [X1: $o,X2: $o] :
        ! [X3: $o > $o] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( X3 @ X1 )
          @ ( X3 @ X2 ) ) ) ) ).

thf(conj,conjecture,
    ~ sP5 ).

thf(h1,negated_conjecture,
    sP5,
    inference(assume_negation,[status(cth)],[conj]) ).

thf(1,plain,
    ( ~ sP6
    | sP2
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP4
    | ~ sP2
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP1
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP1
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP3
    | sP1 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).

thf(6,plain,
    ( ~ sP5
    | ~ sP3 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(8,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[7,h0]) ).

thf(0,theorem,
    ~ sP5,
    inference(contra,[status(thm),contra(discharge,[h1])],[7,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYO030^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n026.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat Aug 26 08:29:48 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.36  % SZS status Theorem
% 0.19/0.36  % Mode: cade22grackle2xfee4
% 0.19/0.36  % Steps: 48
% 0.19/0.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------