%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET062+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art03.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 02:40:24 EST 2010

% Result   : Theorem 0.16s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   21 (  14 unt;   0 def)
%            Number of atoms       :   50 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   53 (  24   ~;  17   |;  10   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   31 (   2 sgn  23   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/tmp/tmpBiRXzn/sel_SET062+3.p_1',subset_defn) ).

fof(2,conjecture,
    ! [X1] : subset(empty_set,X1),
    file('/tmp/tmpBiRXzn/sel_SET062+3.p_1',prove_empty_set_subset) ).

fof(4,axiom,
    ! [X1] : ~ member(X1,empty_set),
    file('/tmp/tmpBiRXzn/sel_SET062+3.p_1',empty_set_defn) ).

fof(6,negated_conjecture,
    ~ ! [X1] : subset(empty_set,X1),
    inference(assume_negation,[status(cth)],[2]) ).

fof(7,plain,
    ! [X1] : ~ member(X1,empty_set),
    inference(fof_simplification,[status(thm)],[4,theory(equality)]) ).

fof(9,plain,
    ! [X1,X2] :
      ( ( ~ subset(X1,X2)
        | ! [X3] :
            ( ~ member(X3,X1)
            | member(X3,X2) ) )
      & ( ? [X3] :
            ( member(X3,X1)
            & ~ member(X3,X2) )
        | subset(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(10,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ member(X6,X4)
            | member(X6,X5) ) )
      & ( ? [X7] :
            ( member(X7,X4)
            & ~ member(X7,X5) )
        | subset(X4,X5) ) ),
    inference(variable_rename,[status(thm)],[9]) ).

fof(11,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ member(X6,X4)
            | member(X6,X5) ) )
      & ( ( member(esk1_2(X4,X5),X4)
          & ~ member(esk1_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(skolemize,[status(esa)],[10]) ).

fof(12,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,X4)
        | member(X6,X5)
        | ~ subset(X4,X5) )
      & ( ( member(esk1_2(X4,X5),X4)
          & ~ member(esk1_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(shift_quantors,[status(thm)],[11]) ).

fof(13,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,X4)
        | member(X6,X5)
        | ~ subset(X4,X5) )
      & ( member(esk1_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ member(esk1_2(X4,X5),X5)
        | subset(X4,X5) ) ),
    inference(distribute,[status(thm)],[12]) ).

cnf(15,plain,
    ( subset(X1,X2)
    | member(esk1_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[13]) ).

fof(17,negated_conjecture,
    ? [X1] : ~ subset(empty_set,X1),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(18,negated_conjecture,
    ? [X2] : ~ subset(empty_set,X2),
    inference(variable_rename,[status(thm)],[17]) ).

fof(19,negated_conjecture,
    ~ subset(empty_set,esk2_0),
    inference(skolemize,[status(esa)],[18]) ).

cnf(20,negated_conjecture,
    ~ subset(empty_set,esk2_0),
    inference(split_conjunct,[status(thm)],[19]) ).

fof(23,plain,
    ! [X2] : ~ member(X2,empty_set),
    inference(variable_rename,[status(thm)],[7]) ).

cnf(24,plain,
    ~ member(X1,empty_set),
    inference(split_conjunct,[status(thm)],[23]) ).

cnf(33,plain,
    subset(empty_set,X1),
    inference(spm,[status(thm)],[24,15,theory(equality)]) ).

cnf(39,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[20,33,theory(equality)]) ).

cnf(40,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[39,theory(equality)]) ).

cnf(41,negated_conjecture,
    $false,
    40,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET062+3.p
% --creating new selector for []
% -running prover on /tmp/tmpBiRXzn/sel_SET062+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET062+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET062+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET062+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
% 
%------------------------------------------------------------------------------