%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET101+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n032.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 12:34:00 EDT 2023

% Result   : Theorem 0.06s 0.28s
% Output   : CNFRefutation 0.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   20 (  14 unt;   0 def)
%            Number of atoms       :   41 (  15 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   37 (  16   ~;  13   |;   7   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   38 (;  36   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [U,X,Y] :
      ( member(U,unordered_pair(X,Y))
    <=> ( member(U,universal_class)
        & ( U = X
          | U = Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [X,Y] : member(unordered_pair(X,Y),universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X] : singleton(X) = unordered_pair(X,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f44,conjecture,
    ! [X,Y] : member(singleton(X),ordered_pair(X,Y)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f45,negated_conjecture,
    ~ ! [X,Y] : member(singleton(X),ordered_pair(X,Y)),
    inference(negated_conjecture,[status(cth)],[f44]) ).

fof(f59,plain,
    ! [U,X,Y] :
      ( ( ~ member(U,unordered_pair(X,Y))
        | ( member(U,universal_class)
          & ( U = X
            | U = Y ) ) )
      & ( member(U,unordered_pair(X,Y))
        | ~ member(U,universal_class)
        | ( U != X
          & U != Y ) ) ),
    inference(NNF_transformation,[status(esa)],[f4]) ).

fof(f60,plain,
    ( ! [U,X,Y] :
        ( ~ member(U,unordered_pair(X,Y))
        | ( member(U,universal_class)
          & ( U = X
            | U = Y ) ) )
    & ! [U,X,Y] :
        ( member(U,unordered_pair(X,Y))
        | ~ member(U,universal_class)
        | ( U != X
          & U != Y ) ) ),
    inference(miniscoping,[status(esa)],[f59]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( member(X0,unordered_pair(X1,X2))
      | ~ member(X0,universal_class)
      | X0 != X1 ),
    inference(cnf_transformation,[status(esa)],[f60]) ).

fof(f65,plain,
    ! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f66,plain,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f67,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f191,plain,
    ? [X,Y] : ~ member(singleton(X),ordered_pair(X,Y)),
    inference(pre_NNF_transformation,[status(esa)],[f45]) ).

fof(f192,plain,
    ~ member(singleton(sk0_7),ordered_pair(sk0_7,sk0_8)),
    inference(skolemization,[status(esa)],[f191]) ).

fof(f193,plain,
    ~ member(singleton(sk0_7),ordered_pair(sk0_7,sk0_8)),
    inference(cnf_transformation,[status(esa)],[f192]) ).

fof(f196,plain,
    ! [X0,X1] :
      ( member(X0,unordered_pair(X0,X1))
      | ~ member(X0,universal_class) ),
    inference(destructive_equality_resolution,[status(esa)],[f63]) ).

fof(f202,plain,
    ! [X0] : member(singleton(X0),universal_class),
    inference(paramodulation,[status(thm)],[f66,f65]) ).

fof(f295,plain,
    ! [X0,X1] :
      ( member(singleton(X0),ordered_pair(X0,X1))
      | ~ member(singleton(X0),universal_class) ),
    inference(paramodulation,[status(thm)],[f67,f196]) ).

fof(f296,plain,
    ! [X0,X1] : member(singleton(X0),ordered_pair(X0,X1)),
    inference(forward_subsumption_resolution,[status(thm)],[f295,f202]) ).

fof(f301,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f193,f296]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : SET101+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.06/0.08  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.06/0.26  % Computer : n032.cluster.edu
% 0.06/0.26  % Model    : x86_64 x86_64
% 0.06/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26  % Memory   : 8042.1875MB
% 0.06/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26  % CPULimit : 300
% 0.06/0.26  % WCLimit  : 300
% 0.06/0.26  % DateTime : Tue May 30 10:22:46 EDT 2023
% 0.06/0.26  % CPUTime  : 
% 0.06/0.27  % Drodi V3.5.1
% 0.06/0.28  % Refutation found
% 0.06/0.28  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.06/0.28  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.06/0.29  % Elapsed time: 0.020815 seconds
% 0.06/0.29  % CPU time: 0.032001 seconds
% 0.06/0.29  % Memory used: 15.112 MB
%------------------------------------------------------------------------------