Consider the following premises. forall y: R(y) or ~U_2(y). ~U_2(a_2). forall y: R(y) -> U_2(y). Can we infer ~R(a_2) from them? If possible, name the inference rules being used at each step.
 From forall y: R(y) or ~U_2(y) we can infer forall y: U_2(y) -> R(y) via universal rewriting. From forall y: R(y) -> U_2(y), forall y: U_2(y) -> R(y) we can infer forall y: R(y) <-> U_2(y) via universal biconditional introduction. From forall y: R(y) <-> U_2(y) we can infer R(a_2) <-> U_2(a_2) via universal instantiation. Finally, from R(a_2) <-> U_2(a_2), ~U_2(a_2) we can infer ~R(a_2) via biconditional elimination. Therefore, the answer is yes.