%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU165+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n017.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 0.07s 0.27s
% Output   : CNFRefutation 0.07s
% 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(f11,conjecture,
    ! [A,B,C,D] :
      ( in(ordered_pair(A,B),cartesian_product2(C,D))
    <=> ( in(A,C)
        & in(B,D) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,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)],[f11]) ).

fof(f13,axiom,
    ! [A,B,C,D] :
      ( in(ordered_pair(A,B),cartesian_product2(C,D))
    <=> ( in(A,C)
        & in(B,D) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f23,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)],[f12]) ).

fof(f24,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)],[f23]) ).

fof(f25,plain,
    ( ( in(ordered_pair(sk0_2,sk0_3),cartesian_product2(sk0_4,sk0_5))
      | ( in(sk0_2,sk0_4)
        & in(sk0_3,sk0_5) ) )
    & ( ~ in(ordered_pair(sk0_2,sk0_3),cartesian_product2(sk0_4,sk0_5))
      | ~ in(sk0_2,sk0_4)
      | ~ in(sk0_3,sk0_5) ) ),
    inference(skolemization,[status(esa)],[f24]) ).

fof(f26,plain,
    ( in(ordered_pair(sk0_2,sk0_3),cartesian_product2(sk0_4,sk0_5))
    | in(sk0_2,sk0_4) ),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f27,plain,
    ( in(ordered_pair(sk0_2,sk0_3),cartesian_product2(sk0_4,sk0_5))
    | in(sk0_3,sk0_5) ),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f28,plain,
    ( ~ in(ordered_pair(sk0_2,sk0_3),cartesian_product2(sk0_4,sk0_5))
    | ~ in(sk0_2,sk0_4)
    | ~ in(sk0_3,sk0_5) ),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f29,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)],[f13]) ).

fof(f30,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)],[f29]) ).

fof(f31,plain,
    ! [X0,X1,X2,X3] :
      ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
      | in(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f32,plain,
    ! [X0,X1,X2,X3] :
      ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
      | in(X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f33,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)],[f30]) ).

fof(f34,plain,
    ( spl0_0
  <=> in(ordered_pair(sk0_2,sk0_3),cartesian_product2(sk0_4,sk0_5)) ),
    introduced(split_symbol_definition) ).

fof(f35,plain,
    ( in(ordered_pair(sk0_2,sk0_3),cartesian_product2(sk0_4,sk0_5))
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f34]) ).

fof(f37,plain,
    ( spl0_1
  <=> in(sk0_2,sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f38,plain,
    ( in(sk0_2,sk0_4)
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f37]) ).

fof(f39,plain,
    ( ~ in(sk0_2,sk0_4)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f37]) ).

fof(f40,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f26,f34,f37]) ).

fof(f41,plain,
    ( spl0_2
  <=> in(sk0_3,sk0_5) ),
    introduced(split_symbol_definition) ).

fof(f42,plain,
    ( in(sk0_3,sk0_5)
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f41]) ).

fof(f44,plain,
    ( spl0_0
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f27,f34,f41]) ).

fof(f45,plain,
    ( ~ spl0_0
    | ~ spl0_1
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f28,f34,f37,f41]) ).

fof(f47,plain,
    ( in(sk0_2,sk0_4)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f31,f35]) ).

fof(f48,plain,
    ( $false
    | spl0_1
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f47,f39]) ).

fof(f49,plain,
    ( spl0_1
    | ~ spl0_0 ),
    inference(contradiction_clause,[status(thm)],[f48]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( in(ordered_pair(X0,sk0_3),cartesian_product2(X1,sk0_5))
      | ~ in(X0,X1)
      | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f33,f42]) ).

fof(f55,plain,
    ( in(ordered_pair(sk0_2,sk0_3),cartesian_product2(sk0_4,sk0_5))
    | ~ spl0_2
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f52,f38]) ).

fof(f56,plain,
    ( spl0_0
    | ~ spl0_2
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f55,f34,f41,f37]) ).

fof(f57,plain,
    ( in(sk0_3,sk0_5)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f35,f32]) ).

fof(f58,plain,
    ( spl0_2
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f57,f41,f34]) ).

fof(f61,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f40,f44,f45,f49,f56,f58]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : SEU165+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.07  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26  % Computer : n017.cluster.edu
% 0.07/0.26  % Model    : x86_64 x86_64
% 0.07/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26  % Memory   : 8042.1875MB
% 0.07/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26  % CPULimit : 300
% 0.07/0.26  % WCLimit  : 300
% 0.07/0.26  % DateTime : Mon Apr 29 19:22:18 EDT 2024
% 0.07/0.26  % CPUTime  : 
% 0.07/0.27  % Drodi V3.6.0
% 0.07/0.27  % Refutation found
% 0.07/0.27  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.27  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.28  % Elapsed time: 0.014125 seconds
% 0.07/0.28  % CPU time: 0.027720 seconds
% 0.07/0.28  % Total memory used: 13.159 MB
% 0.07/0.28  % Net memory used: 13.133 MB
%------------------------------------------------------------------------------