Consider the following premises. u -> P(a_10). forall x_10: P(x_10) -> S_10(x_10). ~S_10(a_10). Can we infer u from them? If possible, name the inference rules being used at each step.
 From forall x_10: P(x_10) -> S_10(x_10) we can infer P(a_10) -> S_10(a_10) via universal instantiation. From u -> P(a_10), P(a_10) -> S_10(a_10) we can infer u -> S_10(a_10) via transitivity. Finally, from u -> S_10(a_10), ~S_10(a_10) we can infer ~u via modus tollens, which contradicts u. Therefore, the answer is no.