Consider the following premises. forall x_1: S(x_1) -> P(x_1). forall x_1: S(x_1) or ~P(x_1). ~P(f). Can we infer S(f) from them?
 From forall x_1: S(x_1) or ~P(x_1) we can infer forall x_1: P(x_1) -> S(x_1). From forall x_1: P(x_1) -> S(x_1), forall x_1: S(x_1) -> P(x_1) we can infer forall x_1: P(x_1) <-> S(x_1). From forall x_1: P(x_1) <-> S(x_1) we can infer P(f) <-> S(f). Finally, from P(f) <-> S(f), ~P(f) we can infer ~S(f), which contradicts S(f). Therefore, the answer is no.