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Let C 2 p denote the class of rst order sentences with two variables and with additional quantiiers \there exists exactly (at most, at least) i", for i p, and let C 2 be the union of C 2 p taken over all integers p. We prove that the satissability problem for C 2 1 sentences is NEXPTIME-complete. This strengthens the results by E. Grr adel, Ph. Kolaitis and(More)