Consider the following premises. p_1 -> w. w -> r_1. p_1. Can we infer ~r_1 from them? If possible, name the inference rules being used at each step.
 From p_1 -> w, w -> r_1 we can infer p_1 -> r_1 via transitivity. Finally, from p_1 -> r_1, p_1 we can infer r_1 via modus ponens, which contradicts ~r_1. Therefore, the answer is no.