Consider the following premises. For all x, if x were a musician, then x is a janitor. For all x, if x were a carpenter, then x is a musician. For all x, if x were a janitor, then x is climbing a mountain. For all x, if x climbs a mountain, then x is a carpenter. Can we infer the following from them? There is at least one x for which the fact that x were a carpenter does not imply that x is climbing a mountain.
 From the fact that for all x, if x were a musician, then x is a janitor, and that for all x, if x were a janitor, then x is climbing a mountain we can infer that for all x, if x were a musician, then x is climbing a mountain. From the fact that for all x, if x were a carpenter, then x is a musician, and that for all x, if x were a musician, then x is climbing a mountain we can infer that for all x, if x were a carpenter, then x is climbing a mountain. From the fact that for all x, if x were a carpenter, then x is climbing a mountain, and that for all x, if x climbs a mountain, then x is a carpenter we can infer that for all x, x is a carpenter if and only if x will climb a mountain. Finally, from the fact that for all x, x is a carpenter if and only if x will climb a mountain we can infer that for all x, if x were a carpenter, then x is climbing a mountain, which contradicts that There is at least one x for which the fact that x were a carpenter does not imply that x is climbing a mountain. Therefore, the answer is no.