Consider the following premises. forall x: S(x) or ~S_2(x). forall x: S_2(x) or ~S(x). Can we infer S_2(j) -> S(j) from them?
 From forall x: S(x) or ~S_2(x) we can infer forall x: S_2(x) -> S(x). From forall x: S_2(x) or ~S(x) we can infer forall x: S(x) -> S_2(x). From forall x: S_2(x) -> S(x), forall x: S(x) -> S_2(x) we can infer forall x: S_2(x) <-> S(x). From forall x: S_2(x) <-> S(x) we can infer S_2(j) <-> S(j). Finally, from S_2(j) <-> S(j) we can infer S_2(j) -> S(j). Therefore, the answer is yes.