Consider the following premises. exists x_3: P_3(x_3). forall x_3: U_2(x_3). forall x_3: P_3(x_3) -> P(x_3). Can we infer exists x_3: P(x_3) and U_2(x_3) from them?
 From forall x_3: P_3(x_3) -> P(x_3), exists x_3: P_3(x_3) we can infer exists x_3: P(x_3). Finally, from exists x_3: P(x_3), forall x_3: U_2(x_3) we can infer exists x_3: P(x_3) and U_2(x_3). Therefore, the answer is yes.