Rosetta, like Foldit, was originally developed at the University of Washington. Rosetta is now supported by a broad consortium called Rosetta Commons.
The 2015 version of the Rosetta Energy Function, known as REF2015, is described in detail in The Rosetta All-Atom Energy Function for Macromolecular Modeling and Design. Various terms or values in REF2015 are grouped to give Foldit score parts and the resulting subscores. REF2015 is the version of Rosetta currently used by Foldit.
Foldit has often featured "Rosetta Decoy" puzzles, where Rosetta@Home has produced a plausible solution that doesn't match the known native structure of the protein. The Foldit revisiting puzzles include a series of Rosetta Decoy puzzles.