Consider the following premises. q_4. t_3 <-> q_4. Can we infer ~t_3 from them? If possible, name the inference rules being used at each step.
 From t_3 <-> q_4 we can infer q_4 -> t_3 via biconditional elimination. Finally, from q_4 -> t_3, q_4 we can infer t_3 via modus ponens, which contradicts ~t_3. Therefore, the answer is no.