%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU165+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n005.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 : Tue Apr 30 20:41:18 EDT 2024

% Result   : Theorem 0.21s 0.39s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   33 (   1 unt;   0 def)
%            Number of atoms       :   92 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   97 (  38   ~;  40   |;  12   &)
%                                         (   6 <=>;   0  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   4 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   46 (  38   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f46,lemma,
    ! [A,B,C,D] :
      ( in(ordered_pair(A,B),cartesian_product2(C,D))
    <=> ( in(A,C)
        & in(B,D) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f51,conjecture,
    ! [A,B,C,D] :
      ( in(ordered_pair(A,B),cartesian_product2(C,D))
    <=> ( in(A,C)
        & in(B,D) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f52,negated_conjecture,
    ~ ! [A,B,C,D] :
        ( in(ordered_pair(A,B),cartesian_product2(C,D))
      <=> ( in(A,C)
          & in(B,D) ) ),
    inference(negated_conjecture,[status(cth)],[f51]) ).

fof(f238,plain,
    ! [A,B,C,D] :
      ( ( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
        | ( in(A,C)
          & in(B,D) ) )
      & ( in(ordered_pair(A,B),cartesian_product2(C,D))
        | ~ in(A,C)
        | ~ in(B,D) ) ),
    inference(NNF_transformation,[status(esa)],[f46]) ).

fof(f239,plain,
    ( ! [A,B,C,D] :
        ( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
        | ( in(A,C)
          & in(B,D) ) )
    & ! [A,B,C,D] :
        ( in(ordered_pair(A,B),cartesian_product2(C,D))
        | ~ in(A,C)
        | ~ in(B,D) ) ),
    inference(miniscoping,[status(esa)],[f238]) ).

fof(f240,plain,
    ! [X0,X1,X2,X3] :
      ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
      | in(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f239]) ).

fof(f241,plain,
    ! [X0,X1,X2,X3] :
      ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
      | in(X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f239]) ).

fof(f242,plain,
    ! [X0,X1,X2,X3] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
      | ~ in(X0,X2)
      | ~ in(X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f239]) ).

fof(f251,plain,
    ? [A,B,C,D] :
      ( in(ordered_pair(A,B),cartesian_product2(C,D))
    <~> ( in(A,C)
        & in(B,D) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f52]) ).

fof(f252,plain,
    ? [A,B,C,D] :
      ( ( in(ordered_pair(A,B),cartesian_product2(C,D))
        | ( in(A,C)
          & in(B,D) ) )
      & ( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
        | ~ in(A,C)
        | ~ in(B,D) ) ),
    inference(NNF_transformation,[status(esa)],[f251]) ).

fof(f253,plain,
    ( ( in(ordered_pair(sk0_18,sk0_19),cartesian_product2(sk0_20,sk0_21))
      | ( in(sk0_18,sk0_20)
        & in(sk0_19,sk0_21) ) )
    & ( ~ in(ordered_pair(sk0_18,sk0_19),cartesian_product2(sk0_20,sk0_21))
      | ~ in(sk0_18,sk0_20)
      | ~ in(sk0_19,sk0_21) ) ),
    inference(skolemization,[status(esa)],[f252]) ).

fof(f254,plain,
    ( in(ordered_pair(sk0_18,sk0_19),cartesian_product2(sk0_20,sk0_21))
    | in(sk0_18,sk0_20) ),
    inference(cnf_transformation,[status(esa)],[f253]) ).

fof(f255,plain,
    ( in(ordered_pair(sk0_18,sk0_19),cartesian_product2(sk0_20,sk0_21))
    | in(sk0_19,sk0_21) ),
    inference(cnf_transformation,[status(esa)],[f253]) ).

fof(f256,plain,
    ( ~ in(ordered_pair(sk0_18,sk0_19),cartesian_product2(sk0_20,sk0_21))
    | ~ in(sk0_18,sk0_20)
    | ~ in(sk0_19,sk0_21) ),
    inference(cnf_transformation,[status(esa)],[f253]) ).

fof(f371,plain,
    ( spl0_0
  <=> in(ordered_pair(sk0_18,sk0_19),cartesian_product2(sk0_20,sk0_21)) ),
    introduced(split_symbol_definition) ).

fof(f372,plain,
    ( in(ordered_pair(sk0_18,sk0_19),cartesian_product2(sk0_20,sk0_21))
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f371]) ).

fof(f374,plain,
    ( spl0_1
  <=> in(sk0_18,sk0_20) ),
    introduced(split_symbol_definition) ).

fof(f375,plain,
    ( in(sk0_18,sk0_20)
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f374]) ).

fof(f376,plain,
    ( ~ in(sk0_18,sk0_20)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f374]) ).

fof(f377,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f254,f371,f374]) ).

fof(f378,plain,
    ( spl0_2
  <=> in(sk0_19,sk0_21) ),
    introduced(split_symbol_definition) ).

fof(f379,plain,
    ( in(sk0_19,sk0_21)
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f378]) ).

fof(f381,plain,
    ( spl0_0
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f255,f371,f378]) ).

fof(f382,plain,
    ( ~ spl0_0
    | ~ spl0_1
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f256,f371,f374,f378]) ).

fof(f415,plain,
    ( in(sk0_18,sk0_20)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f240,f372]) ).

fof(f416,plain,
    ( $false
    | spl0_1
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f415,f376]) ).

fof(f417,plain,
    ( spl0_1
    | ~ spl0_0 ),
    inference(contradiction_clause,[status(thm)],[f416]) ).

fof(f420,plain,
    ! [X0,X1] :
      ( in(ordered_pair(X0,sk0_19),cartesian_product2(X1,sk0_21))
      | ~ in(X0,X1)
      | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f242,f379]) ).

fof(f423,plain,
    ( in(ordered_pair(sk0_18,sk0_19),cartesian_product2(sk0_20,sk0_21))
    | ~ spl0_2
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f420,f375]) ).

fof(f424,plain,
    ( spl0_0
    | ~ spl0_2
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f423,f371,f378,f374]) ).

fof(f425,plain,
    ( in(sk0_19,sk0_21)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f372,f241]) ).

fof(f426,plain,
    ( spl0_2
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f425,f378,f371]) ).

fof(f429,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f377,f381,f382,f417,f424,f426]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SEU165+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35  % Computer : n005.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Apr 29 19:44:56 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  % Drodi V3.6.0
% 0.21/0.39  % Refutation found
% 0.21/0.39  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.39  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.39  % Elapsed time: 0.038163 seconds
% 0.21/0.39  % CPU time: 0.126482 seconds
% 0.21/0.39  % Total memory used: 18.637 MB
% 0.21/0.39  % Net memory used: 18.568 MB
%------------------------------------------------------------------------------