%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO043^1 : 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 : n003.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 04:44:51 EDT 2023

% Result   : Unsatisfiable 0.19s 0.37s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   31 (  12 unt;   3 typ;   0 def)
%            Number of atoms       :   74 (   5 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   54 (  18   ~;  12   |;   0   &;  13   @)
%                                         (   8 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  11 usr;  10 con; 0-2 aty)
%            Number of variables   :    0 (   0   ^;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_q,type,
    q: ( $o > $o ) > $o > $o ).

thf(ty_x,type,
    x: $o ).

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

thf(sP1,plain,
    ( sP1
  <=> ( f @ ( q @ f @ x ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( q @ f @ x )
      = x ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( f @ x )
      = x ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> x ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( f @ ( f @ sP4 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( f @ sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( sP6
      = ( q @ f @ sP4 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( q @ f @ sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(h0,assumption,
    ~ ( sP8
     => ~ sP5 ),
    introduced(assumption,[]) ).

thf(h1,assumption,
    sP1 != sP6,
    introduced(assumption,[]) ).

thf(h2,assumption,
    sP8,
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP5,
    introduced(assumption,[]) ).

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

thf(h5,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ sP1,
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ sP6,
    introduced(assumption,[]) ).

thf(1,plain,
    ( sP2
    | ~ sP8
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP1
    | sP6
    | ~ sP2 ),
    inference(mating_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP3
    | sP6
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP5
    | sP6
    | ~ sP3 ),
    inference(mating_rule,[status(thm)],]) ).

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

thf(6,plain,
    ( sP7
    | ~ sP6
    | ~ sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP5
    | sP1
    | ~ sP7 ),
    inference(mating_rule,[status(thm)],]) ).

thf(8,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h6,h7,h2,h3,h0,h1])],[6,7,h2,h3,h6,h7]) ).

thf(9,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h2,h3,h0,h1]),tab_be(discharge,[h4,h5]),tab_be(discharge,[h6,h7])],[h1,5,8,h4,h5,h6,h7]) ).

thf(10,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0,h1]),tab_negimp(discharge,[h2,h3])],[h0,9,h2,h3]) ).

thf('5_001',axiom,
    ~ ( ~ ( sP8
         => ~ sP5 )
     => ( sP1 = sP6 ) ) ).

thf(11,plain,
    $false,
    inference(tab_negimp,[status(thm),tab_negimp(discharge,[h0,h1])],[5,10,h0,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYO043^1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n003.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sat Aug 26 01:43:39 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.19/0.37  % SZS status Unsatisfiable
% 0.19/0.37  % Mode: cade22grackle2xfee4
% 0.19/0.37  % Steps: 24
% 0.19/0.37  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------