Consider the following premises. q_15 -> t. q_15. t -> q_15. Can we infer ~t from them? If possible, name the inference rules being used at each step.
 From t -> q_15, q_15 -> t we can infer t <-> q_15 via biconditional introduction. From t <-> q_15 we can infer q_15 -> t via biconditional elimination. Finally, from q_15 -> t, q_15 we can infer t via modus ponens, which contradicts ~t. Therefore, the answer is no.