%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET596+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art04.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 02:59:52 EST 2010

% Result   : Theorem 0.23s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   27 (  11 unt;   0 def)
%            Number of atoms       :   48 (  22 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   37 (  16   ~;   9   |;   8   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   37 (   0 sgn  22   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2,X3] :
      ( subset(X1,X2)
     => subset(intersection(X1,X3),intersection(X2,X3)) ),
    file('/tmp/tmpevv1gx/sel_SET596+3.p_1',intersection_of_subset) ).

fof(2,conjecture,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & intersection(X2,X3) = empty_set )
     => intersection(X1,X3) = empty_set ),
    file('/tmp/tmpevv1gx/sel_SET596+3.p_1',prove_th55) ).

fof(3,axiom,
    ! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
    file('/tmp/tmpevv1gx/sel_SET596+3.p_1',commutativity_of_intersection) ).

fof(9,axiom,
    ! [X1] :
      ( subset(X1,empty_set)
     => X1 = empty_set ),
    file('/tmp/tmpevv1gx/sel_SET596+3.p_1',subset_of_empty_set_is_empty_set) ).

fof(12,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( subset(X1,X2)
          & intersection(X2,X3) = empty_set )
       => intersection(X1,X3) = empty_set ),
    inference(assume_negation,[status(cth)],[2]) ).

fof(15,plain,
    ! [X1,X2,X3] :
      ( ~ subset(X1,X2)
      | subset(intersection(X1,X3),intersection(X2,X3)) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(16,plain,
    ! [X4,X5,X6] :
      ( ~ subset(X4,X5)
      | subset(intersection(X4,X6),intersection(X5,X6)) ),
    inference(variable_rename,[status(thm)],[15]) ).

cnf(17,plain,
    ( subset(intersection(X1,X2),intersection(X3,X2))
    | ~ subset(X1,X3) ),
    inference(split_conjunct,[status(thm)],[16]) ).

fof(18,negated_conjecture,
    ? [X1,X2,X3] :
      ( subset(X1,X2)
      & intersection(X2,X3) = empty_set
      & intersection(X1,X3) != empty_set ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(19,negated_conjecture,
    ? [X4,X5,X6] :
      ( subset(X4,X5)
      & intersection(X5,X6) = empty_set
      & intersection(X4,X6) != empty_set ),
    inference(variable_rename,[status(thm)],[18]) ).

fof(20,negated_conjecture,
    ( subset(esk1_0,esk2_0)
    & intersection(esk2_0,esk3_0) = empty_set
    & intersection(esk1_0,esk3_0) != empty_set ),
    inference(skolemize,[status(esa)],[19]) ).

cnf(21,negated_conjecture,
    intersection(esk1_0,esk3_0) != empty_set,
    inference(split_conjunct,[status(thm)],[20]) ).

cnf(22,negated_conjecture,
    intersection(esk2_0,esk3_0) = empty_set,
    inference(split_conjunct,[status(thm)],[20]) ).

cnf(23,negated_conjecture,
    subset(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[20]) ).

fof(24,plain,
    ! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
    inference(variable_rename,[status(thm)],[3]) ).

cnf(25,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(split_conjunct,[status(thm)],[24]) ).

fof(61,plain,
    ! [X1] :
      ( ~ subset(X1,empty_set)
      | X1 = empty_set ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(62,plain,
    ! [X2] :
      ( ~ subset(X2,empty_set)
      | X2 = empty_set ),
    inference(variable_rename,[status(thm)],[61]) ).

cnf(63,plain,
    ( X1 = empty_set
    | ~ subset(X1,empty_set) ),
    inference(split_conjunct,[status(thm)],[62]) ).

cnf(73,negated_conjecture,
    intersection(esk3_0,esk1_0) != empty_set,
    inference(rw,[status(thm)],[21,25,theory(equality)]) ).

cnf(77,negated_conjecture,
    ( subset(intersection(X1,esk3_0),empty_set)
    | ~ subset(X1,esk2_0) ),
    inference(spm,[status(thm)],[17,22,theory(equality)]) ).

cnf(139,negated_conjecture,
    ( empty_set = intersection(X1,esk3_0)
    | ~ subset(X1,esk2_0) ),
    inference(spm,[status(thm)],[63,77,theory(equality)]) ).

cnf(147,negated_conjecture,
    ( empty_set = intersection(esk3_0,X1)
    | ~ subset(X1,esk2_0) ),
    inference(spm,[status(thm)],[25,139,theory(equality)]) ).

cnf(274,negated_conjecture,
    ~ subset(esk1_0,esk2_0),
    inference(spm,[status(thm)],[73,147,theory(equality)]) ).

cnf(286,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[274,23,theory(equality)]) ).

cnf(287,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[286,theory(equality)]) ).

cnf(288,negated_conjecture,
    $false,
    287,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET596+3.p
% --creating new selector for []
% -running prover on /tmp/tmpevv1gx/sel_SET596+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET596+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET596+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET596+3.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
% 
%------------------------------------------------------------------------------