Consider the following premises. forall x_15: R_15(x_15) -> W(x_15). forall x_15: ~P_15(x_15) or R_15(x_15). u -> ~W(i). forall x_15: Q_15(x_15) -> W(x_15). forall x_15: P_15(x_15) or Q_15(x_15). Can we infer u from them? If possible, name the inference rules being used at each step.
 From forall x_15: P_15(x_15) or Q_15(x_15), forall x_15: ~P_15(x_15) or R_15(x_15) we can infer forall x_15: Q_15(x_15) or R_15(x_15) via universal resolution. From forall x_15: Q_15(x_15) -> W(x_15), forall x_15: R_15(x_15) -> W(x_15), forall x_15: Q_15(x_15) or R_15(x_15) we can infer forall x_15: W(x_15) via universal disjunction elimination. From forall x_15: W(x_15) we can infer W(i) via universal instantiation. Finally, from u -> ~W(i), W(i) we can infer ~u via modus tollens, which contradicts u. Therefore, the answer is no.