Consider the following premises. forall y: Q_3(y) <-> P_2(y). exists y: Q_3(y) <-> U_3(y). forall y: U_3(y) or P_2(y). Can we infer forall y: ~Q_3(y) from them?
 From forall y: Q_3(y) <-> P_2(y) we can infer forall y: P_2(y) -> Q_3(y). From exists y: Q_3(y) <-> U_3(y) we can infer exists y: U_3(y) -> Q_3(y). Finally, from exists y: U_3(y) -> Q_3(y), forall y: P_2(y) -> Q_3(y), forall y: U_3(y) or P_2(y) we can infer exists y: Q_3(y), which contradicts forall y: ~Q_3(y). Therefore, the answer is no.