Consider the following premises. r_4 -> t_2. t_2 -> r_1. w -> r_1. w or r_4. Can we infer ~r_1 from them?
 From r_4 -> t_2, t_2 -> r_1 we can infer r_4 -> r_1. Finally, from w -> r_1, r_4 -> r_1, w or r_4 we can infer r_1, which contradicts ~r_1. Therefore, the answer is no.