Consider the following premises. exists x_2: P_2(x_2) -> S(x_2). forall x_2: U_4(x_2). forall x_2: P_2(x_2). Can we infer exists x_2: S(x_2) and U_4(x_2) from them?
 From exists x_2: P_2(x_2) -> S(x_2), forall x_2: P_2(x_2) we can infer exists x_2: S(x_2). Finally, from exists x_2: S(x_2), forall x_2: U_4(x_2) we can infer exists x_2: S(x_2) and U_4(x_2). Therefore, the answer is yes.