An unsatisfiable core is called a minimal unsatisfiable core, if every proper subset (allowing removal of any arbitrary clause or clauses) of it is satisfiable.

Technically, if more than one clause can be used to rewrite a literal in the goal, the non-concurrent version tries in turn all clauses, while the concurrent version chooses a single arbitrary clause: contrary to the non-concurrent version, the other clauses will never be tried.