%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO010^1 : 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 : n027.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 04:44:41 EDT 2023

% Result   : Theorem 20.24s 20.47s
% Output   : Proof 20.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   29 (  10 unt;   3 typ;   2 def)
%            Number of atoms       :   44 (   8 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   74 (  17   ~;   6   |;   0   &;  30   @)
%                                         (   7 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  12 usr;  11 con; 0-2 aty)
%            Number of variables   :   22 (   7   ^;  15   !;   0   ?;  22   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_p,type,
    p: ( $i > $i ) > $o ).

thf(ty_eigen__1,type,
    eigen__1: $i ).

thf(ty_f,type,
    f: $i > $i ).

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

thf(eigendef_eigen__1,definition,
    ( eigen__1
    = ( eps__0
      @ ^ [X1: $i] :
          ( X1
         != ( f @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__1])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( p
      @ ^ [X1: $i] : X1 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( f @ eigen__1 )
      = eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

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

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i] :
        ( ( f @ X1 )
        = X1 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

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

thf(sP6,plain,
    ( sP6
  <=> ( eigen__1
      = ( f @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( ^ [X1: $i] : X1 )
      = f ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

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

thf(conj,conjecture,
    ( ~ ( ! [X1: $i,X2: $i > $o] :
            ( ( X2 @ ( f @ X1 ) )
           => ( X2 @ X1 ) )
       => ~ sP1 )
   => sP5 ) ).

thf(h1,negated_conjecture,
    ~ ( ~ ( ! [X1: $i,X2: $i > $o] :
              ( ( X2 @ ( f @ X1 ) )
             => ( X2 @ X1 ) )
         => ~ sP1 )
     => sP5 ),
    inference(assume_negation,[status(cth)],[conj]) ).

thf(h2,assumption,
    ~ ( ! [X1: $i,X2: $i > $o] :
          ( ( X2 @ ( f @ X1 ) )
         => ( X2 @ X1 ) )
     => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ sP5,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ! [X1: $i,X2: $i > $o] :
      ( ( X2 @ ( f @ X1 ) )
     => ( X2 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP4
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP2
    | sP6 ),
    inference(symeq,[status(thm)],]) ).

thf(3,plain,
    ( sP3
    | ~ sP6 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(4,plain,
    ( sP7
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP1
    | sP5
    | ~ sP7 ),
    inference(mating_rule,[status(thm)],]) ).

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

thf(7,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,6,h4,h5]) ).

thf(8,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,7,h2,h3]) ).

thf(9,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[8,h0]) ).

thf(0,theorem,
    ( ~ ( ! [X1: $i,X2: $i > $o] :
            ( ( X2 @ ( f @ X1 ) )
           => ( X2 @ X1 ) )
       => ~ sP1 )
   => sP5 ),
    inference(contra,[status(thm),contra(discharge,[h1])],[8,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SYO010^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35  % Computer : n027.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sat Aug 26 08:14:35 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 20.24/20.47  % SZS status Theorem
% 20.24/20.47  % Mode: cade22grackle2x798d
% 20.24/20.47  % Steps: 27
% 20.24/20.47  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------