Consider the following premises. forall x_16: P_16(x_16) -> Q_16(x_16). forall x_16: Q_16(x_16) -> R_16(x_16). forall x_15: P_16(x_15). Can we infer R_16(a_15) or q from them? If possible, name the inference rules being used at each step.
 From forall x_16: P_16(x_16) -> Q_16(x_16), forall x_16: Q_16(x_16) -> R_16(x_16) we can infer forall x_16: P_16(x_16) -> R_16(x_16) via universal transitivity. From forall x_15: P_16(x_15) we can infer P_16(a_15) via universal instantiation. From forall x_16: P_16(x_16) -> R_16(x_16) we can infer P_16(a_15) -> R_16(a_15) via universal instantiation. From P_16(a_15) -> R_16(a_15), P_16(a_15) we can infer R_16(a_15) via modus ponens. Finally, from R_16(a_15) we can infer R_16(a_15) or q via addition. Therefore, the answer is yes.