Consider the following premises. ~w. p or q_13. ~p. q <-> w. ~q -> q_1. Can we infer ~q_1 from them? If possible, name the inference rules being used at each step.
 From q <-> w, ~w we can infer ~q via biconditional elimination. From p or q_13, ~p we can infer q_13 via disjunctive syllogism. Finally, from ~q -> q_1, ~q we can infer q_1 via modus ponens, which contradicts ~q_1. Therefore, the answer is no.