Constraint satisfaction problem on a graph
1 in 3 Sat reduces to this problem.
http://en.wikipedia.org/wiki/One-in-three_3SAT

Set d=3, each k_i = 2 and each l_i=1

To implement negation add $x,\overline{x},a$ and $x,\overline{x},b$ and $a,b,c$.
The only possible assignment is a=0,b=0 and c=1, so $x$ and $\overline{x}$ must be different.