Consider the following premises. W(a_7) -> W_1(a_7). ~W_1(a_7). forall x_4: W_1(x_4) <-> W(x_4). Can we infer W(a_7) from them? If possible, name the inference rules being used at each step.
 From forall x_4: W_1(x_4) <-> W(x_4) we can infer forall x_4: W_1(x_4) -> W(x_4) via universal biconditional elimination. From forall x_4: W_1(x_4) -> W(x_4) we can infer W_1(a_7) -> W(a_7) via universal instantiation. From W_1(a_7) -> W(a_7), W(a_7) -> W_1(a_7) we can infer W_1(a_7) <-> W(a_7) via biconditional introduction. Finally, from W_1(a_7) <-> W(a_7), ~W_1(a_7) we can infer ~W(a_7) via biconditional elimination, which contradicts W(a_7). Therefore, the answer is no.