%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO258^5 : 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 : n006.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 04:46:03 EDT 2023

% Result   : Theorem 0.19s 0.40s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_cQ,type,
    cQ: $i > ( $i > $o ) > $o ).

thf(ty_cP,type,
    cP: $i > $i > $o ).

thf(ty_a,type,
    a: $i ).

thf(ty_b,type,
    b: $i ).

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

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

thf(cBLEDSOE_FENG_6,conjecture,
    ( ~ ( ( cP @ a @ b )
       => ~ ! [X1: $i > $o] : ( cQ @ b @ X1 ) )
   => ~ sP2 ) ).

thf(h0,negated_conjecture,
    ~ ( ~ ( ( cP @ a @ b )
         => ~ ! [X1: $i > $o] : ( cQ @ b @ X1 ) )
     => ~ sP2 ),
    inference(assume_negation,[status(cth)],[cBLEDSOE_FENG_6]) ).

thf(h1,assumption,
    ~ ( ( cP @ a @ b )
     => ~ ! [X1: $i > $o] : ( cQ @ b @ X1 ) ),
    introduced(assumption,[]) ).

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

thf(h3,assumption,
    cP @ a @ b,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ! [X1: $i > $o] : ( cQ @ b @ X1 ),
    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([h3,h4,h1,h2,h0])],[1,2,h2]) ).

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,
    ( ~ ( ( cP @ a @ b )
       => ~ ! [X1: $i > $o] : ( cQ @ b @ X1 ) )
   => ~ sP2 ),
    inference(contra,[status(thm),contra(discharge,[h0])],[5,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYO258^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33  % Computer : n006.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 00:09:37 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.40  % SZS status Theorem
% 0.19/0.40  % Mode: cade22grackle2xfee4
% 0.19/0.40  % Steps: 173
% 0.19/0.40  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------