%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEV257^5 : 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 : n029.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 19:33:09 EDT 2023

% Result   : Theorem 20.28s 20.52s
% Output   : Proof 20.28s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_cOPEN,type,
    cOPEN: ( a > $o ) > $o ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: ( a > $o ) > $o] :
        ( ! [X2: a > $o] :
            ( ( X1 @ X2 )
           => ( cOPEN @ X2 ) )
       => ( cOPEN
          @ ^ [X2: a] :
              ~ ! [X3: a > $o] :
                  ( ( X1 @ X3 )
                 => ~ ( X3 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

thf(cTHM625_pme,conjecture,
    ( ~ ( ~ ( ( cOPEN
              @ ^ [X1: a] : ~ $false )
           => ~ sP1 )
       => ~ ! [X1: a > $o,X2: a > $o] :
              ( ~ ( ( cOPEN @ X1 )
                 => ~ ( cOPEN @ X2 ) )
             => ( cOPEN
                @ ^ [X3: a] :
                    ~ ( ( X1 @ X3 )
                     => ~ ( X2 @ X3 ) ) ) ) )
   => sP2 ) ).

thf(h0,negated_conjecture,
    ~ ( ~ ( ~ ( ( cOPEN
                @ ^ [X1: a] : ~ $false )
             => ~ sP1 )
         => ~ ! [X1: a > $o,X2: a > $o] :
                ( ~ ( ( cOPEN @ X1 )
                   => ~ ( cOPEN @ X2 ) )
               => ( cOPEN
                  @ ^ [X3: a] :
                      ~ ( ( X1 @ X3 )
                       => ~ ( X2 @ X3 ) ) ) ) )
     => sP2 ),
    inference(assume_negation,[status(cth)],[cTHM625_pme]) ).

thf(h1,assumption,
    ~ ( ~ ( ( cOPEN
            @ ^ [X1: a] : ~ $false )
         => ~ sP1 )
     => ~ ! [X1: a > $o,X2: a > $o] :
            ( ~ ( ( cOPEN @ X1 )
               => ~ ( cOPEN @ X2 ) )
           => ( cOPEN
              @ ^ [X3: a] :
                  ~ ( ( X1 @ X3 )
                   => ~ ( X2 @ X3 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( ( cOPEN
        @ ^ [X1: a] : ~ $false )
     => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ! [X1: a > $o,X2: a > $o] :
      ( ~ ( ( cOPEN @ X1 )
         => ~ ( cOPEN @ X2 ) )
     => ( cOPEN
        @ ^ [X3: a] :
            ~ ( ( X1 @ X3 )
             => ~ ( X2 @ X3 ) ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ( cOPEN
    @ ^ [X1: a] : ~ $false ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP1
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0])],[1,h6,h2]) ).

thf(3,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,2,h5,h6]) ).

thf(4,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,3,h3,h4]) ).

thf(5,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,4,h1,h2]) ).

thf(0,theorem,
    ( ~ ( ~ ( ( cOPEN
              @ ^ [X1: a] : ~ $false )
           => ~ sP1 )
       => ~ ! [X1: a > $o,X2: a > $o] :
              ( ~ ( ( cOPEN @ X1 )
                 => ~ ( cOPEN @ X2 ) )
             => ( cOPEN
                @ ^ [X3: a] :
                    ~ ( ( X1 @ X3 )
                     => ~ ( X2 @ X3 ) ) ) ) )
   => sP2 ),
    inference(contra,[status(thm),contra(discharge,[h0])],[5,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEV257^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n029.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 : Thu Aug 24 03:41:53 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 20.28/20.52  % SZS status Theorem
% 20.28/20.52  % Mode: cade22grackle2x798d
% 20.28/20.52  % Steps: 28
% 20.28/20.52  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------