Consider the following premises. forall x_5: P_5(x_5) -> S(x_5). forall x_5: P_5(x_5) or ~S(x_5). Can we infer P_5(a_2) -> S(a_2) from them?
 From forall x_5: P_5(x_5) or ~S(x_5) we can infer forall x_5: S(x_5) -> P_5(x_5). From forall x_5: S(x_5) -> P_5(x_5), forall x_5: P_5(x_5) -> S(x_5) we can infer forall x_5: S(x_5) <-> P_5(x_5). From forall x_5: S(x_5) <-> P_5(x_5) we can infer S(a_2) <-> P_5(a_2). Finally, from S(a_2) <-> P_5(a_2) we can infer P_5(a_2) -> S(a_2). Therefore, the answer is yes.