Consider the following premises. forall x_4: P_4(x_4). forall x_4: P_4(x_4) -> Q_4(x_4). forall x_4: S(x_4). Can we infer Q_4(a_2) from them?
 From forall x_4: P_4(x_4) -> Q_4(x_4), forall x_4: P_4(x_4) we can infer forall x_4: Q_4(x_4). From forall x_4: S(x_4), forall x_4: Q_4(x_4) we can infer forall x_4: S(x_4) and Q_4(x_4). From forall x_4: S(x_4) and Q_4(x_4) we can infer S(a_2) and Q_4(a_2). Finally, from S(a_2) and Q_4(a_2) we can infer Q_4(a_2). Therefore, the answer is yes.