Certified Connection Tableaux Proofs for HOL Light and TPTP
This work provides a certified proof system for theorem proving in HOL Light, addressing the need for reliable automation in interactive theorem provers, though it is incremental as it adapts an existing algorithm to a new environment.
The paper tackled the problem of integrating the leanCoP connection tableaux prover into HOL Light to certify its proofs, achieving a direct implementation that can also serve as a general-purpose TPTP prover and comparing its performance against Metis on various datasets.
In the recent years, the Metis prover based on ordered paramodulation and model elimination has replaced the earlier built-in methods for general-purpose proof automation in HOL4 and Isabelle/HOL. In the annual CASC competition, the leanCoP system based on connection tableaux has however performed better than Metis. In this paper we show how the leanCoP's core algorithm can be implemented inside HOLLight. leanCoP's flagship feature, namely its minimalistic core, results in a very simple proof system. This plays a crucial role in extending the MESON proof reconstruction mechanism to connection tableaux proofs, providing an implementation of leanCoP that certifies its proofs. We discuss the differences between our direct implementation using an explicit Prolog stack, to the continuation passing implementation of MESON present in HOLLight and compare their performance on all core HOLLight goals. The resulting prover can be also used as a general purpose TPTP prover. We compare its performance against the resolution based Metis on TPTP and other interesting datasets.