Complex sentence: The Order operates on the basis of the traditions of the medieval Knights Templar, celebrating the spirit of, but not claiming direct descent from the ancient Order founded by Hugues de Payens in 1118 and dissolved by Pope Clement V in 1312.
Split into simpler sentences: The Order operates on the basis of the traditions of the medieval Knights Templar. It reclaims the spirit of, but does not assert any direct descent from the ancient Order founded by Hugues de Payens in 1118 and dissolved by Pope Clement V in 1312.