Consider the following premises. s_2 <-> r. p -> r. s_2 -> r. Can we infer ~(p -> s_2) from them? If possible, name the inference rules being used at each step.
 From s_2 <-> r we can infer r -> s_2 via biconditional elimination. From r -> s_2, s_2 -> r we can infer r <-> s_2 via biconditional introduction. From r <-> s_2 we can infer r -> s_2 via biconditional elimination. Finally, from p -> r, r -> s_2 we can infer p -> s_2 via transitivity, which contradicts ~(p -> s_2). Therefore, the answer is no.