Consider the following premises. forall z: Q_3(z) or ~P(z). forall z: P(z). exists z: Q_1(z). Can we infer exists z: Q_3(z) and Q_1(z) from them?
 From forall z: Q_3(z) or ~P(z) we can infer forall z: P(z) -> Q_3(z). From forall z: P(z) -> Q_3(z), forall z: P(z) we can infer forall z: Q_3(z). Finally, from forall z: Q_3(z), exists z: Q_1(z) we can infer exists z: Q_3(z) and Q_1(z). Therefore, the answer is yes.