Consider the following premises. There is at least one x_6 for which if x_6 cooks, then x_6 is happy. For all x_6, if x_6 were curious, then x_6 is bored. For all x_6, x_6 is curious or x_6 is not 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 if x_6 cooks, then x_6 is bored.
 From the fact that for all x_6, x_6 is curious or x_6 is not happy we can infer that for all x_6, if x_6 were happy, then x_6 is curious via universal rewriting. From the fact that for all x_6, if x_6 were happy, then x_6 is curious, and that for all x_6, if x_6 were curious, then x_6 is bored we can infer that for all x_6, if x_6 were happy, then x_6 is bored via universal transitivity. Finally, from the fact that there is at least one x_6 for which if x_6 cooks, then x_6 is happy, and that for all x_6, if x_6 were happy, then x_6 is bored we can infer that there is at least one x_6 for which if x_6 cooks, then x_6 is bored via existential transitivity. Therefore, the answer is yes.