Consider the following premises. ~t_3 -> s. t_3 -> r_3. ~r_3. s -> u_3. Can we infer ~u_3 from them? If possible, name the inference rules being used at each step.
 From t_3 -> r_3, ~r_3 we can infer ~t_3 via modus tollens. From ~t_3 -> s, ~t_3 we can infer s via modus ponens. Finally, from s -> u_3, s we can infer u_3 via modus ponens, which contradicts ~u_3. Therefore, the answer is no.