Consider the following premises. For all x_6, if x_6 works, then x_6 is a poet. There is at least one x_6 for which x_6 will make tea. For all x_6, x_6 will work. For all x_6, x_6 will climb a mountain. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, either x_6 will make tea or x_6 will climb a mountain are not true.
 From the fact that for all x_6, if x_6 works, then x_6 is a poet, and that for all x_6, x_6 will work we can infer that for all x_6, x_6 is a poet via universal modus ponens. Finally, from the fact that for all x_6, x_6 will climb a mountain, and that for all x_6, x_6 is a poet we can infer that for all x_6, x_6 will climb a mountain and x_6 is a poet via universal conjunction, which contradicts that For all x_6, either x_6 will make tea or x_6 will climb a mountain are not true. Therefore, the answer is no.