No abstract

No abstract

The Intuitionistic Logic Theorem Proving (ILTP) library provides a platform for testing and benchmarking automated theorem proving (ATP) systems for intuitionistic propositional and first-order logic. It includes about 2,800 problems in a standardized syntax from 24 problem domains. For each problem an intuitionistic status and difficulty rating were obtained by running comprehensive tests of currently available intuitionistic ATP systems on all problems in the library. Thus, for the first time, the testing and evaluation of ATP systems for intuitionistic logic have been put on a firm basis.

Connection calculi benefit from a goal-oriented proof search, but are in general not proof confluent. A substantial amount of backtracking is required, which significantly affects the time complexity of the proof search. This paper presents a simple strategy for effectively restricting backtracking in connection calculi. In combination with a few basic techniques it provides the basis for a refined connection calculus. The paper also describes how this calculus can be implemented directly by a few lines of Prolog code. This very compact program is the core of an enhanced version of the automated theorem prover leanCoP. The performance of leanCoP is compared with other lean theorem provers, connection provers, and state-of-the-art theorem provers. The results show that restricted backtracking is a successful technique when performing proof search in connection calculi.

No abstract