Consider the following premises. S(d_4) or s. p_2 -> ~s. forall z_2: ~S(z_2). r <-> p_2. Can we infer r from them? If possible, name the inference rules being used at each step.
 From forall z_2: ~S(z_2) we can infer ~S(d_4) via universal instantiation. From S(d_4) or s, ~S(d_4) we can infer s via disjunctive syllogism. From p_2 -> ~s, s we can infer ~p_2 via modus tollens. Finally, from r <-> p_2, ~p_2 we can infer ~r via biconditional elimination, which contradicts r. Therefore, the answer is no.