%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO882^1 : TPTP v8.1.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n025.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  : 600s
% DateTime : Thu Jul 21 19:35:08 EDT 2022

% Result   : Unsatisfiable 43.89s 44.11s
% Output   : Proof 43.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    1
%            Number of leaves      :   27
% Syntax   : Number of formulae    :   28 (   5 unt;   4 typ;   0 def)
%            Number of atoms       :   64 (  12 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   66 (  18   ~;  11   |;   0   &;  24   @)
%                                         (  11 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  15 usr;  14 con; 0-2 aty)
%            Number of variables   :    1 (   0   ^   1   !;   0   ?;   1   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_h,type,
    h: $i > $i ).

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

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

thf(ty_g,type,
    g: $o > $i ).

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

thf(sP2,plain,
    ( sP2
  <=> ( ( a = a )
      = ( ~ $false ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

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

thf(sP4,plain,
    ( sP4
  <=> ( ( h @ ( g @ sP1 ) )
      = ( h @ ( g @ $false ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( g @ sP3 )
      = ( g @ ~ $false ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( sP4
     => ( ( h @ ( g @ sP3 ) )
       != ( h @ ( g @ ~ $false ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( g @ sP1 )
      = ( g @ $false ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: $i > $i] :
        ( ( ( h @ ( X1 @ b ) )
          = ( h @ ( g @ $false ) ) )
       => ( ( h @ ( X1 @ a ) )
         != ( h @ ( g @ ~ $false ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

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

thf(sP10,plain,
    ( sP10
  <=> ( ( h @ ( g @ sP3 ) )
      = ( h @ ( g @ ~ sP9 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( sP1 = sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(1,plain,
    sP3,
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ~ sP9,
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP2
    | ~ sP3
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP11
    | sP1
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP5
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP7
    | ~ sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP10
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP4
    | ~ sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP6
    | ~ sP4
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP8
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(a2,axiom,
    ~ sP1 ).

thf(a1,axiom,
    sP8 ).

thf(11,plain,
    $false,
    inference(prop_unsat,[status(thm)],[1,2,3,4,5,6,7,8,9,10,a2,a1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYO882^1 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n025.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  : 600
% 0.13/0.34  % DateTime : Sat Jul  9 10:49:15 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 43.89/44.11  % SZS status Unsatisfiable
% 43.89/44.11  % Mode: mode459
% 43.89/44.11  % Inferences: 1783
% 43.89/44.11  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------