Consider the following premises. exists y_1: U(y_1) -> Q_4(y_1). forall y_1: U_1(y_1) -> U(y_1). forall y_1: U_1(y_1) or S_2(y_1). forall y_1: S_2(y_1) -> Q_4(y_1). Can we infer exists y_1: Q_4(y_1) from them? If possible, name the inference rules being used at each step.
 From forall y_1: U_1(y_1) -> U(y_1), exists y_1: U(y_1) -> Q_4(y_1) we can infer exists y_1: U_1(y_1) -> Q_4(y_1) via existential transitivity. Finally, from exists y_1: U_1(y_1) -> Q_4(y_1), forall y_1: S_2(y_1) -> Q_4(y_1), forall y_1: U_1(y_1) or S_2(y_1) we can infer exists y_1: Q_4(y_1) via existential disjunction elimination. Therefore, the answer is yes.