Question: What empire did the a Korean kingdom defeat in 1231?

Context paragraphs:
Asadal: In Korean mythology and history, Asadal (Hangul/ Hanja:아사달/阿斯達) was the mythical capital city of the kingdom of Gojoseon (Hangul/ Hanja: 고조선/ 古朝鮮 - meaning "Older Joseon"), the first ever Korean kingdom and notably founded by the legendary god-king Dan'gun.  It is thought that Asadal was located in Manchuria, northeastern Hwanghae Province (Hangul/ Hanja: 황해/黃海) in North Korea, or Pyongyang Province (Hangul/ Hanja: 평양/平讓) - that is, either the legendary kingdom in situ within the province of Pyongyang, not referring to the modern-day capital of North Korea - Pyongyang.

Goryeo: Goryeo (고려 ; 高麗 ; ] ; 918–1392), also spelled as Koryŏ, was a Korean kingdom established in 918 by King Taejo.  This kingdom later gave name to the modern exonym "Korea".  It united the Later Three Kingdoms in 936 and ruled most of the Korean Peninsula until it was removed by the founder of the Joseon in 1392.  Goryeo expanded Korea's borders to present-day Wonsan in the northeast (936–943), the Yalu River (993) and finally almost the whole of the Korean Peninsula (1374).

Goguryeo: Goguryeo (고구려 ; 高句麗 ; ] , 37 BCE–668 CE), also called Goryeo (고려 ; 高麗 ; ] ), was a Korean kingdom located in the northern and central parts of the Korean Peninsula and the southern and central parts of inner and outer Manchuria.  Goguryeo was an active participant in the power struggle for control of the Korean peninsula and was also associated with the foreign affairs of neighboring polities in China and Japan.  Goguryeo has been described as an empire by Korean scholars.

Later Silla: Later Silla (668–935, Hangul: 후신라 ; Hanja: 後新羅 ; RR: "Hushila " , ] ) or Unified Silla (Hangul: 통일신라 ; Hanja: 統一新羅 , ] ) is the name often applied to the Korean kingdom of Silla, one of the Three Kingdoms of Korea, after it conquered Baekje and Goguryeo in the 7th century, unifying the central and southern regions of the Korean peninsula.  Later Silla was a prosperous and wealthy country, and its metropolitan capital of Seorabeol (modern name Gyeongju) was the fourth-largest city in the world at the time.  During its heyday, the country contested with Balhae, a Goguryeo–Mohe kingdom, to the north for supremacy in the region.  Throughout its existence, Later Silla was plagued by intrigue and political turmoil, mainly by the rebel groups in conquered Baekje and Goguryeo territories, leading to the Later Three Kingdoms period in the late 9th century.

Mongol invasions of Korea: The Mongol invasions of Korea (1231–1259) comprised a series of campaigns between 1231 and 1270 by the Mongol Empire against the Kingdom of Goryeo (the proto-state of modern-day Korea).  There were seven major campaigns at tremendous cost to civilian lives throughout the Korean peninsula, ultimately resulting in Korea becoming a vassal state of the Mongol Yuan Dynasty for approximately 80 years.

Dangun: Dan'gun (Hangul/ Hanja: 단군 ; 檀君 ; ] ) or Dan'gun Wanggeom (Hangul/ Hanja: 단군왕검 ; 檀君王儉 ] ) was known according to ancient Korean mythology - the absolute ancestor of the Korean people and legendary founder of Gojoseon (Hangul: 고조선 ; Hanja: 古朝鮮 - meaning "Older Joseon") - the first ever Korean kingdom, around present-day Liaoning, Manchuria, and the northern part of the Korean Peninsula, which explains the development of the Korean language from the Tungusic-speaking people of the region in ancient times bordering geographically from Mongolian, Russian, Manchurian and Chinese due to ancestry.

Siege of Kuju: The Siege of Kuju which occurred in 1231 was a decisive Goryeo victory against the Mongol Empire.  After the Mongol army crossed the Yalu river, it quickly captured almost all of Goryeo's border defenses.  The Mongol army, however, ran into stiff resistance both at Anju and the city of Kuju (modern-day Kusong), commanded by General Park Seo.

Joseon: The Kingdom of Joseon (Hangul: 대조선국 ; Hanja: 大朝鮮國 , ] , "Great Joseon State"), also known as Chosŏn, Choson and Chosun, was a Korean kingdom founded by Yi Seonggye that lasted for approximately five centuries, from July 1392 to October 1897.  It was officially renamed the Korean Empire in October 1897.  It was founded following the aftermath of the overthrow of Goryeo in what is today the city of Kaesong.  Early on, Korea was retitled and the capital was relocated to modern-day Seoul.  The kingdom's northernmost borders were expanded to the natural boundaries at the Yalu and Tumen Rivers through the subjugation of the Jurchens.  Joseon was the last dynasty of Korea and its longest-ruling Confucian dynasty.

Go dynasty: Go Royal Family (Reigned from 37 BC to 668 AD) was the dynasty that founded and ruled over the ancient Korean kingdom of Goguryeo.  Its founder, Jumong (Hangul: 주몽 ; Hanja: 朱蒙 ), broke away from another ancient Korean kingdom called Dongbuyeo to start his own kingdom.  The Taewangs were all members of the Go Royal Family.

List of monarchs of Majorca: The Kingdom of Majorca (1231–1715) was created by James I of Aragon following his conquest in 1229 and the subsequent surrender of sovereignty by the Muslim rulers in of the Balearic Islands in 1231.  It was ruled in conjunction with the Crown of Aragon until his death when by will it passed to a younger son, James (II), who ruled the kingdom as nominal vassal of the Aragonese Crown.  He was removed by his nephew Alfonso III of Aragon, who conquered the island of Menorca in 1287, effectively recovered Menorca from Moorish rule.

Supporting paragraphs: Siege of Kuju Goryeo
Answer: Mongol Empire