%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : NUM009-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%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 : Wed May 31 12:24:19 EDT 2023

% Result   : Unsatisfiable 2.00s 0.66s
% Output   : CNFRefutation 2.00s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   23 (   7 unt;   0 def)
%            Number of atoms       :   42 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   35 (  16   ~;  17   |;   0   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-1 aty)
%            Number of variables   :   11 (;  11   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X,Y] :
      ( ~ member(X,Y)
      | little_set(X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f61,axiom,
    member(empty_set,infinity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f169,axiom,
    ! [Z] :
      ( member(Z,natural_numbers)
      | ~ little_set(Z)
      | member(empty_set,f44(Z)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f171,axiom,
    ! [Z] :
      ( member(Z,natural_numbers)
      | ~ member(Z,f44(Z)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f220,negated_conjecture,
    ~ member(empty_set,natural_numbers),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f221,plain,
    ! [X] :
      ( ! [Y] : ~ member(X,Y)
      | little_set(X) ),
    inference(miniscoping,[status(esa)],[f1]) ).

fof(f222,plain,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | little_set(X0) ),
    inference(cnf_transformation,[status(esa)],[f221]) ).

fof(f298,plain,
    member(empty_set,infinity),
    inference(cnf_transformation,[status(esa)],[f61]) ).

fof(f434,plain,
    ! [X0] :
      ( member(X0,natural_numbers)
      | ~ little_set(X0)
      | member(empty_set,f44(X0)) ),
    inference(cnf_transformation,[status(esa)],[f169]) ).

fof(f436,plain,
    ! [X0] :
      ( member(X0,natural_numbers)
      | ~ member(X0,f44(X0)) ),
    inference(cnf_transformation,[status(esa)],[f171]) ).

fof(f487,plain,
    ~ member(empty_set,natural_numbers),
    inference(cnf_transformation,[status(esa)],[f220]) ).

fof(f640,plain,
    ( spl0_9
  <=> little_set(empty_set) ),
    introduced(split_symbol_definition) ).

fof(f642,plain,
    ( ~ little_set(empty_set)
    | spl0_9 ),
    inference(component_clause,[status(thm)],[f640]) ).

fof(f667,plain,
    ! [X0] :
      ( ~ member(empty_set,X0)
      | spl0_9 ),
    inference(resolution,[status(thm)],[f642,f222]) ).

fof(f668,plain,
    ( $false
    | spl0_9 ),
    inference(backward_subsumption_resolution,[status(thm)],[f298,f667]) ).

fof(f669,plain,
    spl0_9,
    inference(contradiction_clause,[status(thm)],[f668]) ).

fof(f1849,plain,
    ( spl0_44
  <=> member(empty_set,natural_numbers) ),
    introduced(split_symbol_definition) ).

fof(f1850,plain,
    ( member(empty_set,natural_numbers)
    | ~ spl0_44 ),
    inference(component_clause,[status(thm)],[f1849]) ).

fof(f1852,plain,
    ( member(empty_set,natural_numbers)
    | ~ little_set(empty_set)
    | member(empty_set,natural_numbers) ),
    inference(resolution,[status(thm)],[f434,f436]) ).

fof(f1853,plain,
    ( spl0_44
    | ~ spl0_9 ),
    inference(split_clause,[status(thm)],[f1852,f1849,f640]) ).

fof(f1861,plain,
    ( $false
    | ~ spl0_44 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1850,f487]) ).

fof(f1862,plain,
    ~ spl0_44,
    inference(contradiction_clause,[status(thm)],[f1861]) ).

fof(f1863,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f669,f1853,f1862]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : NUM009-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.09/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32  % Computer : n022.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Tue May 30 09:56:42 EDT 2023
% 0.10/0.32  % CPUTime  : 
% 0.16/0.33  % Drodi V3.5.1
% 2.00/0.66  % Refutation found
% 2.00/0.66  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.00/0.66  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.00/0.66  % Elapsed time: 0.337696 seconds
% 2.00/0.66  % CPU time: 2.274194 seconds
% 2.00/0.66  % Memory used: 94.823 MB
%------------------------------------------------------------------------------