TSTP Solution File: SEU320+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU320+1 : TPTP v5.0.0. Released v3.3.0.
% 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 07:14:49 EST 2010

% Result   : Theorem 0.16s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   39 (   7 unt;   0 def)
%            Number of atoms       :  127 (   4 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  151 (  63   ~;  64   |;  13   &)
%                                         (   3 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   46 (   0 sgn  26   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(3,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(X1))
     => element(subset_complement(X1,X2),powerset(X1)) ),
    file('/tmp/tmpWh3dSb/sel_SEU320+1.p_1',dt_k3_subset_1) ).

fof(4,conjecture,
    ! [X1] :
      ( top_str(X1)
     => ! [X2] :
          ( element(X2,powerset(the_carrier(X1)))
         => ( open_subset(X2,X1)
          <=> closed_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
    file('/tmp/tmpWh3dSb/sel_SEU320+1.p_1',t30_tops_1) ).

fof(6,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(X1))
     => subset_complement(X1,subset_complement(X1,X2)) = X2 ),
    file('/tmp/tmpWh3dSb/sel_SEU320+1.p_1',involutiveness_k3_subset_1) ).

fof(12,axiom,
    ! [X1] :
      ( top_str(X1)
     => ! [X2] :
          ( element(X2,powerset(the_carrier(X1)))
         => ( closed_subset(X2,X1)
          <=> open_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
    file('/tmp/tmpWh3dSb/sel_SEU320+1.p_1',t29_tops_1) ).

fof(15,negated_conjecture,
    ~ ! [X1] :
        ( top_str(X1)
       => ! [X2] :
            ( element(X2,powerset(the_carrier(X1)))
           => ( open_subset(X2,X1)
            <=> closed_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
    inference(assume_negation,[status(cth)],[4]) ).

fof(20,plain,
    ! [X1,X2] :
      ( ~ element(X2,powerset(X1))
      | element(subset_complement(X1,X2),powerset(X1)) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(21,plain,
    ! [X3,X4] :
      ( ~ element(X4,powerset(X3))
      | element(subset_complement(X3,X4),powerset(X3)) ),
    inference(variable_rename,[status(thm)],[20]) ).

cnf(22,plain,
    ( element(subset_complement(X1,X2),powerset(X1))
    | ~ element(X2,powerset(X1)) ),
    inference(split_conjunct,[status(thm)],[21]) ).

fof(23,negated_conjecture,
    ? [X1] :
      ( top_str(X1)
      & ? [X2] :
          ( element(X2,powerset(the_carrier(X1)))
          & ( ~ open_subset(X2,X1)
            | ~ closed_subset(subset_complement(the_carrier(X1),X2),X1) )
          & ( open_subset(X2,X1)
            | closed_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
    inference(fof_nnf,[status(thm)],[15]) ).

fof(24,negated_conjecture,
    ? [X3] :
      ( top_str(X3)
      & ? [X4] :
          ( element(X4,powerset(the_carrier(X3)))
          & ( ~ open_subset(X4,X3)
            | ~ closed_subset(subset_complement(the_carrier(X3),X4),X3) )
          & ( open_subset(X4,X3)
            | closed_subset(subset_complement(the_carrier(X3),X4),X3) ) ) ),
    inference(variable_rename,[status(thm)],[23]) ).

fof(25,negated_conjecture,
    ( top_str(esk2_0)
    & element(esk3_0,powerset(the_carrier(esk2_0)))
    & ( ~ open_subset(esk3_0,esk2_0)
      | ~ closed_subset(subset_complement(the_carrier(esk2_0),esk3_0),esk2_0) )
    & ( open_subset(esk3_0,esk2_0)
      | closed_subset(subset_complement(the_carrier(esk2_0),esk3_0),esk2_0) ) ),
    inference(skolemize,[status(esa)],[24]) ).

