Consider the following premises. p or t_4. q -> r. t_4 <-> q. p -> r. Can we infer ~r from them?
 From t_4 <-> q we can infer t_4 -> q. From t_4 -> q, q -> r we can infer t_4 -> r. Finally, from p -> r, t_4 -> r, p or t_4 we can infer r, which contradicts ~r. Therefore, the answer is no.