%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET917+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art11.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory   : 2006MB
% OS       : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 03:51:33 EST 2010

% Result   : Theorem 0.19s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   24 (  10 unt;   0 def)
%            Number of atoms       :   38 (  15 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   29 (  15   ~;   8   |;   3   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   32 (   0 sgn  22   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
    file('/tmp/tmp3I_zwj/sel_SET917+1.p_1',commutativity_k3_xboole_0) ).

fof(4,conjecture,
    ! [X1,X2] :
      ( disjoint(singleton(X1),X2)
      | set_intersection2(singleton(X1),X2) = singleton(X1) ),
    file('/tmp/tmp3I_zwj/sel_SET917+1.p_1',t58_zfmisc_1) ).

fof(6,axiom,
    ! [X1,X2] :
      ( in(X1,X2)
     => set_intersection2(X2,singleton(X1)) = singleton(X1) ),
    file('/tmp/tmp3I_zwj/sel_SET917+1.p_1',l32_zfmisc_1) ).

fof(8,axiom,
    ! [X1,X2] :
      ( ~ in(X1,X2)
     => disjoint(singleton(X1),X2) ),
    file('/tmp/tmp3I_zwj/sel_SET917+1.p_1',l28_zfmisc_1) ).

fof(10,negated_conjecture,
    ~ ! [X1,X2] :
        ( disjoint(singleton(X1),X2)
        | set_intersection2(singleton(X1),X2) = singleton(X1) ),
    inference(assume_negation,[status(cth)],[4]) ).

fof(12,plain,
    ! [X1,X2] :
      ( ~ in(X1,X2)
     => disjoint(singleton(X1),X2) ),
    inference(fof_simplification,[status(thm)],[8,theory(equality)]) ).

fof(14,plain,
    ! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
    inference(variable_rename,[status(thm)],[1]) ).

cnf(15,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[14]) ).

fof(21,negated_conjecture,
    ? [X1,X2] :
      ( ~ disjoint(singleton(X1),X2)
      & set_intersection2(singleton(X1),X2) != singleton(X1) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(22,negated_conjecture,
    ? [X3,X4] :
      ( ~ disjoint(singleton(X3),X4)
      & set_intersection2(singleton(X3),X4) != singleton(X3) ),
    inference(variable_rename,[status(thm)],[21]) ).

fof(23,negated_conjecture,
    ( ~ disjoint(singleton(esk1_0),esk2_0)
    & set_intersection2(singleton(esk1_0),esk2_0) != singleton(esk1_0) ),
    inference(skolemize,[status(esa)],[22]) ).

cnf(24,negated_conjecture,
    set_intersection2(singleton(esk1_0),esk2_0) != singleton(esk1_0),
    inference(split_conjunct,[status(thm)],[23]) ).

cnf(25,negated_conjecture,
    ~ disjoint(singleton(esk1_0),esk2_0),
    inference(split_conjunct,[status(thm)],[23]) ).

fof(29,plain,
    ! [X1,X2] :
      ( ~ in(X1,X2)
      | set_intersection2(X2,singleton(X1)) = singleton(X1) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(30,plain,
    ! [X3,X4] :
      ( ~ in(X3,X4)
      | set_intersection2(X4,singleton(X3)) = singleton(X3) ),
    inference(variable_rename,[status(thm)],[29]) ).

cnf(31,plain,
    ( set_intersection2(X1,singleton(X2)) = singleton(X2)
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[30]) ).

fof(35,plain,
    ! [X1,X2] :
      ( in(X1,X2)
      | disjoint(singleton(X1),X2) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(36,plain,
    ! [X3,X4] :
      ( in(X3,X4)
      | disjoint(singleton(X3),X4) ),
    inference(variable_rename,[status(thm)],[35]) ).

cnf(37,plain,
    ( disjoint(singleton(X1),X2)
    | in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[36]) ).

cnf(45,negated_conjecture,
    in(esk1_0,esk2_0),
    inference(spm,[status(thm)],[25,37,theory(equality)]) ).

cnf(47,negated_conjecture,
    set_intersection2(esk2_0,singleton(esk1_0)) != singleton(esk1_0),
    inference(rw,[status(thm)],[24,15,theory(equality)]) ).

cnf(49,negated_conjecture,
    set_intersection2(esk2_0,singleton(esk1_0)) = singleton(esk1_0),
    inference(spm,[status(thm)],[31,45,theory(equality)]) ).

cnf(50,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[49,47,theory(equality)]) ).

cnf(51,negated_conjecture,
    $false,
    50,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
%   from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET917+1.p
% --creating new selector for []
% -running prover on /tmp/tmp3I_zwj/sel_SET917+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET917+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET917+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET917+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
% 
%------------------------------------------------------------------------------