Theorem Proving in Large Theories

This paper investigates the performance of automated theo rem provers in formal software veri cation The challenge for the provers in this application is the large number of up to several hundred axioms in typical software speci cations Both the success rates and the proof times strongly depend on how good the provers are able to nd out the few relevant axioms that are really needed in the proofs We present a re duction technique for this problem It takes the axioms of a theory and a theorem and computes a reduced axiom set by eliminating as many irrelevant axioms as possible The proof search for the theorem then is performed in the reduced set Comparative experiments with ve auto mated theorem provers show that with the reduction technique they can prove more theorems than before and were faster for those that could be proved already without reduction