Consider the following premises. s_1 <-> w. p -> r_3. r_3 -> s_1. ~w. Can we infer p from them? If possible, name the inference rules being used at each step.
 From p -> r_3, r_3 -> s_1 we can infer p -> s_1 via transitivity. From s_1 <-> w, ~w we can infer ~s_1 via biconditional elimination. Finally, from p -> s_1, ~s_1 we can infer ~p via modus tollens, which contradicts p. Therefore, the answer is no.