Consider the following premises. forall x_15: P_15(x_15) -> Q_15(x_15). t -> R_15(e_4). forall x_15: Q_15(x_15) -> R_15(x_15). t or P_15(e_4). Can we infer ~R_15(e_4) from them? If possible, name the inference rules being used at each step.
 From forall x_15: P_15(x_15) -> Q_15(x_15), forall x_15: Q_15(x_15) -> R_15(x_15) we can infer forall x_15: P_15(x_15) -> R_15(x_15) via universal transitivity. From forall x_15: P_15(x_15) -> R_15(x_15) we can infer P_15(e_4) -> R_15(e_4) via universal instantiation. Finally, from t -> R_15(e_4), P_15(e_4) -> R_15(e_4), t or P_15(e_4) we can infer R_15(e_4) via disjunction elimination, which contradicts ~R_15(e_4). Therefore, the answer is no.