%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET639+3 : TPTP v5.0.0. Released v2.2.0.
% 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 03:10:52 EST 2010

% Result   : Theorem 0.22s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   21 (  10 unt;   0 def)
%            Number of atoms       :   37 (  23 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   25 (   9   ~;   5   |;   8   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   22 (   0 sgn  14   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
    file('/tmp/tmpmzJZSr/sel_SET639+3.p_1',commutativity_of_intersection) ).

fof(5,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
     => intersection(X1,X2) = X1 ),
    file('/tmp/tmpmzJZSr/sel_SET639+3.p_1',subset_intersection) ).

fof(6,conjecture,
    ! [X1,X2] :
      ( ( subset(X1,X2)
        & intersection(X2,X1) = empty_set )
     => X1 = empty_set ),
    file('/tmp/tmpmzJZSr/sel_SET639+3.p_1',prove_th121) ).

fof(11,negated_conjecture,
    ~ ! [X1,X2] :
        ( ( subset(X1,X2)
          & intersection(X2,X1) = empty_set )
       => X1 = empty_set ),
    inference(assume_negation,[status(cth)],[6]) ).

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

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

fof(36,plain,
    ! [X1,X2] :
      ( ~ subset(X1,X2)
      | intersection(X1,X2) = X1 ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(37,plain,
    ! [X3,X4] :
      ( ~ subset(X3,X4)
      | intersection(X3,X4) = X3 ),
    inference(variable_rename,[status(thm)],[36]) ).

cnf(38,plain,
    ( intersection(X1,X2) = X1
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[37]) ).

fof(39,negated_conjecture,
    ? [X1,X2] :
      ( subset(X1,X2)
      & intersection(X2,X1) = empty_set
      & X1 != empty_set ),
    inference(fof_nnf,[status(thm)],[11]) ).

fof(40,negated_conjecture,
    ? [X3,X4] :
      ( subset(X3,X4)
      & intersection(X4,X3) = empty_set
      & X3 != empty_set ),
    inference(variable_rename,[status(thm)],[39]) ).

fof(41,negated_conjecture,
    ( subset(esk3_0,esk4_0)
    & intersection(esk4_0,esk3_0) = empty_set
    & esk3_0 != empty_set ),
    inference(skolemize,[status(esa)],[40]) ).

cnf(42,negated_conjecture,
    esk3_0 != empty_set,
    inference(split_conjunct,[status(thm)],[41]) ).

cnf(43,negated_conjecture,
    intersection(esk4_0,esk3_0) = empty_set,
    inference(split_conjunct,[status(thm)],[41]) ).

cnf(44,negated_conjecture,
    subset(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[41]) ).

cnf(68,negated_conjecture,
    intersection(esk3_0,esk4_0) = empty_set,
    inference(rw,[status(thm)],[43,15,theory(equality)]) ).

cnf(111,negated_conjecture,
    ( empty_set = esk3_0
    | ~ subset(esk3_0,esk4_0) ),
    inference(spm,[status(thm)],[38,68,theory(equality)]) ).

cnf(115,negated_conjecture,
    ( empty_set = esk3_0
    | $false ),
    inference(rw,[status(thm)],[111,44,theory(equality)]) ).

cnf(116,negated_conjecture,
    empty_set = esk3_0,
    inference(cn,[status(thm)],[115,theory(equality)]) ).

cnf(117,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[116,42,theory(equality)]) ).

cnf(118,negated_conjecture,
    $false,
    117,
    [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/SET639+3.p
% --creating new selector for []
% -running prover on /tmp/tmpmzJZSr/sel_SET639+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET639+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET639+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET639+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
% 
%------------------------------------------------------------------------------