Consider the following premises. exists y: W_1(y) -> U_4(y). forall y: U_4(y) -> Q(y). forall y: T(y) -> W_1(y). forall y: Q_3(y) -> T(y). Can we infer exists y: Q_3(y) -> Q(y) from them?
 From forall y: Q_3(y) -> T(y), forall y: T(y) -> W_1(y) we can infer forall y: Q_3(y) -> W_1(y). From forall y: Q_3(y) -> W_1(y), exists y: W_1(y) -> U_4(y) we can infer exists y: Q_3(y) -> U_4(y). Finally, from exists y: Q_3(y) -> U_4(y), forall y: U_4(y) -> Q(y) we can infer exists y: Q_3(y) -> Q(y). Therefore, the answer is yes.