I have N variables, say $V_1, V_2, ..., V_n$. and I have several logical conditions like $[(V_1 > V_2) \cap (V_2 + V_3 > V_1) \cap (V_1*V_1 > 2*V_2)] \cup [..]$ You can consider they are in the disjunction normal form.
What I am concerning is finding the number of n-tuples $(V_1, V_2, ..., V_n)$ satisfying these conditions. Provided that all $V_i$ are 32 bit integer numbers.
I believe that Mathematica is able to do that, but I just don't know how it does.