Consider the following premises. exists z: Q(z) -> R(z). forall z: U_3(z) or Q(z). forall z: ~U_3(z) or U(z). forall z: U(z) <-> R(z). Can we infer forall z: ~R(z) from them? If possible, name the inference rules being used at each step.
 From forall z: U_3(z) or Q(z), forall z: ~U_3(z) or U(z) we can infer forall z: Q(z) or U(z) via universal resolution. From forall z: U(z) <-> R(z) we can infer forall z: U(z) -> R(z) via universal biconditional elimination. Finally, from exists z: Q(z) -> R(z), forall z: U(z) -> R(z), forall z: Q(z) or U(z) we can infer exists z: R(z) via existential disjunction elimination, which contradicts forall z: ~R(z). Therefore, the answer is no.