  We furnish solid evidence, both theoretical and empirical, towards the
existence of a deterministic algorithm for random sparse $\#\Omega(\log n)$-SAT
instances, which computes the exact counting of satisfying assignments in
sub-exponential time. The algorithm uses a nice combinatorial property that
every CNF formula has, which relates its number of unsatisfying assignments to
the space of its monotone sub-formulae.
