Consider the following premises. forall y: ~P(y). q_1 -> p. w_4. P(f) or ~p. Can we infer ~q_1 and w_4 from them? If possible, name the inference rules being used at each step.
 From forall y: ~P(y) we can infer ~P(f) via universal instantiation. From P(f) or ~p we can infer p -> P(f) via rewriting. From p -> P(f), ~P(f) we can infer ~p via modus tollens. From q_1 -> p, ~p we can infer ~q_1 via modus tollens. Finally, from ~q_1, w_4 we can infer ~q_1 and w_4 via conjunction. Therefore, the answer is yes.