Consider the following premises. forall x_1: ~P_4(x_1). exists x_1: P_4(x_1). Can we infer exists x_1: S_1(x_1) from them?
 From exists x_1: P_4(x_1) we can infer exists x_1: P_4(x_1) or S_1(x_1). Finally, from exists x_1: P_4(x_1) or S_1(x_1), forall x_1: ~P_4(x_1) we can infer exists x_1: S_1(x_1). Therefore, the answer is yes.