Consider the following premises. For all x_6, x_6 will write a letter. For all x_6, x_6 will climb a mountain or x_6 is curious. For all x_6, if x_6 were curious, then x_6 is an artist. For all x_6, if x_6 climbs a mountain, then x_6 is not writing a letter. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 is not an artist.
 From the fact that for all x_6, if x_6 climbs a mountain, then x_6 is not writing a letter, and that for all x_6, x_6 will write a letter we can infer that for all x_6, x_6 will not climb a mountain via universal modus tollens. From the fact that for all x_6, x_6 will climb a mountain or x_6 is curious, and that for all x_6, x_6 will not climb a mountain we can infer that for all x_6, x_6 is curious via universal disjunctive syllogism. Finally, from the fact that for all x_6, if x_6 were curious, then x_6 is an artist, and that for all x_6, x_6 is curious we can infer that for all x_6, x_6 is an artist via universal modus ponens, which contradicts that There is at least one x_6 for which x_6 is not an artist. Therefore, the answer is no.