Consider the following premises. forall y: U(y) or W(y). forall y: ~U(y) or Q(y). exists y: Q(y) -> Q_1(y). forall y: W(y) <-> Q_1(y). Can we infer forall y: ~Q_1(y) from them?
 From forall y: W(y) <-> Q_1(y) we can infer forall y: W(y) -> Q_1(y). From forall y: U(y) or W(y), forall y: ~U(y) or Q(y) we can infer forall y: W(y) or Q(y). Finally, from forall y: W(y) -> Q_1(y), exists y: Q(y) -> Q_1(y), forall y: W(y) or Q(y) we can infer exists y: Q_1(y), which contradicts forall y: ~Q_1(y). Therefore, the answer is no.