Question: Who did the warchief Red Cloud defeat in the Powder River War?

full_context: Document 1: Mount Oread Civil War posts: Lawrence, Kansas was not well defended in the early part of the Civil War. That ended with William Quantrill's devastating guerrilla raid August 21, 1863. By early 1864 Union soldiers were permanently camped on the top and slopes of Mount Oread, then to Lawrence's southwest. It seems the camp was originally named Camp Ewing, after Brig. Gen. Thomas Ewing.
Document 2: John Wallace Crawford: John Wallace ("Captain Jack)" Crawford (1847–1917), known as "The Poet Scout", was an American adventurer, educator, and author. "Captain Jack" was a master storyteller about the Wild West and is known in American history as one of the most popular performers in the late nineteenth century. His daring ride of 350 miles in six days to carry dispatches to Fort Laramie for the "New York Herald", to tell the news of the great victory by Gen. George Crook against the village of Chief American Horse at the Battle of Slim Buttes during the Great Sioux War of 1876-1877, made him a national celebrity.
Document 3: American Horse (elder): American Horse (Oglala Lakota: "Wašíčuŋ Tȟašúŋke" in Standard Lakota Orthography) (a/k/a "American Horse the Elder") (1830–September 9, 1876) was an Oglala Lakota warrior chief renowned for Spartan courage and honor. American Horse is notable in American history as one of the principal war chiefs allied with Crazy Horse during Red Cloud's War (1866–1868) and the Battle of the Little Bighorn during the Great Sioux War of 1876-1877. Chief American Horse was a son of Old Chief Smoke, an Oglala Lakota head chief and one of the last great Shirt Wearers, a highly prestigious Lakota warrior society. He was a signatory to the Fort Laramie Treaty of 1868, along with his brothers Chief Red Cloud and Chief Blue Horse. A month or so after the Treaty, American Horse was chosen a ""Ogle Tanka Un"" (Shirt Wearer, or war leader) along with Crazy Horse, Young-Man-Afraid-of-His-Horses and Man That Owns a Sword. On September 9, 1876, American Horse was mortally wounded in the Battle of Slim Buttes fighting to protect his family and defending against the white invasion of the "“Paha Sapa“" Black Hills.
Document 4: Fort C. F. Smith (Fort Smith, Montana): Fort C. F. Smith was a military post established in the Powder River country by the United States Army in Montana Territory on August 12, 1866, during Red Cloud's War. Established by order of Col. Henry B. Carrington, it was one of five forts proposed to protect the Bozeman Trail against the Oglala Lakota (Sioux), who saw the trail as a violation of the 1851 Treaty of Fort Laramie . The fort was abandoned in 1868 and burned by the Sioux under Red Cloud.
Document 5: Red Cloud: Red Cloud (Lakota: Maȟpíya Lúta) (1822 – December 10, 1909) was one of the most important leaders of the Oglala Lakota. He led from 1868 to 1909. One of the most capable Native American opponents that the United States Army faced in its mission to subdue the western territories, he led a successful campaign in 1866–1868 known as Red Cloud's War over control of the Powder River Country in northeastern Wyoming and southern Montana. The largest action of the war, the Fetterman Fight (with 81 men killed on the US side), was the worst military defeat suffered by the US on the Great Plains until the Battle of the Little Bighorn ten years later.
Document 6: Treaty of Fort Laramie (1868): The Treaty of Fort Laramie (also called the Sioux Treaty of 1868) was an agreement between the United States and the Oglala, Miniconjou, and Brulé bands of Lakota people, Yanktonai Dakota and Arapaho Nation signed on April 29, 1868 at Fort Laramie in the Wyoming Territory, guaranteeing the Lakota ownership of the Black Hills, and further land and hunting rights in South Dakota, Wyoming, and Montana. The Powder River Country was to be henceforth closed to all whites. The treaty ended Red Cloud's War.
Document 7: Powder River Expedition (1865): The Powder River Expedition of 1865 also known as the Powder River War or Powder River Invasion, was a large and far-flung military operation of the United States Army against the Lakota Sioux, Cheyenne, and Arapaho Indians in Montana Territory and Dakota Territory. Although soldiers destroyed one Arapaho village and established Fort Connor to protect travelers on the Bozeman Trail, the expedition is considered a failure because it failed to defeat the Indians and secure peace in the region.
Document 8: Treaty of Old Crossing: By the Treaty of Old Crossing (1863) and the Treaty of Old Crossing (1864), the Pembina and Red Lake bands of the Ojibwe, then known as Chippewa Indians, purportedly ceded to the United States all of their rights to the Red River Valley. On the Minnesota side, the ceded territory included all lands lying west of a line running generally southwest from the Lake of the Woods to Thief Lake, about 30 mi west of Red Lake, and then angling southeast to the headwaters of the Wild Rice River near the low-lying divide separating the watershed of the Red River of the North from the watershed of the Mississippi River. On the North Dakota side, the ceded territory included all of the Red River Valley north of the Sheyenne River. The total land area, roughly 127 mi wide east to west and 188 mi long north to south, consisted of nearly 11000000 acre of rich prairie land and forests.
