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