A technique for obtaining lower bounds for the time versus space complexity of certain functions in a general input-oblivious sequential model of computation is developed. It is demonstrated by studying the intrinsic complexity of the following set equality problem SE(n, m): Given a sequence x//1 , x//2 , . . . ,x//n , y//1 ,. . . ,y//n of 2//n numbers of m bits each, decide whether the sets x//1 ,. . . ,x//n and y//1 ,. . . ,y//n coincide. It is shown that for any log log n less than equivalent to m less than equivalent to (log n)/2, any input-oblivious sequential computation that solves SE(n, m) using 2**m/s space, takes OMEGA (n multiplied by (times) s) time.