Consider the following premises. forall z: ~Q_3(z) or W(z). forall z: W_3(z) -> R_2(z). forall z: Q_3(z) or Q(z). exists z: W_3(z) <-> W(z). forall z: R_2(z) <-> Q(z). Can we infer forall z: ~R_2(z) from them?
 From forall z: Q_3(z) or Q(z), forall z: ~Q_3(z) or W(z) we can infer forall z: Q(z) or W(z). From exists z: W_3(z) <-> W(z) we can infer exists z: W(z) -> W_3(z). From forall z: R_2(z) <-> Q(z) we can infer forall z: Q(z) -> R_2(z). From exists z: W(z) -> W_3(z), forall z: W_3(z) -> R_2(z) we can infer exists z: W(z) -> R_2(z). Finally, from forall z: Q(z) -> R_2(z), exists z: W(z) -> R_2(z), forall z: Q(z) or W(z) we can infer exists z: R_2(z), which contradicts forall z: ~R_2(z). Therefore, the answer is no.