Consider the following premises. forall x_26: P_26(x_26). u_2 <-> q_12. q_12 -> w_1. P_26(a_26) -> q_12. Can we infer ~w_1 from them? If possible, name the inference rules being used at each step.
 From forall x_26: P_26(x_26) we can infer P_26(a_26) via universal instantiation. From P_26(a_26) we can infer P_26(a_26) or u_2 via addition. From u_2 <-> q_12 we can infer u_2 -> q_12 via biconditional elimination. From P_26(a_26) -> q_12, u_2 -> q_12, P_26(a_26) or u_2 we can infer q_12 via disjunction elimination. Finally, from q_12 -> w_1, q_12 we can infer w_1 via modus ponens, which contradicts ~w_1. Therefore, the answer is no.