Consider the following premises. For all x_10, if x_10 plays squash, then x_10 is a lawyer. There is at least one x_10 for which if x_10 takes a plane, then x_10 is a server. For all x_10, x_10 will play squash. For all x_10, x_10 will take a plane. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, either x_10 is a lawyer or x_10 is a server are not true.
 From the fact that for all x_10, if x_10 plays squash, then x_10 is a lawyer, and that for all x_10, x_10 will play squash we can infer that for all x_10, x_10 is a lawyer via universal modus ponens. From the fact that there is at least one x_10 for which if x_10 takes a plane, then x_10 is a server, and that for all x_10, x_10 will take a plane we can infer that there is at least one x_10 for which x_10 is a server via existential modus ponens. Finally, from the fact that for all x_10, x_10 is a lawyer, and that there is at least one x_10 for which x_10 is a server we can infer that some lawyers are servers via existential conjunction, which contradicts that For all x_10, either x_10 is a lawyer or x_10 is a server are not true. Therefore, the answer is no.