Consider the following premises. forall x: S(x) or W_1(x). forall x: S(x) -> P(x). r_3 -> ~P(j). forall x: W_1(x) -> P(x). Can we infer r_3 from them? If possible, name the inference rules being used at each step.
 From forall x: S(x) -> P(x), forall x: W_1(x) -> P(x), forall x: S(x) or W_1(x) we can infer forall x: P(x) via universal disjunction elimination. From forall x: P(x) we can infer P(j) via universal instantiation. Finally, from r_3 -> ~P(j), P(j) we can infer ~r_3 via modus tollens, which contradicts r_3. Therefore, the answer is no.