Question: What was founded by Robert Kay and is the largest public research library in the state of South Australia?

Context paragraphs:
Robert Kay (librarian): Robert Kay (19 June 1825 – 23 April 1904) was one of the founders of the Library, Art Gallery and Museum in Adelaide, South Australia, and the originator of the circulating library.  At his death he was general director and secretary of the Public Library, Museum, and Art Gallery of South Australia.

Combined Arms Research Library: The Combined Arms Research Library (CARL) at Fort Leavenworth, Kansas is a United States Army library which supports the United States Army Command and General Staff College.  Its collection of over 300,000 books covers all aspects of military science: joint and combined operations; tactics and doctrinal development; leadership, intelligence, weapons, equipment, and training.  The Archives and Special Collections house a unique collection of over 200,000 items and the documents collection consists of another 250,000.  Each year, the CARL reference staff answers some 30,000 queries for soldiers, faculty and staff at Fort Leavenworth, Kansas and throughout the world via the Defense Digital Library Reference Service.  Scholars, writers and the DoD community use the Combined Arms Research Library's archival materials, extensive research materials, and historical documents.  The Combined Arms Research Library is one of the largest and most well respected libraries in the Army and was named the 2007 Federal Library of the Year by the Federal Library and Information Center Committee (FLICC).

Free Public Library of Petaluma: The Free Public Library of Petaluma (also Old Carnegie Library, Carnegie Free Library and Petaluma Historical Library and Museum) is a research library and history museum at 20 Fourth Street in Petaluma, Sonoma County, California, US.  Built in 1904 as a Carnegie Free Library, it was designed by Brainerd Jones as his first major commission before the architect gained regional recognition.  In the 1970s, it was re-purposed as a research library and historical museum.  The building is listed on the National Register of Historic Places.

Blair-Caldwell African American Research Library: The Blair-Caldwell African American Research Library is a branch of the Denver Public Library in Denver, Colorado, in the United States that serves the Five Points neighborhood.  It is also a research library with collections focusing on the history of African Americans in Denver and the American West.  The library was conceived by Denver's first African American mayor, Wellington Webb, and his wife Wilma Webb, who observed that the history of African-Americans in Denver and the American West was under-represented.  The library was envisioned in 1999 and designated the Blair-Caldwell African American Research Library in honor of Omar Blair, the first black president of the Denver school board, and Elvin Caldwell, the first black city council member.  Ground breaking occurred in early 2002.

Library of Birmingham: The Library of Birmingham is a public library in Birmingham, England.  It is situated on the west side of the city centre at Centenary Square, beside the Birmingham Rep (to which it connects, and with which it shares some facilities) and Baskerville House.  Upon opening on 3 September 2013, it replaced Birmingham Central Library.  The library, which is estimated to have cost £188.8 million, is viewed by the Birmingham City Council as a flagship project for the city's redevelopment.  It has been described as the largest public library in the United Kingdom, the largest public cultural space in Europe, and the largest regional library in Europe.  2,414,860 million visitors came to the library in 2014 making it the 10th most popular visitor attraction in the UK.

Schlesinger Library: The Arthur and Elizabeth Schlesinger Library on the History of Women in America is a research library at the Radcliffe Institute for Advanced Study, Harvard University.  According to Nancy F. Cott, the Carl and Lily Pforzheimer Foundation Director, it is "the largest and most significant repository of documents covering women's lives and activities in the United States."  The library is named after Arthur M. Schlesinger, Sr., a noted history professor at Harvard during the 20th century; and his wife Elizabeth Bancroft Schlesinger, a noted feminist.  The library was begun on August 26, 1943, when the Radcliffe College alumna Maud Wood Park '98, a former suffragist, donated her collection of books, papers, and memorabilia on female reformers to Radcliffe.  This grew into a research library called the "Women's Archives", which was renamed in 1965 after Elizabeth Bancroft Schlesinger and her husband Arthur M. Schlesinger, as they were strong supporters of the library's mission.

Rijksmuseum Research Library: The Rijksmuseum Research Library is the largest public art history research library in the Netherlands.  The library is part of the Rijksmuseum in Amsterdam.  The online web catalogue contains about 300,000 monographs, 3,400 periodicals and 90,000 art sales catalogues.  About 50,000 art sales catalogues published before 1989 are not yet entered in the online catalogue.

State Library of South Australia: The State Library of South Australia, located on North Terrace, Adelaide, is the official library of the Australian state of South Australia.  It is the largest public research library in the state with a collection focus on South Australian information, and general reference material for information and research purposes.

New York Public Library: The New York Public Library (NYPL) is a public library system in New York City.  With nearly 53 million items, the New York Public Library is the second largest public library in the United States (behind the Library of Congress), and fourth largest in the world.  It is a private, non-governmental, independently managed, nonprofit corporation operating with both private and public financing.  The library has branches in the boroughs of Manhattan, The Bronx, and Staten Island, and affiliations with academic and professional libraries in the metropolitan area of New York State.  The City of New York's other two boroughs, Brooklyn and Queens, are served by the Brooklyn Public Library and the Queens Library, respectively.  The branch libraries are open to the general public and consist of circulating libraries.  The New York Public Library also has four research libraries which are also open to the general public.

Billy Ireland Cartoon Library &amp; Museum: The Billy Ireland Cartoon Library & Museum is a research library of American cartoons and comic art affiliated with the Ohio State University library system in Columbus, Ohio.  Formerly known as the Cartoon Research Library and the Cartoon Library & Museum, it holds the world's largest and most comprehensive academic research facility documenting and displaying original and printed comic strips, editorial cartoons and cartoon art.  The Museum is named after the Ohio cartoonist Billy Ireland.

Supporting paragraphs: Robert Kay (librarian) State Library of South Australia
Answer: State Library of South Australia