Consider the following premises. forall x_10: W(x_10) -> S_10(x_10). S_10(a_10) <-> W(a_10). Can we infer ~(W(a_10) <-> S_10(a_10)) from them? If possible, name the inference rules being used at each step.
 From forall x_10: W(x_10) -> S_10(x_10) we can infer W(a_10) -> S_10(a_10) via universal instantiation. From S_10(a_10) <-> W(a_10) we can infer S_10(a_10) -> W(a_10) via biconditional elimination. Finally, from W(a_10) -> S_10(a_10), S_10(a_10) -> W(a_10) we can infer W(a_10) <-> S_10(a_10) via biconditional introduction, which contradicts ~(W(a_10) <-> S_10(a_10)). Therefore, the answer is no.