Consider the following premises. forall z: P(z) -> P_4(z). forall z: P_4(z) -> P(z). forall z: P(z). Can we infer forall z: P_4(z) or U_2(z) from them?
 From forall z: P(z) -> P_4(z), forall z: P_4(z) -> P(z) we can infer forall z: P(z) <-> P_4(z). From forall z: P(z) <-> P_4(z) we can infer forall z: P(z) -> P_4(z). From forall z: P(z) -> P_4(z), forall z: P(z) we can infer forall z: P_4(z). Finally, from forall z: P_4(z) we can infer forall z: P_4(z) or U_2(z). Therefore, the answer is yes.