(defun eliminate (square digit)
  (without-contradictions
    (when (candidate digit square)
      (remove-candidate digit square)
      (if (or (no-candidates square)
              (and (single-candidate square)
                   (notevery (curry 'eliminate (single-candidate square))
                             (peers square))))
          (contradiction)
          (dolist (unit (units square))
            (let ((dplaces (square-candidates digit unit)))
              (when (or (no-candidates dplaces)
                        (and (single-candidate dplaces)
                             (not (assign (single-candidate dplaces) digit))))
                (contradiction))))))))