%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU167+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n027.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 12:36:06 EDT 2023

% Result   : Theorem 0.16s 0.32s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   29 (   6 unt;   0 def)
%            Number of atoms       :   63 (   0 equ)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   58 (  24   ~;  18   |;  10   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   42 (;  38   !;   4   ?)

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

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

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

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

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

fof(f15,plain,
    ! [A,B] :
      ( ~ subset(A,B)
      | ( ! [C] : subset(cartesian_product2(A,C),cartesian_product2(B,C))
        & ! [C] : subset(cartesian_product2(C,A),cartesian_product2(C,B)) ) ),
    inference(miniscoping,[status(esa)],[f14]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f18,plain,
    ? [A,B,C,D] :
      ( subset(A,B)
      & subset(C,D)
      & ~ subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f19,plain,
    ( subset(sk0_2,sk0_3)
    & subset(sk0_4,sk0_5)
    & ~ subset(cartesian_product2(sk0_2,sk0_4),cartesian_product2(sk0_3,sk0_5)) ),
    inference(skolemization,[status(esa)],[f18]) ).

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

fof(f21,plain,
    subset(sk0_4,sk0_5),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f22,plain,
    ~ subset(cartesian_product2(sk0_2,sk0_4),cartesian_product2(sk0_3,sk0_5)),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f23,plain,
    ! [A,B,C] :
      ( ~ subset(A,B)
      | ~ subset(B,C)
      | subset(A,C) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f24,plain,
    ! [A,C] :
      ( ! [B] :
          ( ~ subset(A,B)
          | ~ subset(B,C) )
      | subset(A,C) ),
    inference(miniscoping,[status(esa)],[f23]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | ~ subset(X1,X2)
      | subset(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f26,plain,
    ! [X0] :
      ( ~ subset(cartesian_product2(sk0_2,sk0_4),X0)
      | ~ subset(X0,cartesian_product2(sk0_3,sk0_5)) ),
    inference(resolution,[status(thm)],[f25,f22]) ).

fof(f29,plain,
    ! [X0] :
      ( ~ subset(sk0_2,X0)
      | ~ subset(cartesian_product2(X0,sk0_4),cartesian_product2(sk0_3,sk0_5)) ),
    inference(resolution,[status(thm)],[f16,f26]) ).

fof(f31,plain,
    ( spl0_0
  <=> subset(sk0_2,sk0_3) ),
    introduced(split_symbol_definition) ).

fof(f33,plain,
    ( ~ subset(sk0_2,sk0_3)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f31]) ).

fof(f34,plain,
    ( spl0_1
  <=> subset(sk0_4,sk0_5) ),
    introduced(split_symbol_definition) ).

fof(f36,plain,
    ( ~ subset(sk0_4,sk0_5)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f34]) ).

fof(f37,plain,
    ( ~ subset(sk0_2,sk0_3)
    | ~ subset(sk0_4,sk0_5) ),
    inference(resolution,[status(thm)],[f29,f17]) ).

fof(f38,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f37,f31,f34]) ).

fof(f40,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f33,f20]) ).

fof(f41,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f40]) ).

fof(f42,plain,
    ( $false
    | spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f36,f21]) ).

fof(f43,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f42]) ).

fof(f44,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f38,f41,f43]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : SEU167+3 : TPTP v8.1.2. Released v3.2.0.
% 0.02/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31  % Computer : n027.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 09:30:02 EDT 2023
% 0.10/0.31  % CPUTime  : 
% 0.16/0.31  % Drodi V3.5.1
% 0.16/0.32  % Refutation found
% 0.16/0.32  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.32  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.55  % Elapsed time: 0.022382 seconds
% 0.16/0.55  % CPU time: 0.011370 seconds
% 0.16/0.55  % Memory used: 1.792 MB
%------------------------------------------------------------------------------