Consider the following premises. exists z: Q_3(z) <-> U_4(z). forall z: Q_3(z) or W(z). forall z: W(z) -> U_4(z). Can we infer exists z: U_4(z) from them?
 From exists z: Q_3(z) <-> U_4(z) we can infer exists z: Q_3(z) -> U_4(z). Finally, from exists z: Q_3(z) -> U_4(z), forall z: W(z) -> U_4(z), forall z: Q_3(z) or W(z) we can infer exists z: U_4(z). Therefore, the answer is yes.