Consider the following premises. P_12(a_11) -> q. forall x_16: Q_16(x_16) -> R_16(x_16). forall x_16: P_12(x_16). forall x_16: P_16(x_16) -> R_16(x_16). forall x_16: P_16(x_16) or Q_16(x_16). Can we infer q from them? If possible, name the inference rules being used at each step.
 From forall x_16: P_16(x_16) -> R_16(x_16), forall x_16: Q_16(x_16) -> R_16(x_16), forall x_16: P_16(x_16) or Q_16(x_16) we can infer forall x_16: R_16(x_16) via universal disjunction elimination. From forall x_16: P_12(x_16), forall x_16: R_16(x_16) we can infer forall x_16: P_12(x_16) and R_16(x_16) via universal conjunction. From forall x_16: P_12(x_16) and R_16(x_16) we can infer P_12(a_11) and R_16(a_11) via universal instantiation. From P_12(a_11) and R_16(a_11) we can infer P_12(a_11) via simplification. Finally, from P_12(a_11) -> q, P_12(a_11) we can infer q via modus ponens. Therefore, the answer is yes.