Consider the following premises. forall x_1: R(x_1) -> T(x_1). exists x_1: ~R(x_1). forall x_1: T(x_1) <-> R(x_1). Can we infer forall x_1: T(x_1) from them? If possible, name the inference rules being used at each step.
 From forall x_1: T(x_1) <-> R(x_1) we can infer forall x_1: T(x_1) -> R(x_1) via universal biconditional elimination. From forall x_1: R(x_1) -> T(x_1), forall x_1: T(x_1) -> R(x_1) we can infer forall x_1: R(x_1) <-> T(x_1) via universal biconditional introduction. Finally, from forall x_1: R(x_1) <-> T(x_1), exists x_1: ~R(x_1) we can infer exists x_1: ~T(x_1) via existential biconditional elimination, which contradicts forall x_1: T(x_1). Therefore, the answer is no.