Consider the following premises. For all x_7, x_7 is not curious. For all x_7, x_7 will make tea or x_7 will climb a mountain. For all x_7, x_7 will climb a mountain if and only if x_7 is curious. There is at least one x_7 for which x_7 will not make tea or x_7 is a musician. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 is not a musician.
 From the fact that for all x_7, x_7 will climb a mountain if and only if x_7 is curious, and that for all x_7, x_7 is not curious we can infer that for all x_7, x_7 will not climb a mountain via universal biconditional elimination. From the fact that for all x_7, x_7 will make tea or x_7 will climb a mountain, and that there is at least one x_7 for which x_7 will not make tea or x_7 is a musician we can infer that there is at least one x_7 for which x_7 will climb a mountain or x_7 is a musician via existential resolution. Finally, from the fact that there is at least one x_7 for which x_7 will climb a mountain or x_7 is a musician, and that for all x_7, x_7 will not climb a mountain we can infer that there is at least one x_7 for which x_7 is a musician via existential disjunctive syllogism, which contradicts that For all x_7, x_7 is not a musician. Therefore, the answer is no.