Consider the following premises. forall y_2: U(y_2) or ~P_5(y_2). P_5(a_5). Can we infer exists y_2: U(y_2) from them? If possible, name the inference rules being used at each step.
 From P_5(a_5) we can infer exists y_2: P_5(y_2) via existential generalization. From forall y_2: U(y_2) or ~P_5(y_2) we can infer forall y_2: P_5(y_2) -> U(y_2) via universal rewriting. Finally, from forall y_2: P_5(y_2) -> U(y_2), exists y_2: P_5(y_2) we can infer exists y_2: U(y_2) via existential modus ponens. Therefore, the answer is yes.