%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO085^5 : 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 : n022.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 0.14s 0.38s
% Output   : Proof 0.14s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_c,type,
    c: $o ).

thf(ty_s,type,
    s: $o ).

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

thf(ty_d,type,
    d: $o ).

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

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

thf(sP2,plain,
    ( sP2
  <=> ( ~ ( sP1
         => ~ d )
     => ( a
       => ~ b ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> s ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ~ sP2
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

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

thf(sP6,plain,
    ( sP6
  <=> b ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

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

thf(sP8,plain,
    ( sP8
  <=> ( sP1
     => ~ sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

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

thf(cCOM_DMG02,conjecture,
    ( sP4
   => ( ~ ( ~ sP3
         => sP5 )
     => sP8 ) ) ).

thf(h0,negated_conjecture,
    ~ ( sP4
     => ( ~ ( ~ sP3
           => sP5 )
       => sP8 ) ),
    inference(assume_negation,[status(cth)],[cCOM_DMG02]) ).

thf(h1,assumption,
    sP4,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( ~ ( ~ sP3
         => sP5 )
     => sP8 ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( ~ sP3
     => sP5 ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ sP8,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ sP3,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ sP5,
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP9,
    introduced(assumption,[]) ).

thf(h8,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(h9,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h10,assumption,
    sP7,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP5
    | ~ sP9
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP8
    | ~ sP1
    | ~ sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP2
    | sP8
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP4
    | sP2
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,h1,h5,h7,h8,h9,h10]) ).

thf(6,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h4,5,h9,h10]) ).

thf(7,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,6,h7,h8]) ).

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

thf(9,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,8,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,
    ( sP4
   => ( ~ ( ~ sP3
         => sP5 )
     => sP8 ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYO085^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34  % Computer : n022.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Sat Aug 26 02:56:55 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.14/0.38  % SZS status Theorem
% 0.14/0.38  % Mode: cade22grackle2xfee4
% 0.14/0.38  % Steps: 10
% 0.14/0.38  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------