TSTP Solution File: SET630+3 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET630+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 03:05:39 EST 2010

% Result   : Theorem 0.17s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   37 (  23 unt;   0 def)
%            Number of atoms       :   70 (   6 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   59 (  26   ~;  22   |;   8   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   55 (   0 sgn  36   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,axiom,
    ! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
    file('/tmp/tmp6MsawO/sel_SET630+3.p_1',commutativity_of_intersection) ).

fof(4,axiom,
    ! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
    file('/tmp/tmp6MsawO/sel_SET630+3.p_1',symmetric_difference_defn) ).

fof(5,conjecture,
    ! [X1,X2] : disjoint(intersection(X1,X2),symmetric_difference(X1,X2)),
    file('/tmp/tmp6MsawO/sel_SET630+3.p_1',prove_intersection_and_symmetric_difference_disjoint) ).

fof(7,axiom,
    ! [X1,X2] : disjoint(intersection(X1,X2),difference(X1,X2)),
    file('/tmp/tmp6MsawO/sel_SET630+3.p_1',intersection_and_union_disjoint) ).

fof(10,axiom,
    ! [X1,X2] :
      ( disjoint(X1,X2)
    <=> ~ intersect(X1,X2) ),
    file('/tmp/tmp6MsawO/sel_SET630+3.p_1',disjoint_defn) ).

fof(12,axiom,
    ! [X1,X2,X3] :
      ( intersect(X1,union(X2,X3))
    <=> ( intersect(X1,X2)
        | intersect(X1,X3) ) ),
    file('/tmp/tmp6MsawO/sel_SET630+3.p_1',intersect_with_union) ).

fof(13,negated_conjecture,
    ~ ! [X1,X2] : disjoint(intersection(X1,X2),symmetric_difference(X1,X2)),
    inference(assume_negation,[status(cth)],[5]) ).

fof(14,plain,
    ! [X1,X2] :
      ( disjoint(X1,X2)
    <=> ~ intersect(X1,X2) ),
    inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).

fof(17,plain,
    ! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
    inference(variable_rename,[status(thm)],[2]) ).

cnf(18,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(split_conjunct,[status(thm)],[17]) ).

fof(21,plain,
    ! [X3,X4] : symmetric_difference(X3,X4) = union(difference(X3,X4),difference(X4,X3)),
    inference(variable_rename,[status(thm)],[4]) ).

cnf(22,plain,
    symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
    inference(split_conjunct,[status(thm)],[21]) ).

fof(23,negated_conjecture,
    ? [X1,X2] : ~ disjoint(intersection(X1,X2),symmetric_difference(X1,X2)),
    inference(fof_nnf,[status(thm)],[13]) ).

fof(24,negated_conjecture,
    ? [X3,X4] : ~ disjoint(intersection(X3,X4),symmetric_difference(X3,X4)),
    inference(variable_rename,[status(thm)],[23]) ).

fof(25,negated_conjecture,
    ~ disjoint(intersection(esk1_0,esk2_0),symmetric_difference(esk1_0,esk2_0)),
    inference(skolemize,[status(esa)],[24]) ).

cnf(26,negated_conjecture,
    ~ disjoint(intersection(esk1_0,esk2_0),symmetric_difference(esk1_0,esk2_0)),
    inference(split_conjunct,[status(thm)],[25]) ).

fof(35,plain,
    ! [X3,X4] : disjoint(intersection(X3,X4),difference(X3,X4)),
    inference(variable_rename,[status(thm)],[7]) ).

cnf(36,plain,
    disjoint(intersection(X1,X2),difference(X1,X2)),
    inference(split_conjunct,[status(thm)],[35]) ).

fof(49,plain,
    ! [X1,X2] :
      ( ( ~ disjoint(X1,X2)
        | ~ intersect(X1,X2) )
      & ( intersect(X1,X2)
        | disjoint(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[14]) ).

fof(50,plain,
    ! [X3,X4] :
      ( ( ~ disjoint(X3,X4)
        | ~ intersect(X3,X4) )
      & ( intersect(X3,X4)
        | disjoint(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[49]) ).

