Consider the following premises. For all x_11, if x_11 were a carpenter, then x_11 is a scientist. For all x_11, if x_11 drinks water, then x_11 is an artist. For all x_11, x_11 will listen to a song. For all x_11, if x_11 listens to a song, then x_11 is drinking water. There is at least one x_11 for which x_11 is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: For all x_11, either x_11 is an artist or x_11 is a scientist are not true.
 From the fact that for all x_11, if x_11 were a carpenter, then x_11 is a scientist, and that there is at least one x_11 for which x_11 is a carpenter we can infer that there is at least one x_11 for which x_11 is a scientist via existential modus ponens. From the fact that for all x_11, if x_11 listens to a song, then x_11 is drinking water, and that for all x_11, x_11 will listen to a song we can infer that for all x_11, x_11 will drink water via universal modus ponens. From the fact that for all x_11, if x_11 drinks water, then x_11 is an artist, and that for all x_11, x_11 will drink water we can infer that for all x_11, x_11 is an artist via universal modus ponens. Finally, from the fact that for all x_11, x_11 is an artist, and that there is at least one x_11 for which x_11 is a scientist we can infer that there is at least one x_11 for which x_11 is an artist and x_11 is a scientist via existential conjunction, which contradicts that For all x_11, either x_11 is an artist or x_11 is a scientist are not true. Therefore, the answer is no.