%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% 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 : n024.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 12:33:55 EDT 2023

% Result   : Theorem 0.16s 0.35s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   50 (  11 unt;   0 def)
%            Number of atoms       :  120 (  42 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  110 (  40   ~;  42   |;  19   &)
%                                         (   6 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   6 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   42 (;  38   !;   4   ?)

% 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(f16,axiom,
    ! [X] : ~ member(X,null_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f41,axiom,
    ! [X] :
      ( X != null_class
     => ? [U] :
          ( member(U,universal_class)
          & member(U,X)
          & disjoint(U,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(f96,plain,
    ! [X0] : ~ member(X0,null_class),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f181,plain,
    ! [X] :
      ( X = null_class
      | ? [U] :
          ( member(U,universal_class)
          & member(U,X)
          & disjoint(U,X) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f41]) ).

fof(f182,plain,
    ! [X] :
      ( X = null_class
      | ( member(sk0_5(X),universal_class)
        & member(sk0_5(X),X)
        & disjoint(sk0_5(X),X) ) ),
    inference(skolemization,[status(esa)],[f181]) ).

fof(f184,plain,
    ! [X0] :
      ( X0 = null_class
      | member(sk0_5(X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f182]) ).

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(f258,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1
      | X0 = X1 ),
    inference(paramodulation,[status(thm)],[f66,f62]) ).

fof(f259,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1 ),
    inference(duplicate_literals_removal,[status(esa)],[f258]) ).

fof(f260,plain,
    ! [X0] :
      ( member(X0,singleton(X0))
      | ~ member(X0,universal_class) ),
    inference(paramodulation,[status(thm)],[f66,f198]) ).

fof(f264,plain,
    ! [X0] :
      ( ~ member(X0,singleton(sk0_7))
      | X0 = sk0_8 ),
    inference(paramodulation,[status(thm)],[f193,f259]) ).

fof(f265,plain,
    ( spl0_7
  <=> sk0_5(singleton(sk0_7)) = sk0_8 ),
    introduced(split_symbol_definition) ).

fof(f266,plain,
    ( sk0_5(singleton(sk0_7)) = sk0_8
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f265]) ).

fof(f268,plain,
    ( spl0_8
  <=> singleton(sk0_7) = null_class ),
    introduced(split_symbol_definition) ).

fof(f269,plain,
    ( singleton(sk0_7) = null_class
    | ~ spl0_8 ),
    inference(component_clause,[status(thm)],[f268]) ).

fof(f271,plain,
    ( sk0_5(singleton(sk0_7)) = sk0_8
    | singleton(sk0_7) = null_class ),
    inference(resolution,[status(thm)],[f264,f184]) ).

fof(f272,plain,
    ( spl0_7
    | spl0_8 ),
    inference(split_clause,[status(thm)],[f271,f265,f268]) ).

fof(f275,plain,
    ( spl0_9
  <=> member(sk0_8,universal_class) ),
    introduced(split_symbol_definition) ).

fof(f277,plain,
    ( ~ member(sk0_8,universal_class)
    | spl0_9 ),
    inference(component_clause,[status(thm)],[f275]) ).

fof(f285,plain,
    ( spl0_11
  <=> member(sk0_8,singleton(sk0_7)) ),
    introduced(split_symbol_definition) ).

fof(f286,plain,
    ( member(sk0_8,singleton(sk0_7))
    | ~ spl0_11 ),
    inference(component_clause,[status(thm)],[f285]) ).

fof(f288,plain,
    ( singleton(sk0_7) = null_class
    | member(sk0_8,singleton(sk0_7))
    | ~ spl0_7 ),
    inference(paramodulation,[status(thm)],[f266,f184]) ).

fof(f289,plain,
    ( spl0_8
    | spl0_11
    | ~ spl0_7 ),
    inference(split_clause,[status(thm)],[f288,f268,f285,f265]) ).

fof(f293,plain,
    ( null_class = singleton(sk0_8)
    | ~ spl0_8 ),
    inference(backward_demodulation,[status(thm)],[f269,f193]) ).

fof(f307,plain,
    ( spl0_14
  <=> member(sk0_8,null_class) ),
    introduced(split_symbol_definition) ).

fof(f308,plain,
    ( member(sk0_8,null_class)
    | ~ spl0_14 ),
    inference(component_clause,[status(thm)],[f307]) ).

fof(f352,plain,
    ( sk0_8 = sk0_7
    | ~ spl0_11 ),
    inference(resolution,[status(thm)],[f286,f259]) ).

fof(f353,plain,
    ( $false
    | ~ spl0_11 ),
    inference(forward_subsumption_resolution,[status(thm)],[f352,f195]) ).

fof(f354,plain,
    ~ spl0_11,
    inference(contradiction_clause,[status(thm)],[f353]) ).

fof(f441,plain,
    ( member(sk0_8,null_class)
    | ~ member(sk0_8,universal_class)
    | ~ spl0_8 ),
    inference(paramodulation,[status(thm)],[f293,f260]) ).

fof(f442,plain,
    ( spl0_14
    | ~ spl0_9
    | ~ spl0_8 ),
    inference(split_clause,[status(thm)],[f441,f307,f275,f268]) ).

fof(f451,plain,
    ( $false
    | ~ spl0_14 ),
    inference(forward_subsumption_resolution,[status(thm)],[f308,f96]) ).

fof(f452,plain,
    ~ spl0_14,
    inference(contradiction_clause,[status(thm)],[f451]) ).

fof(f454,plain,
    ( $false
    | spl0_9 ),
    inference(forward_subsumption_resolution,[status(thm)],[f277,f194]) ).

fof(f455,plain,
    spl0_9,
    inference(contradiction_clause,[status(thm)],[f454]) ).

fof(f456,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f272,f289,f354,f442,f452,f455]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12  % Problem  : SET084+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.09/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33  % Computer : n024.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Tue May 30 10:13:33 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.16/0.34  % Drodi V3.5.1
% 0.16/0.35  % Refutation found
% 0.16/0.35  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.35  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.57  % Elapsed time: 0.019101 seconds
% 0.16/0.57  % CPU time: 0.019641 seconds
% 0.16/0.57  % Memory used: 3.971 MB
%------------------------------------------------------------------------------