%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU089+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n002.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 12:35:48 EDT 2023

% Result   : Theorem 0.15s 0.32s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   33 (  10 unt;   0 def)
%            Number of atoms       :   70 (   2 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   59 (  22   ~;  19   |;  11   &)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   5 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-3 aty)
%            Number of variables   :   24 (;  21   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f14,axiom,
    ! [A,B,C] : cartesian_product3(A,B,C) = cartesian_product2(cartesian_product2(A,B),C),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    ! [A,B] :
      ( ( finite(A)
        & finite(B) )
     => finite(cartesian_product2(A,B)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f53,conjecture,
    ! [A,B,C] :
      ( ( finite(A)
        & finite(B)
        & finite(C) )
     => finite(cartesian_product3(A,B,C)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f54,negated_conjecture,
    ~ ! [A,B,C] :
        ( ( finite(A)
          & finite(B)
          & finite(C) )
       => finite(cartesian_product3(A,B,C)) ),
    inference(negated_conjecture,[status(cth)],[f53]) ).

fof(f102,plain,
    ! [X0,X1,X2] : cartesian_product3(X0,X1,X2) = cartesian_product2(cartesian_product2(X0,X1),X2),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f108,plain,
    ! [A,B] :
      ( ~ finite(A)
      | ~ finite(B)
      | finite(cartesian_product2(A,B)) ),
    inference(pre_NNF_transformation,[status(esa)],[f17]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( ~ finite(X0)
      | ~ finite(X1)
      | finite(cartesian_product2(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f108]) ).

fof(f245,plain,
    ? [A,B,C] :
      ( finite(A)
      & finite(B)
      & finite(C)
      & ~ finite(cartesian_product3(A,B,C)) ),
    inference(pre_NNF_transformation,[status(esa)],[f54]) ).

fof(f246,plain,
    ( finite(sk0_26)
    & finite(sk0_27)
    & finite(sk0_28)
    & ~ finite(cartesian_product3(sk0_26,sk0_27,sk0_28)) ),
    inference(skolemization,[status(esa)],[f245]) ).

fof(f247,plain,
    finite(sk0_26),
    inference(cnf_transformation,[status(esa)],[f246]) ).

fof(f248,plain,
    finite(sk0_27),
    inference(cnf_transformation,[status(esa)],[f246]) ).

fof(f249,plain,
    finite(sk0_28),
    inference(cnf_transformation,[status(esa)],[f246]) ).

fof(f250,plain,
    ~ finite(cartesian_product3(sk0_26,sk0_27,sk0_28)),
    inference(cnf_transformation,[status(esa)],[f246]) ).

fof(f631,plain,
    ! [X0,X1,X2] :
      ( ~ finite(cartesian_product2(X0,X1))
      | ~ finite(X2)
      | finite(cartesian_product3(X0,X1,X2)) ),
    inference(paramodulation,[status(thm)],[f102,f109]) ).

fof(f636,plain,
    ( spl0_56
  <=> finite(cartesian_product2(sk0_26,sk0_27)) ),
    introduced(split_symbol_definition) ).

fof(f638,plain,
    ( ~ finite(cartesian_product2(sk0_26,sk0_27))
    | spl0_56 ),
    inference(component_clause,[status(thm)],[f636]) ).

fof(f639,plain,
    ( spl0_57
  <=> finite(sk0_28) ),
    introduced(split_symbol_definition) ).

fof(f641,plain,
    ( ~ finite(sk0_28)
    | spl0_57 ),
    inference(component_clause,[status(thm)],[f639]) ).

fof(f642,plain,
    ( ~ finite(cartesian_product2(sk0_26,sk0_27))
    | ~ finite(sk0_28) ),
    inference(resolution,[status(thm)],[f631,f250]) ).

fof(f643,plain,
    ( ~ spl0_56
    | ~ spl0_57 ),
    inference(split_clause,[status(thm)],[f642,f636,f639]) ).

fof(f646,plain,
    ( spl0_58
  <=> finite(sk0_26) ),
    introduced(split_symbol_definition) ).

fof(f648,plain,
    ( ~ finite(sk0_26)
    | spl0_58 ),
    inference(component_clause,[status(thm)],[f646]) ).

fof(f649,plain,
    ( spl0_59
  <=> finite(sk0_27) ),
    introduced(split_symbol_definition) ).

fof(f651,plain,
    ( ~ finite(sk0_27)
    | spl0_59 ),
    inference(component_clause,[status(thm)],[f649]) ).

fof(f652,plain,
    ( ~ finite(sk0_26)
    | ~ finite(sk0_27)
    | spl0_56 ),
    inference(resolution,[status(thm)],[f638,f109]) ).

fof(f653,plain,
    ( ~ spl0_58
    | ~ spl0_59
    | spl0_56 ),
    inference(split_clause,[status(thm)],[f652,f646,f649,f636]) ).

fof(f654,plain,
    ( $false
    | spl0_57 ),
    inference(forward_subsumption_resolution,[status(thm)],[f641,f249]) ).

fof(f655,plain,
    spl0_57,
    inference(contradiction_clause,[status(thm)],[f654]) ).

fof(f656,plain,
    ( $false
    | spl0_58 ),
    inference(forward_subsumption_resolution,[status(thm)],[f648,f247]) ).

fof(f657,plain,
    spl0_58,
    inference(contradiction_clause,[status(thm)],[f656]) ).

fof(f658,plain,
    ( $false
    | spl0_59 ),
    inference(forward_subsumption_resolution,[status(thm)],[f651,f248]) ).

fof(f659,plain,
    spl0_59,
    inference(contradiction_clause,[status(thm)],[f658]) ).

fof(f660,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f643,f653,f655,f657,f659]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : SEU089+1 : TPTP v8.1.2. Released v3.2.0.
% 0.05/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30  % Computer : n002.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 09:24:58 EDT 2023
% 0.09/0.30  % CPUTime  : 
% 0.09/0.31  % Drodi V3.5.1
% 0.15/0.32  % Refutation found
% 0.15/0.32  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.32  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.58  % Elapsed time: 0.059107 seconds
% 0.15/0.58  % CPU time: 0.017387 seconds
% 0.15/0.58  % Memory used: 3.997 MB
%------------------------------------------------------------------------------