Consider the following premises. forall y: ~T_4(y). exists y: Q(y) -> U(y). forall y: T_4(y) -> Q(y). forall y: U(y) -> T_4(y). Can we infer exists y: ~Q(y) from them? If possible, name the inference rules being used at each step.
 From exists y: Q(y) -> U(y), forall y: U(y) -> T_4(y) we can infer exists y: Q(y) -> T_4(y) via existential transitivity. From exists y: Q(y) -> T_4(y), forall y: T_4(y) -> Q(y) we can infer exists y: Q(y) <-> T_4(y) via existential biconditional introduction. Finally, from exists y: Q(y) <-> T_4(y), forall y: ~T_4(y) we can infer exists y: ~Q(y) via existential biconditional elimination. Therefore, the answer is yes.