cnf(26,negated_conjecture,
    ( closed_subset(subset_complement(the_carrier(esk2_0),esk3_0),esk2_0)
    | open_subset(esk3_0,esk2_0) ),
    inference(split_conjunct,[status(thm)],[25]) ).

cnf(27,negated_conjecture,
    ( ~ closed_subset(subset_complement(the_carrier(esk2_0),esk3_0),esk2_0)
    | ~ open_subset(esk3_0,esk2_0) ),
    inference(split_conjunct,[status(thm)],[25]) ).

cnf(28,negated_conjecture,
    element(esk3_0,powerset(the_carrier(esk2_0))),
    inference(split_conjunct,[status(thm)],[25]) ).

cnf(29,negated_conjecture,
    top_str(esk2_0),
    inference(split_conjunct,[status(thm)],[25]) ).

fof(33,plain,
    ! [X1,X2] :
      ( ~ element(X2,powerset(X1))
      | subset_complement(X1,subset_complement(X1,X2)) = X2 ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(34,plain,
    ! [X3,X4] :
      ( ~ element(X4,powerset(X3))
      | subset_complement(X3,subset_complement(X3,X4)) = X4 ),
    inference(variable_rename,[status(thm)],[33]) ).

cnf(35,plain,
    ( subset_complement(X1,subset_complement(X1,X2)) = X2
    | ~ element(X2,powerset(X1)) ),
    inference(split_conjunct,[status(thm)],[34]) ).

fof(45,plain,
    ! [X1] :
      ( ~ top_str(X1)
      | ! [X2] :
          ( ~ element(X2,powerset(the_carrier(X1)))
          | ( ( ~ closed_subset(X2,X1)
              | open_subset(subset_complement(the_carrier(X1),X2),X1) )
            & ( ~ open_subset(subset_complement(the_carrier(X1),X2),X1)
              | closed_subset(X2,X1) ) ) ) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(46,plain,
    ! [X3] :
      ( ~ top_str(X3)
      | ! [X4] :
          ( ~ element(X4,powerset(the_carrier(X3)))
          | ( ( ~ closed_subset(X4,X3)
              | open_subset(subset_complement(the_carrier(X3),X4),X3) )
            & ( ~ open_subset(subset_complement(the_carrier(X3),X4),X3)
              | closed_subset(X4,X3) ) ) ) ),
    inference(variable_rename,[status(thm)],[45]) ).

fof(47,plain,
    ! [X3,X4] :
      ( ~ element(X4,powerset(the_carrier(X3)))
      | ( ( ~ closed_subset(X4,X3)
          | open_subset(subset_complement(the_carrier(X3),X4),X3) )
        & ( ~ open_subset(subset_complement(the_carrier(X3),X4),X3)
          | closed_subset(X4,X3) ) )
      | ~ top_str(X3) ),
    inference(shift_quantors,[status(thm)],[46]) ).

fof(48,plain,
    ! [X3,X4] :
      ( ( ~ closed_subset(X4,X3)
        | open_subset(subset_complement(the_carrier(X3),X4),X3)
        | ~ element(X4,powerset(the_carrier(X3)))
        | ~ top_str(X3) )
      & ( ~ open_subset(subset_complement(the_carrier(X3),X4),X3)
        | closed_subset(X4,X3)
        | ~ element(X4,powerset(the_carrier(X3)))
        | ~ top_str(X3) ) ),
    inference(distribute,[status(thm)],[47]) ).

cnf(49,plain,
    ( closed_subset(X2,X1)
    | ~ top_str(X1)
    | ~ element(X2,powerset(the_carrier(X1)))
    | ~ open_subset(subset_complement(the_carrier(X1),X2),X1) ),
    inference(split_conjunct,[status(thm)],[48]) ).

cnf(50,plain,
    ( open_subset(subset_complement(the_carrier(X1),X2),X1)
    | ~ top_str(X1)
    | ~ element(X2,powerset(the_carrier(X1)))
    | ~ closed_subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[48]) ).

