Consider the following premises. forall x_5: T(x_5) -> S_1(x_5). forall x_5: P_5(x_5). forall x_5: P_5(x_5) -> T(x_5). Can we infer S_1(f_1) from them?
 From forall x_5: P_5(x_5) -> T(x_5), forall x_5: P_5(x_5) we can infer forall x_5: T(x_5). From forall x_5: T(x_5) -> S_1(x_5), forall x_5: T(x_5) we can infer forall x_5: S_1(x_5). Finally, from forall x_5: S_1(x_5) we can infer S_1(f_1). Therefore, the answer is yes.