Consider the following premises. There is at least one x_7 for which x_7 is a carpenter or x_7 is not an electrician. For all x_7, x_7 is a carpenter if and only if x_7 will climb a mountain. For all x_7, x_7 will climb a mountain or x_7 is an electrician. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 is not a carpenter.
 From the fact that there is at least one x_7 for which x_7 is a carpenter or x_7 is not an electrician we can infer that there is at least one x_7 for which if x_7 were an electrician, then x_7 is a carpenter via existential rewriting. From the fact that for all x_7, x_7 is a carpenter if and only if x_7 will climb a mountain we can infer that for all x_7, if x_7 climbs a mountain, then x_7 is a carpenter via universal biconditional elimination. Finally, from the fact that for all x_7, if x_7 climbs a mountain, then x_7 is a carpenter, that there is at least one x_7 for which if x_7 were an electrician, then x_7 is a carpenter, and that for all x_7, x_7 will climb a mountain or x_7 is an electrician we can infer that there is at least one x_7 for which x_7 is a carpenter via existential disjunction elimination, which contradicts that For all x_7, x_7 is not a carpenter. Therefore, the answer is no.