cnf(61,plain,
    ( open_subset(X2,X1)
    | ~ closed_subset(subset_complement(the_carrier(X1),X2),X1)
    | ~ top_str(X1)
    | ~ element(subset_complement(the_carrier(X1),X2),powerset(the_carrier(X1)))
    | ~ element(X2,powerset(the_carrier(X1))) ),
    inference(spm,[status(thm)],[50,35,theory(equality)]) ).

cnf(62,plain,
    ( closed_subset(subset_complement(the_carrier(X1),X2),X1)
    | ~ open_subset(X2,X1)
    | ~ top_str(X1)
    | ~ element(subset_complement(the_carrier(X1),X2),powerset(the_carrier(X1)))
    | ~ element(X2,powerset(the_carrier(X1))) ),
    inference(spm,[status(thm)],[49,35,theory(equality)]) ).

cnf(64,plain,
    ( open_subset(X2,X1)
    | ~ closed_subset(subset_complement(the_carrier(X1),X2),X1)
    | ~ top_str(X1)
    | ~ element(X2,powerset(the_carrier(X1))) ),
    inference(csr,[status(thm)],[61,22]) ).

cnf(70,plain,
    ( closed_subset(subset_complement(the_carrier(X1),X2),X1)
    | ~ open_subset(X2,X1)
    | ~ top_str(X1)
    | ~ element(X2,powerset(the_carrier(X1))) ),
    inference(csr,[status(thm)],[62,22]) ).

cnf(71,negated_conjecture,
    ( ~ open_subset(esk3_0,esk2_0)
    | ~ top_str(esk2_0)
    | ~ element(esk3_0,powerset(the_carrier(esk2_0))) ),
    inference(spm,[status(thm)],[27,70,theory(equality)]) ).

cnf(74,negated_conjecture,
    ( ~ open_subset(esk3_0,esk2_0)
    | $false
    | ~ element(esk3_0,powerset(the_carrier(esk2_0))) ),
    inference(rw,[status(thm)],[71,29,theory(equality)]) ).

cnf(75,negated_conjecture,
    ( ~ open_subset(esk3_0,esk2_0)
    | $false
    | $false ),
    inference(rw,[status(thm)],[74,28,theory(equality)]) ).

cnf(76,negated_conjecture,
    ~ open_subset(esk3_0,esk2_0),
    inference(cn,[status(thm)],[75,theory(equality)]) ).

cnf(77,negated_conjecture,
    closed_subset(subset_complement(the_carrier(esk2_0),esk3_0),esk2_0),
    inference(sr,[status(thm)],[26,76,theory(equality)]) ).

cnf(78,negated_conjecture,
    ( open_subset(esk3_0,esk2_0)
    | ~ top_str(esk2_0)
    | ~ element(esk3_0,powerset(the_carrier(esk2_0))) ),
    inference(spm,[status(thm)],[64,77,theory(equality)]) ).

cnf(81,negated_conjecture,
    ( open_subset(esk3_0,esk2_0)
    | $false
    | ~ element(esk3_0,powerset(the_carrier(esk2_0))) ),
    inference(rw,[status(thm)],[78,29,theory(equality)]) ).

cnf(82,negated_conjecture,
    ( open_subset(esk3_0,esk2_0)
    | $false
    | $false ),
    inference(rw,[status(thm)],[81,28,theory(equality)]) ).

cnf(83,negated_conjecture,
    open_subset(esk3_0,esk2_0),
    inference(cn,[status(thm)],[82,theory(equality)]) ).

cnf(84,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[83,76,theory(equality)]) ).

cnf(85,negated_conjecture,
    $false,
    84,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU320+1.p
% --creating new selector for []
% -running prover on /tmp/tmpWh3dSb/sel_SEU320+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU320+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU320+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU320+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
% 
%------------------------------------------------------------------------------