Consider the following premises. forall x_4: Q_4(x_4) -> R_4(x_4). ~T(a_2). forall x_4: T(x_4) -> Q_4(x_4). forall x_4: R_4(x_4) -> T(x_4). Can we infer R_4(a_2) from them? If possible, name the inference rules being used at each step.
 From forall x_4: T(x_4) -> Q_4(x_4), forall x_4: Q_4(x_4) -> R_4(x_4) we can infer forall x_4: T(x_4) -> R_4(x_4) via universal transitivity. From forall x_4: T(x_4) -> R_4(x_4), forall x_4: R_4(x_4) -> T(x_4) we can infer forall x_4: T(x_4) <-> R_4(x_4) via universal biconditional introduction. From forall x_4: T(x_4) <-> R_4(x_4) we can infer T(a_2) <-> R_4(a_2) via universal instantiation. Finally, from T(a_2) <-> R_4(a_2), ~T(a_2) we can infer ~R_4(a_2) via biconditional elimination, which contradicts R_4(a_2). Therefore, the answer is no.