Consider the following premises. forall z_4: W(z_4) -> Q(z_4). exists z_4: Q(z_4) -> W(z_4). forall z_4: W(z_4) -> U_4(z_4). Can we infer exists z_4: Q(z_4) -> U_4(z_4) from them?
 From forall z_4: W(z_4) -> Q(z_4), exists z_4: Q(z_4) -> W(z_4) we can infer exists z_4: W(z_4) <-> Q(z_4). From exists z_4: W(z_4) <-> Q(z_4) we can infer exists z_4: Q(z_4) -> W(z_4). Finally, from exists z_4: Q(z_4) -> W(z_4), forall z_4: W(z_4) -> U_4(z_4) we can infer exists z_4: Q(z_4) -> U_4(z_4). Therefore, the answer is yes.