Consider the following premises. forall x_16: ~Q_16(x_16) or R_14(x_16). forall x_16: ~P_16(x_16) or R_16(x_16). R_14(a_12) -> p. R_16(a_12) -> p. forall x_16: P_16(x_16) or Q_16(x_16). Can we infer p or q from them? If possible, name the inference rules being used at each step.
 From forall x_16: P_16(x_16) or Q_16(x_16), forall x_16: ~P_16(x_16) or R_16(x_16) we can infer forall x_16: Q_16(x_16) or R_16(x_16) via universal resolution. From forall x_16: Q_16(x_16) or R_16(x_16), forall x_16: ~Q_16(x_16) or R_14(x_16) we can infer forall x_16: R_16(x_16) or R_14(x_16) via universal resolution. From forall x_16: R_16(x_16) or R_14(x_16) we can infer R_16(a_12) or R_14(a_12) via universal instantiation. From R_16(a_12) -> p, R_14(a_12) -> p, R_16(a_12) or R_14(a_12) we can infer p via disjunction elimination. Finally, from p we can infer p or q via addition. Therefore, the answer is yes.