Consider the following premises. s_4 <-> t. q -> q_8. q_8 -> t. s_4 -> q. Can we infer ~(t -> q) from them? If possible, name the inference rules being used at each step.
 From s_4 <-> t we can infer t -> s_4 via biconditional elimination. From q -> q_8, q_8 -> t we can infer q -> t via transitivity. Finally, from t -> s_4, s_4 -> q we can infer t -> q via transitivity, which contradicts ~(t -> q). Therefore, the answer is no.