It's 2**n at worst and inductive:

You get the solution S(i) for i sets by combining set s_i with all members of S(i-1). For i=2..n and S(1)={s_1}

This can be further optimized - no point in trying (A/B)/C if A/C is empty - but 2**7 is only 128.

To speed up intersection you can use hash slices in Perl or specialized CPAN modules.