Consider the following premises. forall z_4: ~Q(z_4). u -> Q(a_13). u. Can we infer s from them? If possible, name the inference rules being used at each step.
 From forall z_4: ~Q(z_4) we can infer ~Q(a_13) via universal instantiation. From u we can infer u or s via addition. From u -> Q(a_13), ~Q(a_13) we can infer ~u via modus tollens. Finally, from u or s, ~u we can infer s via disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.