%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET002+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art06.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 02:36:01 EST 2010

% Result   : Theorem 0.27s
% Output   : CNFRefutation 0.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   17 (  13 unt;   0 def)
%            Number of atoms       :   21 (  10 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   13 (   9   ~;   3   |;   0   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-2 aty)
%            Number of variables   :   15 (   0 sgn  10   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
     => union(X1,X2) = X2 ),
    file('/tmp/tmpF14ULh/sel_SET002+3.p_1',subset_union) ).

fof(5,conjecture,
    ! [X1] : union(X1,X1) = X1,
    file('/tmp/tmpF14ULh/sel_SET002+3.p_1',prove_idempotency_of_union) ).

fof(8,axiom,
    ! [X1] : subset(X1,X1),
    file('/tmp/tmpF14ULh/sel_SET002+3.p_1',reflexivity_of_subset) ).

fof(9,negated_conjecture,
    ~ ! [X1] : union(X1,X1) = X1,
    inference(assume_negation,[status(cth)],[5]) ).

fof(12,plain,
    ! [X1,X2] :
      ( ~ subset(X1,X2)
      | union(X1,X2) = X2 ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(13,plain,
    ! [X3,X4] :
      ( ~ subset(X3,X4)
      | union(X3,X4) = X4 ),
    inference(variable_rename,[status(thm)],[12]) ).

cnf(14,plain,
    ( union(X1,X2) = X2
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[13]) ).

fof(27,negated_conjecture,
    ? [X1] : union(X1,X1) != X1,
    inference(fof_nnf,[status(thm)],[9]) ).

fof(28,negated_conjecture,
    ? [X2] : union(X2,X2) != X2,
    inference(variable_rename,[status(thm)],[27]) ).

fof(29,negated_conjecture,
    union(esk1_0,esk1_0) != esk1_0,
    inference(skolemize,[status(esa)],[28]) ).

cnf(30,negated_conjecture,
    union(esk1_0,esk1_0) != esk1_0,
    inference(split_conjunct,[status(thm)],[29]) ).

fof(48,plain,
    ! [X2] : subset(X2,X2),
    inference(variable_rename,[status(thm)],[8]) ).

cnf(49,plain,
    subset(X1,X1),
    inference(split_conjunct,[status(thm)],[48]) ).

cnf(58,negated_conjecture,
    ~ subset(esk1_0,esk1_0),
    inference(spm,[status(thm)],[30,14,theory(equality)]) ).

cnf(59,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[58,49,theory(equality)]) ).

cnf(60,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[59,theory(equality)]) ).

cnf(61,negated_conjecture,
    $false,
    60,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET002+3.p
% --creating new selector for []
% -running prover on /tmp/tmpF14ULh/sel_SET002+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET002+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET002+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET002+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
% 
%------------------------------------------------------------------------------