Consider the following premises. forall y_1: R(y_1) <-> Q(y_1). forall y_1: R(y_1) -> T(y_1). forall y_1: T(y_1) -> R(y_1). exists y_1: ~Q(y_1). Can we infer forall y_1: T(y_1) from them? If possible, name the inference rules being used at each step.
 From forall y_1: R(y_1) <-> Q(y_1), exists y_1: ~Q(y_1) we can infer exists y_1: ~R(y_1) via existential biconditional elimination. From forall y_1: T(y_1) -> R(y_1), forall y_1: R(y_1) -> T(y_1) we can infer forall y_1: T(y_1) <-> R(y_1) via universal biconditional introduction. Finally, from forall y_1: T(y_1) <-> R(y_1), exists y_1: ~R(y_1) we can infer exists y_1: ~T(y_1) via existential biconditional elimination, which contradicts forall y_1: T(y_1). Therefore, the answer is no.