Consider the following premises. For all x_14, x_14 is happy if and only if x_14 will climb a mountain. For all x_14, x_14 will not go running. For all x_14, x_14 is happy or x_14 will not sleep. For all x_14, x_14 will go running or x_14 will sleep. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_14 for which x_14 is not happy.
 From the fact that for all x_14, x_14 is happy if and only if x_14 will climb a mountain we can infer that for all x_14, if x_14 climbs a mountain, then x_14 is happy via universal biconditional elimination. From the fact that for all x_14, x_14 will go running or x_14 will sleep, and that for all x_14, x_14 will not go running we can infer that for all x_14, x_14 will sleep via universal disjunctive syllogism. From the fact that for all x_14, x_14 will sleep we can infer that for all x_14, x_14 will sleep or x_14 will climb a mountain via universal addition. From the fact that for all x_14, x_14 is happy or x_14 will not sleep we can infer that for all x_14, if x_14 sleeps, then x_14 is happy via universal rewriting. Finally, from the fact that for all x_14, if x_14 sleeps, then x_14 is happy, that for all x_14, if x_14 climbs a mountain, then x_14 is happy, and that for all x_14, x_14 will sleep or x_14 will climb a mountain we can infer that for all x_14, x_14 is happy via universal disjunction elimination, which contradicts that There is at least one x_14 for which x_14 is not happy. Therefore, the answer is no.