Consider the following premises. For all x, if x goes running, then x is a musician. For all x, if x were happy, then x is a carpenter. For all x, if x were a musician, then x is a carpenter. For all x, x is happy or x will go running. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which x is not a carpenter.
 From the fact that for all x, if x goes running, then x is a musician, and that for all x, if x were a musician, then x is a carpenter we can infer that for all x, if x goes running, then x is a carpenter via universal transitivity. Finally, from the fact that for all x, if x were happy, then x is a carpenter, that for all x, if x goes running, then x is a carpenter, and that for all x, x is happy or x will go running we can infer that for all x, x is a carpenter via universal disjunction elimination, which contradicts that There is at least one x for which x is not a carpenter. Therefore, the answer is no.