%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET954+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n003.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 12:35:36 EDT 2023

% Result   : Theorem 0.16s 0.54s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   17 (   6 unt;   0 def)
%            Number of atoms       :   38 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   36 (  15   ~;  11   |;   7   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   42 (;  38   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,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(f8,conjecture,
    ! [A,B,C,D] :
      ( in(ordered_pair(A,B),cartesian_product2(C,D))
     => in(ordered_pair(B,A),cartesian_product2(D,C)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,negated_conjecture,
    ~ ! [A,B,C,D] :
        ( in(ordered_pair(A,B),cartesian_product2(C,D))
       => in(ordered_pair(B,A),cartesian_product2(D,C)) ),
    inference(negated_conjecture,[status(cth)],[f8]) ).

fof(f15,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)],[f5]) ).

fof(f16,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)],[f15]) ).

fof(f17,plain,
    ! [X0,X1,X2,X3] :
      ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
      | in(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f18,plain,
    ! [X0,X1,X2,X3] :
      ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
      | in(X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f19,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)],[f16]) ).

fof(f24,plain,
    ? [A,B,C,D] :
      ( in(ordered_pair(A,B),cartesian_product2(C,D))
      & ~ in(ordered_pair(B,A),cartesian_product2(D,C)) ),
    inference(pre_NNF_transformation,[status(esa)],[f9]) ).

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

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

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

fof(f29,plain,
    in(sk0_2,sk0_4),
    inference(resolution,[status(thm)],[f17,f26]) ).

fof(f31,plain,
    in(sk0_3,sk0_5),
    inference(resolution,[status(thm)],[f18,f26]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( in(ordered_pair(X0,sk0_2),cartesian_product2(X1,sk0_4))
      | ~ in(X0,X1) ),
    inference(resolution,[status(thm)],[f19,f29]) ).

fof(f44,plain,
    in(ordered_pair(sk0_3,sk0_2),cartesian_product2(sk0_5,sk0_4)),
    inference(resolution,[status(thm)],[f34,f31]) ).

fof(f45,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f44,f27]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SET954+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31  % Computer : n003.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Tue May 30 10:14:53 EDT 2023
% 0.10/0.31  % CPUTime  : 
% 0.16/0.32  % Drodi V3.5.1
% 0.16/0.54  % Refutation found
% 0.16/0.54  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.54  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.54  % Elapsed time: 0.010517 seconds
% 0.16/0.54  % CPU time: 0.011203 seconds
% 0.16/0.54  % Memory used: 2.280 MB
%------------------------------------------------------------------------------