  Over an algebraically closed fields, an alternative to the method due to
Kostrikin and Shafarevich was recently suggested. It produces all known simple
finite dimensional Lie algebras in characteristic p>2. For p=2, we investigate
one of the steps of this method, interpret several other simple Lie algebras,
previously known only as sums of their components, as Lie algebras of vector
fields. One new series of exceptional simple Lie algebras is discovered,
together with its "hidden supersymmetries".
  In characteristic 2, certain simple Lie algebras are "desuperizations" of
simple Lie superalgebras. Several simple Lie algebras we describe as results of
generalized Cartan prolongation of the non-positive parts, relative a simplest
(by declaring degree of just one pair of root vectors corresponding to opposite
simple roots nonzero) grading by integers, of Lie algebras with Cartan matrix
are "desuperizations" of characteristic 2 versions of complex simple
exceptional vectorial Lie superalgebras. We list the Lie superalgebras (some of
them new) obtained from the Lie algebras considered by declaring certain
generators odd.
  One of the simple Lie algebras obtained is the prolong relative to a
non-simplest grading, so the classification to be obtained might be more
involved than we previously thought.
