Consider the following premises. forall z_3: P_1(z_3) or W_1(z_3). forall z_3: W_1(z_3) -> Q(z_3). forall z_3: P_1(z_3) -> Q(z_3). exists z_3: U_1(z_3) -> U(z_3). forall z_3: U_1(z_3). Can we infer exists z_3: U(z_3) and Q(z_3) from them?
 From exists z_3: U_1(z_3) -> U(z_3), forall z_3: U_1(z_3) we can infer exists z_3: U(z_3). From forall z_3: P_1(z_3) -> Q(z_3), forall z_3: W_1(z_3) -> Q(z_3), forall z_3: P_1(z_3) or W_1(z_3) we can infer forall z_3: Q(z_3). Finally, from exists z_3: U(z_3), forall z_3: Q(z_3) we can infer exists z_3: U(z_3) and Q(z_3). Therefore, the answer is yes.