%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO514^1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n028.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 04:47:20 EDT 2023

% Result   : Theorem 81.04s 81.25s
% Output   : Proof 81.04s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

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

thf(choiceoo,conjecture,
    ~ ! [X1: ( ( $o > $o ) > $o ) > $o > $o] :
        ~ ! [X2: ( $o > $o ) > $o] :
            ( ~ ! [X3: $o > $o] :
                  ~ ( X2 @ X3 )
           => ( X2 @ ( X1 @ X2 ) ) ) ).

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

thf(1,plain,
    ~ sP1,
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP2
    | sP1 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(0,theorem,
    ~ ! [X1: ( ( $o > $o ) > $o ) > $o > $o] :
        ~ ! [X2: ( $o > $o ) > $o] :
            ( ~ ! [X3: $o > $o] :
                  ~ ( X2 @ X3 )
           => ( X2 @ ( X1 @ X2 ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SYO514^1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33  % Computer : n028.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Sat Aug 26 07:05:37 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 81.04/81.25  % SZS status Theorem
% 81.04/81.25  % Mode: cade22grackle2x4fb9
% 81.04/81.25  % Steps: 2
% 81.04/81.25  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------