Consider the following premises. For all x_10, x_10 will play a game or x_10 is a nurse. For all x_10, x_10 will not play a game. For all x_10, x_10 is a lawyer or x_10 is not a nurse. For all x_10, if x_10 were a lawyer, then x_10 is playing squash. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 will not play squash.
 From the fact that for all x_10, x_10 is a lawyer or x_10 is not a nurse we can infer that for all x_10, if x_10 were a nurse, then x_10 is a lawyer via universal rewriting. From the fact that for all x_10, x_10 will play a game or x_10 is a nurse, and that for all x_10, x_10 will not play a game we can infer that for all x_10, x_10 is a nurse via universal disjunctive syllogism. From the fact that for all x_10, if x_10 were a nurse, then x_10 is a lawyer, and that for all x_10, x_10 is a nurse we can infer that for all x_10, x_10 is a lawyer via universal modus ponens. Finally, from the fact that for all x_10, if x_10 were a lawyer, then x_10 is playing squash, and that for all x_10, x_10 is a lawyer we can infer that for all x_10, x_10 will play squash via universal modus ponens, which contradicts that There is at least one x_10 for which x_10 will not play squash. Therefore, the answer is no.