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