  We introduce a new decidable fragment of first-order logic with equality,
which strictly generalizes two already well-known ones -- the
Bernays-Sch\"onfinkel-Ramsey (BSR) Fragment and the Monadic Fragment. The
defining principle is the syntactic separation of universally quantified
variables from existentially quantified ones at the level of atoms. Thus, our
classification neither rests on restrictions on quantifier prefixes (as in the
BSR case) nor on restrictions on the arity of predicate symbols (as in the
monadic case). We demonstrate that the new fragment exhibits the finite model
property and derive a non-elementary upper bound on the computing time required
for deciding satisfiability in the new fragment. For the subfragment of prenex
sentences with the quantifier prefix $\exists^* \forall^* \exists^*$ the
satisfiability problem is shown to be complete for NEXPTIME. Finally, we
discuss how automated reasoning procedures can take advantage of our results.
