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