Consider the following premises. r -> p_6. p_6 -> s. s -> p_6. Can we infer ~(r -> s) from them? If possible, name the inference rules being used at each step.
 From p_6 -> s, s -> p_6 we can infer p_6 <-> s via biconditional introduction. From p_6 <-> s we can infer p_6 -> s via biconditional elimination. Finally, from r -> p_6, p_6 -> s we can infer r -> s via transitivity, which contradicts ~(r -> s). Therefore, the answer is no.