%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO154^5 : 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 04:45:34 EDT 2023

% Result   : Theorem 0.20s 0.40s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_g,type,
    g: $i > $i ).

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

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

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

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

thf(ty_f,type,
    f: $i > $i ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i] :
        ( ( cQ @ X1 )
       => ( cR @ ( g @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( cP @ a )
     => ( cQ @ ( f @ a ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i] :
        ( ( cP @ X1 )
       => ( cQ @ ( f @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i] :
        ~ ( cR @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

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

thf(sP6,plain,
    ( sP6
  <=> ( sP5
     => ( cR @ ( g @ ( f @ a ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( cP @ a ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( cR @ ( g @ ( f @ a ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(cDEMO_TRIV1,conjecture,
    ( ~ ( ~ ( sP7
           => ~ sP3 )
       => ~ sP1 )
   => ~ sP4 ) ).

thf(h0,negated_conjecture,
    ~ ( ~ ( ~ ( sP7
             => ~ sP3 )
         => ~ sP1 )
     => ~ sP4 ),
    inference(assume_negation,[status(cth)],[cDEMO_TRIV1]) ).

thf(h1,assumption,
    ~ ( ~ ( sP7
         => ~ sP3 )
     => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    sP4,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( sP7
     => ~ sP3 ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h5,assumption,
    sP7,
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP4
    | ~ sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP6
    | ~ sP5
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP1
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP2
    | ~ sP7
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP3
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

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

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

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

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

thf(0,theorem,
    ( ~ ( ~ ( sP7
           => ~ sP3 )
       => ~ sP1 )
   => ~ sP4 ),
    inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYO154^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n006.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat Aug 26 03:13:22 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.40  % SZS status Theorem
% 0.20/0.40  % Mode: cade22grackle2xfee4
% 0.20/0.40  % Steps: 95
% 0.20/0.40  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------