Consider the following premises. p <-> s. w_1 -> u_1. p -> w_1. Can we infer ~(s -> u_1) from them? If possible, name the inference rules being used at each step.
 From p <-> s we can infer s -> p via biconditional elimination. From p -> w_1, w_1 -> u_1 we can infer p -> u_1 via transitivity. Finally, from s -> p, p -> u_1 we can infer s -> u_1 via transitivity, which contradicts ~(s -> u_1). Therefore, the answer is no.