Consider the following premises. forall z_4: U(z_4) -> P(z_4). forall z_4: U(z_4). exists z_4: T_3(z_4). Can we infer exists z_4: P(z_4) from them?
 From forall z_4: U(z_4) -> P(z_4), forall z_4: U(z_4) we can infer forall z_4: P(z_4). From forall z_4: P(z_4), exists z_4: T_3(z_4) we can infer exists z_4: P(z_4) and T_3(z_4). Finally, from exists z_4: P(z_4) and T_3(z_4) we can infer exists z_4: P(z_4). Therefore, the answer is yes.