Consider the following premises. For all x_6, if x_6 were a writer, then x_6 is playing squash. For all x_6, if x_6 plays squash, then x_6 is bored. For all x_6, x_6 will work or x_6 is not bored. 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 the fact that x_6 were a writer does not imply that x_6 is working.
 From the fact that for all x_6, x_6 will work or x_6 is not bored we can infer that for all x_6, if x_6 were bored, then x_6 is working via universal rewriting. From the fact that for all x_6, if x_6 were a writer, then x_6 is playing squash, and that for all x_6, if x_6 plays squash, then x_6 is bored we can infer that for all x_6, if x_6 were a writer, then x_6 is bored via universal transitivity. Finally, from the fact that for all x_6, if x_6 were a writer, then x_6 is bored, and that for all x_6, if x_6 were bored, then x_6 is working we can infer that for all x_6, if x_6 were a writer, then x_6 is working via universal transitivity, which contradicts that There is at least one x_6 for which the fact that x_6 were a writer does not imply that x_6 is working. Therefore, the answer is no.