On unit-refutation complete formulae with existentially quantified variables

We analyze, along the lines of the knowledge compilation map, both the tractability and the succinctness of the propositional language URC-C of unit-refutation complete propositional formulae, as well as its disjunctive closure URC-C[V, ∃], and a superset of URC-C where variables can be existentially quantified and unit-refutation completeness concerns only consequences built up from free variables.