Consider the following premises. forall y: U(y) or S(y). u or ~S(a_8). U(a_8) -> u. Can we infer u from them? If possible, name the inference rules being used at each step.
 From forall y: U(y) or S(y) we can infer U(a_8) or S(a_8) via universal instantiation. From u or ~S(a_8) we can infer S(a_8) -> u via rewriting. Finally, from U(a_8) -> u, S(a_8) -> u, U(a_8) or S(a_8) we can infer u via disjunction elimination. Therefore, the answer is yes.