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