Consider the following premises. For all x_14, if x_14 were an artist, then x_14 is not playing squash. For all x_14, x_14 will write a letter. For all x_14, if x_14 were a musician, then x_14 is not writing a letter. There is at least one x_14 for which x_14 is a musician. Can we infer the following from them? If we can, name the inference rule being used: For all x_14, x_14 is an artist.
 From the fact that for all x_14, if x_14 were a musician, then x_14 is not writing a letter, and that for all x_14, x_14 will write a letter we can infer that for all x_14, x_14 is not a musician via universal modus tollens. From the fact that there is at least one x_14 for which x_14 is a musician we can infer that there is at least one x_14 for which x_14 is a musician or x_14 will play squash via existential addition. From the fact that there is at least one x_14 for which x_14 is a musician or x_14 will play squash, and that for all x_14, x_14 is not a musician we can infer that there is at least one x_14 for which x_14 will play squash via existential disjunctive syllogism. Finally, from the fact that for all x_14, if x_14 were an artist, then x_14 is not playing squash, and that there is at least one x_14 for which x_14 will play squash we can infer that there is at least one x_14 for which x_14 is not an artist via existential modus tollens, which contradicts that For all x_14, x_14 is an artist. Therefore, the answer is no.