Consider the following premises. s or r_2. p -> q. p <-> s. r_2 -> p. Can we infer ~q from them?
 From p <-> s we can infer s -> p. From s -> p, r_2 -> p, s or r_2 we can infer p. Finally, from p -> q, p we can infer q, which contradicts ~q. Therefore, the answer is no.