%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET204-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n010.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 12:34:16 EDT 2023

% Result   : Unsatisfiable 0.14s 0.53s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   25 (   9 unt;   0 def)
%            Number of atoms       :   43 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   36 (  18   ~;  16   |;   0   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   32 (;  32   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f14,axiom,
    ! [U,V,X,Y] :
      ( ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(U,X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [U,V,X,Y] :
      ( ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(V,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [U,X,V,Y] :
      ( ~ member(U,X)
      | ~ member(V,Y)
      | member(ordered_pair(U,V),cross_product(X,Y)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f113,negated_conjecture,
    member(ordered_pair(u,v),cross_product(x,y)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f114,negated_conjecture,
    ~ member(ordered_pair(v,u),cross_product(y,x)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f132,plain,
    ! [U,X] :
      ( ! [V,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(U,X) ),
    inference(miniscoping,[status(esa)],[f14]) ).

fof(f133,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f132]) ).

fof(f134,plain,
    ! [V,Y] :
      ( ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(V,Y) ),
    inference(miniscoping,[status(esa)],[f15]) ).

fof(f135,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | member(X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f134]) ).

fof(f136,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(X0,X1)
      | ~ member(X2,X3)
      | member(ordered_pair(X0,X2),cross_product(X1,X3)) ),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f246,plain,
    member(ordered_pair(u,v),cross_product(x,y)),
    inference(cnf_transformation,[status(esa)],[f113]) ).

fof(f247,plain,
    ~ member(ordered_pair(v,u),cross_product(y,x)),
    inference(cnf_transformation,[status(esa)],[f114]) ).

fof(f252,plain,
    member(u,x),
    inference(resolution,[status(thm)],[f133,f246]) ).

fof(f253,plain,
    member(v,y),
    inference(resolution,[status(thm)],[f135,f246]) ).

fof(f254,plain,
    ( spl0_0
  <=> member(v,y) ),
    introduced(split_symbol_definition) ).

fof(f256,plain,
    ( ~ member(v,y)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f254]) ).

fof(f257,plain,
    ( spl0_1
  <=> member(u,x) ),
    introduced(split_symbol_definition) ).

fof(f259,plain,
    ( ~ member(u,x)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f257]) ).

fof(f260,plain,
    ( ~ member(v,y)
    | ~ member(u,x) ),
    inference(resolution,[status(thm)],[f136,f247]) ).

fof(f261,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f260,f254,f257]) ).

fof(f272,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f256,f253]) ).

fof(f273,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f272]) ).

fof(f274,plain,
    ( $false
    | spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f259,f252]) ).

fof(f275,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f274]) ).

fof(f276,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f261,f273,f275]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SET204-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30  % Computer : n010.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 300
% 0.09/0.30  % DateTime : Tue May 30 10:10:37 EDT 2023
% 0.14/0.30  % CPUTime  : 
% 0.14/0.31  % Drodi V3.5.1
% 0.14/0.53  % Refutation found
% 0.14/0.53  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.53  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.53  % Elapsed time: 0.015756 seconds
% 0.14/0.53  % CPU time: 0.014722 seconds
% 0.14/0.53  % Memory used: 3.834 MB
%------------------------------------------------------------------------------