Consider the following premises. forall x_6: Q_6(x_6) -> R_6(x_6). r_3 or P_6(h). forall x_6: P_6(x_6) -> Q_6(x_6). r_3 -> R_6(h). Can we infer ~R_6(h) from them? If possible, name the inference rules being used at each step.
 From forall x_6: P_6(x_6) -> Q_6(x_6), forall x_6: Q_6(x_6) -> R_6(x_6) we can infer forall x_6: P_6(x_6) -> R_6(x_6) via universal transitivity. From forall x_6: P_6(x_6) -> R_6(x_6) we can infer P_6(h) -> R_6(h) via universal instantiation. Finally, from r_3 -> R_6(h), P_6(h) -> R_6(h), r_3 or P_6(h) we can infer R_6(h) via disjunction elimination, which contradicts ~R_6(h). Therefore, the answer is no.