The deficiency of a propositional formula F in CNF with n variables
and m clauses is defined as m-n. It is known that minimal
unsatisfiable formulas (unsatisfiable formulas which become
satisfiable by removing any clause) have positive deficiency.
Recognition of minimal unsatisfiable formulas is NP-hard, and it was
shown recently ... more >>>

In the context of proving lower bounds on proof space in $k$-DNF
resolution, [Ben-Sasson and Nordström 2009] introduced the concept of
minimally unsatisfiable sets of $k$-DNF formulas and proved that a
minimally unsatisfiable $k$-DNF set with $m$ formulas can have at most
$O((mk)^{k+1})$ variables. They also gave an example of ... more >>>