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In general, first-order predicate logic extended with linear integerarithmetic is undecidable. We show that the Bernays-Sch\"onfinkel-Ramseyfragment ($\exists^* \forall^*$-sentences) extended with a restricted form oflinear integer arithmetic is decidable via finite ground instantiation. Theidentified ground instances can be employed to restrict the search space ofexisting automated reasoning procedures considerably, e.g., when reasoningabout quantified properties of array data structures formalized in Bradley,Manna, and Sipma's array property fragment. Typically, decision procedures forthe array property fragment are based on an exhaustive instantiation ofuniversally quantified array indices with all the ground index terms that occurin the formula at hand. Our results reveal that one can get along withsignificantly fewer instances.

On the Combination of the Bernays-Sch\"onfinkel-Ramsey Fragment with Simple Linear Integer Arithmetic