Consider the following premises. s -> t. u_4 -> q. ~q. ~t. Can we infer u_4 from them? If possible, name the inference rules being used at each step.
 From s -> t, ~t we can infer ~s via modus tollens. Finally, from u_4 -> q, ~q we can infer ~u_4 via modus tollens, which contradicts u_4. Therefore, the answer is no.