Consider the following premises. forall x_4: P_4(x_4) or P_2(x_4). forall x_4: ~P_4(x_4). forall x_4: ~P_2(x_4). Can we infer forall x_4: S_1(x_4) from them?
 From forall x_4: P_4(x_4) or P_2(x_4), forall x_4: ~P_4(x_4) we can infer forall x_4: P_2(x_4). From forall x_4: P_2(x_4) we can infer forall x_4: P_2(x_4) or S_1(x_4). Finally, from forall x_4: P_2(x_4) or S_1(x_4), forall x_4: ~P_2(x_4) we can infer forall x_4: S_1(x_4). Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.