%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO087^5 : 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 : n012.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 04:45:09 EDT 2023

% Result   : Theorem 0.12s 0.38s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

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

thf(ty_cR,type,
    cR: $o ).

thf(sP1,plain,
    ( sP1
  <=> ( ( cP
       => ~ cQ )
     => ~ ( ~ cP
         => cQ ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( cQ
     => cR ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( cP
     => ~ cQ ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ~ cP
     => cQ ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> cQ ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( sP2
     => ~ ( ~ sP5
         => ~ cR ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> cR ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ~ sP5
     => ~ sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> cP ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(cTHM50_13,conjecture,
    ( ~ ( ~ sP9
       => ~ sP6 )
   => ( sP1
     => sP7 ) ) ).

thf(h0,negated_conjecture,
    ~ ( ~ ( ~ sP9
         => ~ sP6 )
     => ( sP1
       => sP7 ) ),
    inference(assume_negation,[status(cth)],[cTHM50_13]) ).

thf(h1,assumption,
    ~ ( ~ sP9
     => ~ sP6 ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( sP1
     => sP7 ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ sP9,
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(h5,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ sP7,
    introduced(assumption,[]) ).

thf(1,plain,
    ( sP8
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( sP4
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP3
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP2
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP6
    | ~ sP2
    | ~ sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP1
    | ~ sP3
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,h3,h4,h5,h6]) ).

thf(8,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h2,7,h5,h6]) ).

thf(9,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,8,h3,h4]) ).

thf(10,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,9,h1,h2]) ).

thf(0,theorem,
    ( ~ ( ~ sP9
       => ~ sP6 )
   => ( sP1
     => sP7 ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYO087^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n012.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Sat Aug 26 05:43:41 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.12/0.38  % SZS status Theorem
% 0.12/0.38  % Mode: cade22grackle2xfee4
% 0.12/0.38  % Steps: 11
% 0.12/0.38  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------