Consider the following premises. exists y: Q_4(y) -> T(y). forall y: R_4(y) -> T(y). forall y: T(y) -> Q_4(y). forall y: Q_4(y) or R_4(y). Can we infer forall y: ~T(y) from them? If possible, name the inference rules being used at each step.
 From exists y: Q_4(y) -> T(y), forall y: T(y) -> Q_4(y) we can infer exists y: Q_4(y) <-> T(y) via existential biconditional introduction. From exists y: Q_4(y) <-> T(y) we can infer exists y: Q_4(y) -> T(y) via existential biconditional elimination. Finally, from exists y: Q_4(y) -> T(y), forall y: R_4(y) -> T(y), forall y: Q_4(y) or R_4(y) we can infer exists y: T(y) via existential disjunction elimination, which contradicts forall y: ~T(y). Therefore, the answer is no.