cnf(51,plain,
    ( disjoint(X1,X2)
    | intersect(X1,X2) ),
    inference(split_conjunct,[status(thm)],[50]) ).

cnf(52,plain,
    ( ~ intersect(X1,X2)
    | ~ disjoint(X1,X2) ),
    inference(split_conjunct,[status(thm)],[50]) ).

fof(59,plain,
    ! [X1,X2,X3] :
      ( ( ~ intersect(X1,union(X2,X3))
        | intersect(X1,X2)
        | intersect(X1,X3) )
      & ( ( ~ intersect(X1,X2)
          & ~ intersect(X1,X3) )
        | intersect(X1,union(X2,X3)) ) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(60,plain,
    ! [X4,X5,X6] :
      ( ( ~ intersect(X4,union(X5,X6))
        | intersect(X4,X5)
        | intersect(X4,X6) )
      & ( ( ~ intersect(X4,X5)
          & ~ intersect(X4,X6) )
        | intersect(X4,union(X5,X6)) ) ),
    inference(variable_rename,[status(thm)],[59]) ).

fof(61,plain,
    ! [X4,X5,X6] :
      ( ( ~ intersect(X4,union(X5,X6))
        | intersect(X4,X5)
        | intersect(X4,X6) )
      & ( ~ intersect(X4,X5)
        | intersect(X4,union(X5,X6)) )
      & ( ~ intersect(X4,X6)
        | intersect(X4,union(X5,X6)) ) ),
    inference(distribute,[status(thm)],[60]) ).

cnf(64,plain,
    ( intersect(X1,X2)
    | intersect(X1,X3)
    | ~ intersect(X1,union(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[61]) ).

cnf(66,negated_conjecture,
    ~ disjoint(intersection(esk1_0,esk2_0),union(difference(esk1_0,esk2_0),difference(esk2_0,esk1_0))),
    inference(rw,[status(thm)],[26,22,theory(equality)]),
    [unfolding] ).

cnf(67,negated_conjecture,
    intersect(intersection(esk1_0,esk2_0),union(difference(esk1_0,esk2_0),difference(esk2_0,esk1_0))),
    inference(spm,[status(thm)],[66,51,theory(equality)]) ).

cnf(68,plain,
    disjoint(intersection(X2,X1),difference(X1,X2)),
    inference(spm,[status(thm)],[36,18,theory(equality)]) ).

cnf(93,negated_conjecture,
    ( intersect(intersection(esk1_0,esk2_0),difference(esk2_0,esk1_0))
    | intersect(intersection(esk1_0,esk2_0),difference(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[64,67,theory(equality)]) ).

cnf(108,negated_conjecture,
    ( intersect(intersection(esk1_0,esk2_0),difference(esk1_0,esk2_0))
    | ~ disjoint(intersection(esk1_0,esk2_0),difference(esk2_0,esk1_0)) ),
    inference(spm,[status(thm)],[52,93,theory(equality)]) ).

cnf(114,negated_conjecture,
    ( intersect(intersection(esk1_0,esk2_0),difference(esk1_0,esk2_0))
    | $false ),
    inference(rw,[status(thm)],[108,68,theory(equality)]) ).

cnf(115,negated_conjecture,
    intersect(intersection(esk1_0,esk2_0),difference(esk1_0,esk2_0)),
    inference(cn,[status(thm)],[114,theory(equality)]) ).

cnf(116,negated_conjecture,
    ~ disjoint(intersection(esk1_0,esk2_0),difference(esk1_0,esk2_0)),
    inference(spm,[status(thm)],[52,115,theory(equality)]) ).

cnf(123,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[116,36,theory(equality)]) ).

cnf(124,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[123,theory(equality)]) ).

cnf(125,negated_conjecture,
    $false,
    124,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET630+3.p
% --creating new selector for []
% -running prover on /tmp/tmp6MsawO/sel_SET630+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET630+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET630+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET630+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
% 
%------------------------------------------------------------------------------