Consider the following premises. w_4 -> r_6. p -> w_4. p <-> r_6. Can we infer ~(r_6 <-> p) from them? If possible, name the inference rules being used at each step.
 From p -> w_4, w_4 -> r_6 we can infer p -> r_6 via transitivity. From p <-> r_6 we can infer r_6 -> p via biconditional elimination. Finally, from r_6 -> p, p -> r_6 we can infer r_6 <-> p via biconditional introduction, which contradicts ~(r_6 <-> p). Therefore, the answer is no.