%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO300^5 : 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 : n002.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 04:46:12 EDT 2023

% Result   : Theorem 20.19s 20.40s
% Output   : Proof 20.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
    eigen__0: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o ).

thf(sP1,plain,
    ( sP1
  <=> ( ! [X1: ( $i > $i ) > $i] : ( eigen__0 @ X1 @ X1 )
     => ( eigen__0
        @ ^ [X1: $i > $i] :
            ( X1
            @ @+[X2: $i] : $false )
        @ ^ [X1: $i > $i] :
          @+[X2: $i] : $false ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ! [X1: ( $i > $i ) > $i] : ( eigen__0 @ X1 @ X1 )
     => ( eigen__0
        @ ^ [X1: $i > $i] :
            ( X1
            @ @+[X2: $i] : $false )
        @ ^ [X1: $i > $i] :
            ( X1
            @ @+[X2: $i] : $false ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

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

thf(sP4,plain,
    ( sP4
  <=> ! [X1: ( $i > $i ) > $i] :
        ~ ( sP3
         => ( eigen__0
            @ ^ [X2: $i > $i] :
                ( X2
                @ ( X1
                  @ ^ [X3: $i] : X3 ) )
            @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( eigen__0
      @ ^ [X1: $i > $i] :
          ( X1
          @ @+[X2: $i] : $false )
      @ ^ [X1: $i > $i] :
          ( X1
          @ @+[X2: $i] : $false ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(cUNIFTHM1,conjecture,
    ! [X1: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
      ~ ! [X2: ( $i > $i ) > $i] :
          ~ ( ! [X3: ( $i > $i ) > $i] : ( X1 @ X3 @ X3 )
           => ( X1
              @ ^ [X3: $i > $i] :
                  ( X3
                  @ ( X2
                    @ ^ [X4: $i] : X4 ) )
              @ X2 ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
        ~ ! [X2: ( $i > $i ) > $i] :
            ~ ( ! [X3: ( $i > $i ) > $i] : ( X1 @ X3 @ X3 )
             => ( X1
                @ ^ [X3: $i > $i] :
                    ( X3
                    @ ( X2
                      @ ^ [X4: $i] : X4 ) )
                @ X2 ) ),
    inference(assume_negation,[status(cth)],[cUNIFTHM1]) ).

thf(h1,assumption,
    sP4,
    introduced(assumption,[]) ).

thf(1,plain,
    ( sP2
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

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

thf(3,plain,
    ( ~ sP3
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP1
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP4
    | ~ sP1 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(7,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,6,h1]) ).

thf(0,theorem,
    ! [X1: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
      ~ ! [X2: ( $i > $i ) > $i] :
          ~ ( ! [X3: ( $i > $i ) > $i] : ( X1 @ X3 @ X3 )
           => ( X1
              @ ^ [X3: $i > $i] :
                  ( X3
                  @ ( X2
                    @ ^ [X4: $i] : X4 ) )
              @ X2 ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SYO300^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n002.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 03:54:02 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 20.19/20.40  % SZS status Theorem
% 20.19/20.40  % Mode: cade22grackle2x798d
% 20.19/20.40  % Steps: 64
% 20.19/20.40  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------