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