Consider the following premises. forall y_2: S(y_2) <-> P(y_2). p_3 <-> S(c). ~p_3. Can we infer P(c) from them? If possible, name the inference rules being used at each step.
 From forall y_2: S(y_2) <-> P(y_2) we can infer S(c) <-> P(c) via universal instantiation. From p_3 <-> S(c), ~p_3 we can infer ~S(c) via biconditional elimination. Finally, from S(c) <-> P(c), ~S(c) we can infer ~P(c) via biconditional elimination, which contradicts P(c). Therefore, the answer is no.