Consider the following premises. w -> p. q_8 -> w. u <-> q_8. Can we infer ~(u -> p) from them? If possible, name the inference rules being used at each step.
 From u <-> q_8 we can infer u -> q_8 via biconditional elimination. From q_8 -> w, w -> p we can infer q_8 -> p via transitivity. Finally, from u -> q_8, q_8 -> p we can infer u -> p via transitivity, which contradicts ~(u -> p). Therefore, the answer is no.