Document 9: Red River War: The Red River War was a military campaign launched by the United States Army in 1874 to remove the Comanche, Kiowa, Southern Cheyenne, and Arapaho Native American tribes from the Southern Plains and forcibly relocate them to reservations in Indian Territory. Lasting only a few months, the war had several army columns crisscross the Texas Panhandle in an effort to locate, harass, and capture highly mobile Indian bands. Most of the engagements were small skirmishes in which neither side suffered many casualties. The war wound down over the last few months of 1874, as fewer and fewer Indian bands had the strength and supplies to remain in the field. Though the last significantly sized group did not surrender until mid-1875, the war marked the end of free-roaming Indian populations on the southern Great Plains.
Document 10: Henry B. Carrington: Henry Beebee Carrington (March 2, 1824 – October 26, 1912) was a lawyer, professor, prolific author, and an officer in the United States Army during the American Civil War and in the Old West during Red Cloud's War. A noted engineer, he constructed a series of forts to protect the Bozeman Trail, but suffered a major defeat at the hands of the warchief Red Cloud.
Document 11: Kit Carson: Christopher Houston Carson (December 24, 1809 – May 23, 1868), better known as Kit Carson, was an American frontiersman. He was a mountain man (fur trapper), wilderness guide, Indian agent, and U.S. Army officer. Carson became a frontier legend in his own lifetime via biographies and news articles. Exaggerated versions of his exploits were the subject of dime novels.
Document 12: Johnson County War: The Johnson County War, also known as the War on Powder River and the Wyoming Range War, was a series of range conflicts that took place in Johnson County, Wyoming between 1889 and 1893. The conflicts started when cattle companies ruthlessly persecuted supposed rustlers throughout the grazing lands of Wyoming. As tensions swelled between the large established ranchers and the smaller settlers in the state, violence finally culminated in Powder River Country, when the ranchers hired armed gunmen to invade the county and wipe out or scare off the small settlers they were competing against. When word came out of the gunmen's initial incursion in the territory, the small farmers and ranchers, as well as the state lawmen, formed a posse of 200 men to fight them, which led to a grueling stand-off. The conflict ended when the United States Cavalry, on the orders of President Benjamin Harrison, relieved the two forces, although further conflicts persisted in the following months.
Document 13: George Bent: George Bent, also named Ho—my-ike in Cheyenne (Cheyenne people, 1843 – May 19, 1918), was a Cheyenne who became a Confederate soldier during the American Civil War and waged war against Americans as a Cheyenne warrior afterward. He was the mixed-race son of Owl Woman, daughter of a Cheyenne chief, and the American William Bent, founder of the trading post named Bent's Fort and a trading partnership with his brothers and Ceran St. Vrain. Bent was born near present-day La Junta, Colorado, and was reared among both his mother's people, his father and other European Americans at the fort, and other whites from the age of 10 while attending boarding school in St. Louis, Missouri. He identified as Cheyenne.
Document 14: Red Cloud's War: Red Cloud's War (also referred to as the Bozeman War or the Powder River War) was an armed conflict between the Lakota, Northern Cheyenne, and Northern Arapaho on one side and the United States in Wyoming and Montana territories from 1866 to 1868. The war was fought over control of the western Powder River Country in present north-central Wyoming. This grassland, rich in buffalo, was traditionally Crow Indian land, but the Lakota had recently taken control. The Crow tribe held the treaty right to the disputed area, according to the major agreement reached at Fort Laramie in 1851. All involved in "Red Cloud's War" were parties in that treaty.
Document 15: Bozeman Trail: The Bozeman Trail was an overland route connecting the gold rush territory of Montana to the Oregon Trail. Its most important period was from 1863–68. Despite its name, "the major part of the route in Wyoming used by all Bozeman Trail travelers in 1864 was pioneered by Allen Hurlbut". Many miles of the Bozeman Trail in present Montana followed the tracks of Bridger Trail, opened by Jim Bridger in 1864. The flow of pioneers and settlers through territory of American Indians provoked their resentment and caused attacks. The challengers to the route were newly arrived Lakotas and their Indian allies, the Arapahoe and the Cheyenne. The United States put emphasis on a right to "establish roads, military and other posts" as described in Article 2 in the Fort Laramie Treaty of 1851. All parties in the conflict had signed that treaty. The Crow Indians held the treaty right to the contested area and had called it their homeland for decades. They sided with the whites. The U.S. Army undertook several military campaigns against the hostile Indians to try to control the trail. Because of its association with frontier history and conflict with American Indians, various segments of the trail are listed on the National Register of Historic Places (NRHP).
ground_truth: Henry Beebee Carrington