Consider the following premises. forall x: P_4(x) <-> Q(x). exists x: ~P_4(x). forall x: U_3(x) -> Q(x). Can we infer forall x: U_3(x) from them?
 From forall x: P_4(x) <-> Q(x) we can infer forall x: Q(x) -> P_4(x). From forall x: U_3(x) -> Q(x), forall x: Q(x) -> P_4(x) we can infer forall x: U_3(x) -> P_4(x). Finally, from forall x: U_3(x) -> P_4(x), exists x: ~P_4(x) we can infer exists x: ~U_3(x), which contradicts forall x: U_3(x). Therefore, the answer is no.