Case Splitting in an Automatic Theorem Prover for Real-Valued Special Functions

Abstract

Case splitting, with and without backtracking, is compared with straightforward ordered resolution. Both forms of splitting have been implemented for MetiTarski, 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.

Automated theorem proving

“…Inference systems with resolution, paramodulation, and rewriting yield decision procedures for some decidable fragments of first‐order logic and first‐order theories . In addition, the merger of resolution, paramodulation, Knuth‐Bendix completion, rewriting, and sometimes theory reasoning is at the foundation of todays' most competitive generic first‐order theorem provers, such as Vampire, E, SPASS, and MetiTarksi …”

Automated theorem proving for special functions

“…Finally, MetiTarski augments resolution with backtracking, as seen in SAT and SMT solvers [8]. Case splitting effectively solves subproblems that naturally arise during the search.…”

MetiTarski’s Menagerie of Cooperating Systems

“…By now, however, we have extended MetiTarski's code base extensively. We introduced case-splitting with backtracking [4], as is found in SMT solvers. We also included our own code for interval constraint solving, to either supplement or replace the external decision procedures.…”