Consider the following premises. forall x: R_3(x) or P(x). forall x: ~R_3(x). P(d_2) -> q_3. Can we infer ~q_3 from them? If possible, name the inference rules being used at each step.
 From forall x: R_3(x) or P(x), forall x: ~R_3(x) we can infer forall x: P(x) via universal disjunctive syllogism. From forall x: P(x) we can infer P(d_2) via universal instantiation. Finally, from P(d_2) -> q_3, P(d_2) we can infer q_3 via modus ponens, which contradicts ~q_3. Therefore, the answer is no.