%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEV056^5 : 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 : n020.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 19:32:28 EDT 2023

% Result   : Theorem 0.21s 0.40s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_eigen__0,type,
    eigen__0: a > a > $o ).

thf(sP1,plain,
    ( sP1
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: a > a > $o] :
        ( ! [X2: a,X3: a] :
            ( ( eigen__0 @ X2 @ X3 )
           => ( X1 @ X2 @ X3 ) )
       => ~ ! [X2: a,X3: a,X4: a] :
              ( ~ ( ( X1 @ X2 @ X3 )
                 => ~ ( X1 @ X3 @ X4 ) )
             => ( X1 @ X2 @ X4 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(cTHM275_pme,conjecture,
    ! [X1: a > a > $o] :
      ~ ! [X2: a > a > $o] :
          ( ! [X3: a,X4: a] :
              ( ( X1 @ X3 @ X4 )
             => ( X2 @ X3 @ X4 ) )
         => ~ ! [X3: a,X4: a,X5: a] :
                ( ~ ( ( X2 @ X3 @ X4 )
                   => ~ ( X2 @ X4 @ X5 ) )
               => ( X2 @ X3 @ X5 ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: a > a > $o] :
        ~ ! [X2: a > a > $o] :
            ( ! [X3: a,X4: a] :
                ( ( X1 @ X3 @ X4 )
               => ( X2 @ X3 @ X4 ) )
           => ~ ! [X3: a,X4: a,X5: a] :
                  ( ~ ( ( X2 @ X3 @ X4 )
                     => ~ ( X2 @ X4 @ X5 ) )
                 => ( X2 @ X3 @ X5 ) ) ),
    inference(assume_negation,[status(cth)],[cTHM275_pme]) ).

thf(h1,assumption,
    sP2,
    introduced(assumption,[]) ).

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

thf(2,plain,
    ~ sP1,
    inference(prop_rule,[status(thm)],]) ).

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

thf(4,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,3,h1]) ).

thf(0,theorem,
    ! [X1: a > a > $o] :
      ~ ! [X2: a > a > $o] :
          ( ! [X3: a,X4: a] :
              ( ( X1 @ X3 @ X4 )
             => ( X2 @ X3 @ X4 ) )
         => ~ ! [X3: a,X4: a,X5: a] :
                ( ~ ( ( X2 @ X3 @ X4 )
                   => ~ ( X2 @ X4 @ X5 ) )
               => ( X2 @ X3 @ X5 ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[4,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEV056^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35  % Computer : n020.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug 24 03:20:45 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.40  % SZS status Theorem
% 0.21/0.40  % Mode: cade22grackle2xfee4
% 0.21/0.40  % Steps: 27
% 0.21/0.40  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------