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Longman Dictionary of Contemporary English
show jumping
noun
EXAMPLES FROM CORPUS
▪ Before we had her she did a lot of show jumping and has bred a foal.
▪ He has bought himself a couple of Hunters and he plans to do some show jumping of all things.
Wiktionary
show jumping

n. An equestrian event in which a rider's horse is jumped over an array of obstacles.

Wikipedia
Show jumping

Show Jumping, also known as "stadium jumping", "open jumping", or simply "jumping", is a part of a group of English riding equestrian events that also includes dressage, eventing, hunters, and equitation. Jumping classes are commonly seen at horse shows throughout the world, including the Olympics. Sometimes shows are limited exclusively to jumpers, sometimes jumper classes are offered in conjunction with other English-style events, and sometimes show jumping is but one division of very large, all-breed competitions that include a very wide variety of disciplines. Jumping classes may be governed by various national horse show sanctioning organizations, such as the United States Equestrian Federation in the USA or the British Showjumping Association in Great Britain. International competitions are governed by the rules of the International Federation for Equestrian Sports (FEI, from the body's French name of Fédération Équestre Internationale).