Consider the following premises. For all x_4, if x_4 makes tea, then x_4 is an artist. For all x_4, if x_4 makes tea, then x_4 is an artist. For all x_4, if x_4 were an artist, then x_4 is a carpenter. For all x_4, if x_4 were a carpenter, then x_4 is making tea. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_4 for which the fact that x_4 were an artist does not imply that x_4 is making tea.
 From the fact that for all x_4, if x_4 were an artist, then x_4 is a carpenter, and that for all x_4, if x_4 were a carpenter, then x_4 is making tea we can infer that for all x_4, if x_4 were an artist, then x_4 is making tea via universal transitivity. From the fact that for all x_4, if x_4 were an artist, then x_4 is making tea, and that for all x_4, if x_4 makes tea, then x_4 is an artist we can infer that for all x_4, x_4 is an artist if and only if x_4 will make tea via universal biconditional introduction. From the fact that for all x_4, x_4 is an artist if and only if x_4 will make tea we can infer that for all x_4, if x_4 were an artist, then x_4 is making tea via universal biconditional elimination. From the fact that for all x_4, if x_4 makes tea, then x_4 is an artist, and that for all x_4, if x_4 were an artist, then x_4 is making tea we can infer that for all x_4, x_4 will make tea if and only if x_4 is an artist via universal biconditional introduction. Finally, from the fact that for all x_4, x_4 will make tea if and only if x_4 is an artist we can infer that for all x_4, if x_4 were an artist, then x_4 is making tea via universal biconditional elimination, which contradicts that There is at least one x_4 for which the fact that x_4 were an artist does not imply that x_4 is making tea. Therefore, the answer is no.