Consider the following premises. ~p_3. forall x_7: S(x_7) <-> S_7(x_7). p_3 <-> S(b). Can we infer S_7(b) from them? If possible, name the inference rules being used at each step.
 From forall x_7: S(x_7) <-> S_7(x_7) we can infer S(b) <-> S_7(b) via universal instantiation. From p_3 <-> S(b), ~p_3 we can infer ~S(b) via biconditional elimination. Finally, from S(b) <-> S_7(b), ~S(b) we can infer ~S_7(b) via biconditional elimination, which contradicts S_7(b). Therefore, the answer is no.