Consider the following premises. forall x_2: ~P_2(x_2) or S(x_2). forall x_2: P_2(x_2) or S_2(x_2). forall x_2: ~S_2(x_2). Can we infer forall x_2: S(x_2) from them?
 From forall x_2: P_2(x_2) or S_2(x_2), forall x_2: ~P_2(x_2) or S(x_2) we can infer forall x_2: S_2(x_2) or S(x_2). Finally, from forall x_2: S_2(x_2) or S(x_2), forall x_2: ~S_2(x_2) we can infer forall x_2: S(x_2). Therefore, the answer is yes.