TSTP Solution File: SET063+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET063+1 : TPTP v5.3.0. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art08.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory   : 2005MB
% OS       : Linux 2.6.32.26-175.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Fri Jun 15 08:04:29 EDT 2012

% Result   : Theorem 0.18s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   29 (  11 unt;   0 def)
%            Number of atoms       :   84 (   3 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   93 (  38   ~;  30   |;  20   &)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   41 (   2 sgn  31   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( equal(X1,X2)
    <=> ( subclass(X1,X2)
        & subclass(X2,X1) ) ),
    file('/tmp/tmpuY5fZO/sel_SET063+1.p_1',extensionality) ).

fof(2,axiom,
    ! [X1] : ~ member(X1,null_class),
    file('/tmp/tmpuY5fZO/sel_SET063+1.p_1',null_class_defn) ).

fof(3,axiom,
    ! [X1,X2] :
      ( subclass(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/tmp/tmpuY5fZO/sel_SET063+1.p_1',subclass_defn) ).

fof(5,conjecture,
    ! [X1] :
      ( subclass(X1,null_class)
     => equal(X1,null_class) ),
    file('/tmp/tmpuY5fZO/sel_SET063+1.p_1',corollary_of_null_class_is_subclass) ).

fof(6,negated_conjecture,
    ~ ! [X1] :
        ( subclass(X1,null_class)
       => equal(X1,null_class) ),
    inference(assume_negation,[status(cth)],[5]) ).

fof(7,plain,
    ! [X1] : ~ member(X1,null_class),
    inference(fof_simplification,[status(thm)],[2,theory(equality)]) ).

fof(8,plain,
    ! [X1,X2] :
      ( ( ~ equal(X1,X2)
        | ( subclass(X1,X2)
          & subclass(X2,X1) ) )
      & ( ~ subclass(X1,X2)
        | ~ subclass(X2,X1)
        | equal(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(9,plain,
    ! [X3,X4] :
      ( ( ~ equal(X3,X4)
        | ( subclass(X3,X4)
          & subclass(X4,X3) ) )
      & ( ~ subclass(X3,X4)
        | ~ subclass(X4,X3)
        | equal(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[8]) ).

fof(10,plain,
    ! [X3,X4] :
      ( ( subclass(X3,X4)
        | ~ equal(X3,X4) )
      & ( subclass(X4,X3)
        | ~ equal(X3,X4) )
      & ( ~ subclass(X3,X4)
        | ~ subclass(X4,X3)
        | equal(X3,X4) ) ),
    inference(distribute,[status(thm)],[9]) ).

cnf(11,plain,
    ( X1 = X2
    | ~ subclass(X2,X1)
    | ~ subclass(X1,X2) ),
    inference(split_conjunct,[status(thm)],[10]) ).

fof(14,plain,
    ! [X2] : ~ member(X2,null_class),
    inference(variable_rename,[status(thm)],[7]) ).

cnf(15,plain,
    ~ member(X1,null_class),
    inference(split_conjunct,[status(thm)],[14]) ).

fof(16,plain,
    ! [X1,X2] :
      ( ( ~ subclass(X1,X2)
        | ! [X3] :
            ( ~ member(X3,X1)
            | member(X3,X2) ) )
      & ( ? [X3] :
            ( member(X3,X1)
            & ~ member(X3,X2) )
        | subclass(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(17,plain,
    ! [X4,X5] :
      ( ( ~ subclass(X4,X5)
        | ! [X6] :
            ( ~ member(X6,X4)
            | member(X6,X5) ) )
      & ( ? [X7] :
            ( member(X7,X4)
            & ~ member(X7,X5) )
        | subclass(X4,X5) ) ),
    inference(variable_rename,[status(thm)],[16]) ).

fof(18,plain,
    ! [X4,X5] :
      ( ( ~ subclass(X4,X5)
        | ! [X6] :
            ( ~ member(X6,X4)
            | member(X6,X5) ) )
      & ( ( member(esk1_2(X4,X5),X4)
          & ~ member(esk1_2(X4,X5),X5) )
        | subclass(X4,X5) ) ),
    inference(skolemize,[status(esa)],[17]) ).

fof(19,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,X4)
        | member(X6,X5)
        | ~ subclass(X4,X5) )
      & ( ( member(esk1_2(X4,X5),X4)
          & ~ member(esk1_2(X4,X5),X5) )
        | subclass(X4,X5) ) ),
    inference(shift_quantors,[status(thm)],[18]) ).

fof(20,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,X4)
        | member(X6,X5)
        | ~ subclass(X4,X5) )
      & ( member(esk1_2(X4,X5),X4)
        | subclass(X4,X5) )
      & ( ~ member(esk1_2(X4,X5),X5)
        | subclass(X4,X5) ) ),
    inference(distribute,[status(thm)],[19]) ).

cnf(22,plain,
    ( subclass(X1,X2)
    | member(esk1_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[20]) ).

fof(26,negated_conjecture,
    ? [X1] :
      ( subclass(X1,null_class)
      & ~ equal(X1,null_class) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(27,negated_conjecture,
    ? [X2] :
      ( subclass(X2,null_class)
      & ~ equal(X2,null_class) ),
    inference(variable_rename,[status(thm)],[26]) ).

fof(28,negated_conjecture,
    ( subclass(esk2_0,null_class)
    & ~ equal(esk2_0,null_class) ),
    inference(skolemize,[status(esa)],[27]) ).

cnf(29,negated_conjecture,
    esk2_0 != null_class,
    inference(split_conjunct,[status(thm)],[28]) ).

cnf(30,negated_conjecture,
    subclass(esk2_0,null_class),
    inference(split_conjunct,[status(thm)],[28]) ).

cnf(33,negated_conjecture,
    ( null_class = esk2_0
    | ~ subclass(null_class,esk2_0) ),
    inference(spm,[status(thm)],[11,30,theory(equality)]) ).

cnf(35,negated_conjecture,
    ~ subclass(null_class,esk2_0),
    inference(sr,[status(thm)],[33,29,theory(equality)]) ).

cnf(36,plain,
    subclass(null_class,X1),
    inference(spm,[status(thm)],[15,22,theory(equality)]) ).

cnf(43,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[35,36,theory(equality)]) ).

cnf(44,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[43,theory(equality)]) ).

cnf(45,negated_conjecture,
    $false,
    44,
    [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/SET063+1.p
% --creating new selector for [SET005+0.ax]
% -running prover on /tmp/tmpuY5fZO/sel_SET063+1.p_1 with time limit 29
% -running prover with command ['/davis/home/graph/tptp/Systems/SInE---0.4/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=29', '/tmp/tmpuY5fZO/sel_SET063+1.p_1']
% -prover status Theorem
% Problem SET063+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET063+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET063+1.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
% 
%------------------------------------------------------------------------------