Solution to the problem described here: http://www.javaworld.com/community/?q=node/13412&source=IFWNLE_nlt_jw_2013-07-09

disjoint-sets-of-a-collection-of-sets.clj

;;; The solution relies on the following implementation of the partitions function:
;;; https://gist.github.com/ray1729/5830608

(defn partition-combination-sets [partition]
  (let [partition (vec partition)
        c (count partition)]
    (for [i (range 1 (inc c))
          combination (combinatorics/combinations (range c) i)]
      ;; the following (map partition combination) may be a bit confusing, because it does use the vector
      ;; defined above as a function and has nothing to do with the standard partition function of the clojure core language.
      (apply union (map partition combination)))))

(defn does-partition-cover-set-of-sets [partition set-of-sets]
  (let [pcss (partition-combination-sets partition)]
    (every? identity(map (fn [s] (some (fn [pcs] (= pcs s)) pcss)) set-of-sets))))

(defn smallest-partition-that-covers-set-of-sets [set-of-sets]
  (let [all-element-set (reduce union set-of-sets)
        all-partitions (partitions all-element-set)]
    (apply (partial min-key (fn [p] (count p)))
     (filter (fn [partition] (does-partition-cover-set-of-sets partition set-of-sets)) all-partitions))))

(smallest-partition-that-covers-set-of-sets #{#{1 2 3} #{1 2 4} #{1 2 5}})
-> #{#{1 2} #{3} #{4} #{5}}