12.4.7 Various Olympiad problems

Problem: The expert company assesses \( n \) girls in accordance with 3 criteria: intelligence, beauty and kindness, in points (arbitrary natural numbers, they can be considered real numbers, it's not important). The ratings for each criterion are different for all girls, that is, they can be sorted by their intelligence, beauty or kindness. Prove or disprove that it is possible to choose three such girls, that for any of the unchosen ones, one of these three will exceed her in at least two criteria.