Case Splitting in an Automatic Theorem Prover for Real-Valued Special Functions James P. Bridge and Lawrence C. Paulson Computer Laboratory, University of Cambridge, England {jpb65,lp15}@cam.ac.uk 22 February 2012 Abstract Case splitting, with and without backtracking, is compared with straightfor- ward ordered resolution. Both forms of splitting have been implemented for Meti- Tarski, an automatic theorem prover for real-valued special functions such as exp, ln, sin, cos and tan −1 . The experimental findings confirm the superiority of true backtracking over the simulation of backtracking through the introduction of new predicate symbols, and the superiority of both over straightforward resolution. 1