seq-intersect-p v2 - simplified

(require 'seq)
(require 'cl-lib)

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(defun seq-intersect-p (first second &rest sequences)
  "Determine if FIRST, SECOND and any of the sequences in SEQUENCES have
an intersection."
  (if (seq-empty-p sequences)
      (seq-intersection first second)
    (or (seq-intersection first second)
        (apply #'seq-intersect-p
               first
               (seq-first sequences)
               `,@(seq-rest sequences))
        (apply #'seq-intersect-p
               second
               (seq-first sequences)
               `,@(seq-rest sequences))
        (apply #'seq-intersect-p
               (seq-first sequences)
               (seq-elt sequences 2)
               `,@(seq-rest (seq-rest sequences))))))

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(progn

  ;;; lists

  (cl-assert (not (seq-intersect-p '()
                                   '()))
             t
             "Empty lists do not intersect.")

  (cl-assert (not (seq-intersect-p '(1)
                                   '()))
             t
             "Empty lists do not intersect w/ non-empty lists.")

  (cl-assert (not (seq-intersect-p '(1 2)
                                   '(3 4)
                                   '(5 6)))
             t
             "Lists w/ unique elements do not intersect.")

  (cl-assert (seq-intersect-p '(1 2)
                              '(3 4)
                              '(4))
             t
             "This must have an intersection!")


  (cl-assert (not (seq-intersect-p '(1 1 2)
                                   '(3 4)
                                   '(5 6)))
             t
             "Duplicate elements contained to a list should not count towards intersection.")

  ;;; strings

  (cl-assert (not (seq-intersect-p ""
                                   ""))
             t
             "Empty strings do not intersect.")

  (cl-assert (not (seq-intersect-p "a"
                                   ""))
             t
             "Empty strings do not intersect w/ non-empty strings.")

  (cl-assert (not (seq-intersect-p "fep"
                                   "bar"
                                   "zug"))
             t
             "Strings w/ unique elements do not intersect.")

  (cl-assert (seq-intersect-p "fep"
                              "bar"
                              "zug"
                              "z")
             t
             "This must have an intersection!")


  (cl-assert (not (seq-intersect-p "foo"
                                   "bar"
                                   "zug"))
             t
             "Duplicate chars contained to a list should not count towards intersection."))