%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET084+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 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 : Tue Apr 30 20:39:03 EDT 2024

% Result   : Theorem 0.10s 0.33s
% Output   : CNFRefutation 0.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   22 (  10 unt;   0 def)
%            Number of atoms       :   55 (  29 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   51 (  18   ~;  17   |;  13   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   33 (  31   !;   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(f6,axiom,
    ! [X] : singleton(X) = unordered_pair(X,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

fof(f45,negated_conjecture,
    ~ ! [X,Y] :
        ( ( singleton(X) = singleton(Y)
          & member(Y,universal_class) )
       => 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(f62,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,unordered_pair(X1,X2))
      | X0 = X1
      | X0 = X2 ),
    inference(cnf_transformation,[status(esa)],[f60]) ).

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

fof(f191,plain,
    ? [X,Y] :
      ( singleton(X) = singleton(Y)
      & member(Y,universal_class)
      & X != Y ),
    inference(pre_NNF_transformation,[status(esa)],[f45]) ).

fof(f192,plain,
    ( singleton(sk0_7) = singleton(sk0_8)
    & member(sk0_8,universal_class)
    & sk0_7 != sk0_8 ),
    inference(skolemization,[status(esa)],[f191]) ).

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

fof(f194,plain,
    member(sk0_8,universal_class),
    inference(cnf_transformation,[status(esa)],[f192]) ).

fof(f195,plain,
    sk0_7 != sk0_8,
    inference(cnf_transformation,[status(esa)],[f192]) ).

fof(f198,plain,
    ! [X0,X1] :
      ( member(X0,unordered_pair(X0,X1))
      | ~ member(X0,universal_class) ),
    inference(destructive_equality_resolution,[status(esa)],[f63]) ).

fof(f246,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1
      | X0 = X1 ),
    inference(paramodulation,[status(thm)],[f66,f62]) ).

fof(f247,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1 ),
    inference(duplicate_literals_removal,[status(esa)],[f246]) ).

fof(f261,plain,
    ! [X0] : member(sk0_8,unordered_pair(sk0_8,X0)),
    inference(resolution,[status(thm)],[f198,f194]) ).

fof(f322,plain,
    member(sk0_8,singleton(sk0_8)),
    inference(paramodulation,[status(thm)],[f66,f261]) ).

fof(f323,plain,
    member(sk0_8,singleton(sk0_7)),
    inference(forward_demodulation,[status(thm)],[f193,f322]) ).

fof(f333,plain,
    sk0_8 = sk0_7,
    inference(resolution,[status(thm)],[f247,f323]) ).

fof(f334,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f333,f195]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem  : SET084+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.06/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31  % Computer : n002.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 : Mon Apr 29 21:49:54 EDT 2024
% 0.10/0.32  % CPUTime  : 
% 0.10/0.33  % Drodi V3.6.0
% 0.10/0.33  % Refutation found
% 0.10/0.33  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.33  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.34  % Elapsed time: 0.020620 seconds
% 0.10/0.34  % CPU time: 0.035291 seconds
% 0.10/0.34  % Total memory used: 13.630 MB
% 0.10/0.34  % Net memory used: 13.613 MB
%------------------------------------------------------------------------------