Consider the following premises. ~P_2(g). forall x: S(x) or ~P_2(x). forall x: S(x) -> P_2(x). Can we infer S(g) from them?
 From forall x: S(x) or ~P_2(x) we can infer forall x: P_2(x) -> S(x). From forall x: S(x) -> P_2(x), forall x: P_2(x) -> S(x) we can infer forall x: S(x) <-> P_2(x). From forall x: S(x) <-> P_2(x) we can infer S(g) <-> P_2(g). Finally, from S(g) <-> P_2(g), ~P_2(g) we can infer ~S(g), which contradicts S(g). Therefore, the answer is no.