%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET618+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 03:03:45 EST 2010

% Result   : Theorem 0.16s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   19 (  19 unt;   0 def)
%            Number of atoms       :   19 (  16 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    6 (   6   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   16 (   0 sgn  10   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(4,axiom,
    ! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
    file('/tmp/tmpMGrFJs/sel_SET618+3.p_1',symmetric_difference_defn) ).

fof(5,conjecture,
    ! [X1] : symmetric_difference(X1,X1) = empty_set,
    file('/tmp/tmpMGrFJs/sel_SET618+3.p_1',prove_th93) ).

fof(6,axiom,
    ! [X1] : union(X1,X1) = X1,
    file('/tmp/tmpMGrFJs/sel_SET618+3.p_1',idempotency_of_union) ).

fof(7,axiom,
    ! [X1] : difference(X1,X1) = empty_set,
    file('/tmp/tmpMGrFJs/sel_SET618+3.p_1',self_difference_is_empty_set) ).

fof(13,negated_conjecture,
    ~ ! [X1] : symmetric_difference(X1,X1) = empty_set,
    inference(assume_negation,[status(cth)],[5]) ).

fof(26,plain,
    ! [X3,X4] : symmetric_difference(X3,X4) = union(difference(X3,X4),difference(X4,X3)),
    inference(variable_rename,[status(thm)],[4]) ).

cnf(27,plain,
    symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
    inference(split_conjunct,[status(thm)],[26]) ).

fof(28,negated_conjecture,
    ? [X1] : symmetric_difference(X1,X1) != empty_set,
    inference(fof_nnf,[status(thm)],[13]) ).

fof(29,negated_conjecture,
    ? [X2] : symmetric_difference(X2,X2) != empty_set,
    inference(variable_rename,[status(thm)],[28]) ).

fof(30,negated_conjecture,
    symmetric_difference(esk2_0,esk2_0) != empty_set,
    inference(skolemize,[status(esa)],[29]) ).

cnf(31,negated_conjecture,
    symmetric_difference(esk2_0,esk2_0) != empty_set,
    inference(split_conjunct,[status(thm)],[30]) ).

fof(32,plain,
    ! [X2] : union(X2,X2) = X2,
    inference(variable_rename,[status(thm)],[6]) ).

cnf(33,plain,
    union(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[32]) ).

fof(34,plain,
    ! [X2] : difference(X2,X2) = empty_set,
    inference(variable_rename,[status(thm)],[7]) ).

cnf(35,plain,
    difference(X1,X1) = empty_set,
    inference(split_conjunct,[status(thm)],[34]) ).

cnf(64,negated_conjecture,
    union(difference(esk2_0,esk2_0),difference(esk2_0,esk2_0)) != empty_set,
    inference(rw,[status(thm)],[31,27,theory(equality)]),
    [unfolding] ).

cnf(75,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[64,35,theory(equality)]),35,theory(equality)]),33,theory(equality)]) ).

cnf(76,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[75,theory(equality)]) ).

cnf(77,negated_conjecture,
    $false,
    76,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET618+3.p
% --creating new selector for []
% -running prover on /tmp/tmpMGrFJs/sel_SET618+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET618+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET618+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET618+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
% 
%------------------------------------------------------------------------------