Consider the following premises. t -> r_1. p -> t. u -> r_1. p. Can we infer ~r_1 from them?
 From p we can infer p or u. From p -> t, t -> r_1 we can infer p -> r_1. Finally, from p -> r_1, u -> r_1, p or u we can infer r_1, which contradicts ~r_1. Therefore, the answer is no.