Consider the following premises. W_4(a_9) -> w_3. ~w_3. w_3 -> W_4(a_9). forall y: U(y) <-> W_4(y). Can we infer U(a_9) from them? If possible, name the inference rules being used at each step.
 From forall y: U(y) <-> W_4(y) we can infer U(a_9) <-> W_4(a_9) via universal instantiation. From w_3 -> W_4(a_9), W_4(a_9) -> w_3 we can infer w_3 <-> W_4(a_9) via biconditional introduction. From w_3 <-> W_4(a_9), ~w_3 we can infer ~W_4(a_9) via biconditional elimination. Finally, from U(a_9) <-> W_4(a_9), ~W_4(a_9) we can infer ~U(a_9) via biconditional elimination, which contradicts U(a_9). Therefore, the answer is no.