Consider the following premises. forall y: R(y) or ~U_1(y). forall y: U_1(y) or ~Q(y). Can we infer exists y: ~(Q(y) -> R(y)) from them?
 From forall y: U_1(y) or ~Q(y) we can infer forall y: Q(y) -> U_1(y). From forall y: R(y) or ~U_1(y) we can infer forall y: U_1(y) -> R(y). Finally, from forall y: Q(y) -> U_1(y), forall y: U_1(y) -> R(y) we can infer forall y: Q(y) -> R(y), which contradicts exists y: ~(Q(y) -> R(y)). Therefore, the answer is no.