%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET978+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n006.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 12:35:38 EDT 2023

% Result   : Theorem 0.19s 0.36s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   28 (   4 unt;   0 def)
%            Number of atoms       :   59 (  11 equ)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   57 (  26   ~;  19   |;   6   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   40 (;  30   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [A,B,C,D] :
      ( ( disjoint(A,B)
        | disjoint(C,D) )
     => disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,conjecture,
    ! [A,B,C,D] :
      ( A != B
     => ( disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D))
        & disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,negated_conjecture,
    ~ ! [A,B,C,D] :
        ( A != B
       => ( disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D))
          & disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B))) ) ),
    inference(negated_conjecture,[status(cth)],[f5]) ).

fof(f7,axiom,
    ! [A,B] :
      ( A != B
     => disjoint(singleton(A),singleton(B)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,plain,
    ! [A,B,C,D] :
      ( ( ~ disjoint(A,B)
        & ~ disjoint(C,D) )
      | disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f15,plain,
    ! [X0,X1,X2,X3] :
      ( ~ disjoint(X0,X1)
      | disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f16,plain,
    ! [X0,X1,X2,X3] :
      ( ~ disjoint(X0,X1)
      | disjoint(cartesian_product2(X2,X0),cartesian_product2(X3,X1)) ),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f17,plain,
    ? [A,B,C,D] :
      ( A != B
      & ( ~ disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D))
        | ~ disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B))) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f18,plain,
    ? [A,B] :
      ( A != B
      & ( ? [C,D] : ~ disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D))
        | ? [C,D] : ~ disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B))) ) ),
    inference(miniscoping,[status(esa)],[f17]) ).

fof(f19,plain,
    ( sk0_2 != sk0_3
    & ( ~ disjoint(cartesian_product2(singleton(sk0_2),sk0_4),cartesian_product2(singleton(sk0_3),sk0_5))
      | ~ disjoint(cartesian_product2(sk0_6,singleton(sk0_2)),cartesian_product2(sk0_7,singleton(sk0_3))) ) ),
    inference(skolemization,[status(esa)],[f18]) ).

fof(f20,plain,
    sk0_2 != sk0_3,
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f21,plain,
    ( ~ disjoint(cartesian_product2(singleton(sk0_2),sk0_4),cartesian_product2(singleton(sk0_3),sk0_5))
    | ~ disjoint(cartesian_product2(sk0_6,singleton(sk0_2)),cartesian_product2(sk0_7,singleton(sk0_3))) ),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f22,plain,
    ! [A,B] :
      ( A = B
      | disjoint(singleton(A),singleton(B)) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( X0 = X1
      | disjoint(singleton(X0),singleton(X1)) ),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f24,plain,
    ( spl0_0
  <=> disjoint(cartesian_product2(singleton(sk0_2),sk0_4),cartesian_product2(singleton(sk0_3),sk0_5)) ),
    introduced(split_symbol_definition) ).

fof(f26,plain,
    ( ~ disjoint(cartesian_product2(singleton(sk0_2),sk0_4),cartesian_product2(singleton(sk0_3),sk0_5))
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f24]) ).

fof(f27,plain,
    ( spl0_1
  <=> disjoint(cartesian_product2(sk0_6,singleton(sk0_2)),cartesian_product2(sk0_7,singleton(sk0_3))) ),
    introduced(split_symbol_definition) ).

fof(f29,plain,
    ( ~ disjoint(cartesian_product2(sk0_6,singleton(sk0_2)),cartesian_product2(sk0_7,singleton(sk0_3)))
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f27]) ).

fof(f30,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f21,f24,f27]) ).

fof(f32,plain,
    ( ~ disjoint(singleton(sk0_2),singleton(sk0_3))
    | spl0_0 ),
    inference(resolution,[status(thm)],[f26,f15]) ).

fof(f36,plain,
    ( sk0_2 = sk0_3
    | spl0_0 ),
    inference(resolution,[status(thm)],[f32,f23]) ).

fof(f37,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f36,f20]) ).

fof(f38,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f37]) ).

fof(f39,plain,
    ( ~ disjoint(singleton(sk0_2),singleton(sk0_3))
    | spl0_1 ),
    inference(resolution,[status(thm)],[f29,f16]) ).

fof(f44,plain,
    ( sk0_2 = sk0_3
    | spl0_1 ),
    inference(resolution,[status(thm)],[f39,f23]) ).

fof(f45,plain,
    ( $false
    | spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f44,f20]) ).

fof(f46,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f45]) ).

fof(f47,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f30,f38,f46]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET978+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n006.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue May 30 10:07:47 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 0.19/0.36  % Refutation found
% 0.19/0.36  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.57  % Elapsed time: 0.012393 seconds
% 0.22/0.57  % CPU time: 0.028395 seconds
% 0.22/0.57  % Memory used: 11.379 MB
%------------------------------------------------------------------------------