Towards a Unified Ordering for Superposition-Based Automated Reasoning

Abstract

We propose an extension of the automated theorem prover E by the weighted path ordering. Weighted path ordering is theoretically stronger than all the orderings used in E-prover, however its parametrization is more involved than those normally used in automated reasoning. In particular, it depends on a term algebra. We discuss how the parameters for the ordering can be proposed automatically for particular theorem proving problem strategies. We integrate the ordering in E-prover and perform an evaluation on the standard theorem proving benchmarks. The ordering is complementary to the ones used in E prover so far.

Relaxed Weighted Path Order in Theorem Proving

“…This paper extends our previous research [2] where we attempt to overcome both of these obstacles and propose an efficient way to implement WPO as part of an automated reasoning system. We also propose parameters that allow WPO to function efficiently within a state-of-the-art automated theorem prover and help with actual theorem proving problems.…”

“…The strategy was randomly selected and is provided in "Appendix A". Section 6.1 describes previously published [2] evaluation of standard WPO. Section 6.2 provides evaluation of WPO with relaxed algebras, first published here.…”

“…As we evaluate a large number of different ordering instances on all of the benchmark problems, it is important to limit the number of problems, so that the evaluation can be done in a reasonable time. 2 We, however, believe that our collection of about 800 benchmark problems is reasonably orthogonal to allow us to perform an objective evaluation. All the selected benchmark domains rely heavily on equational reasoning, and hence can be expected to benefit from improvements in term rewriting.…”

“…• Additionally to our previous research, we provide an evaluation of effectiveness of our implementation based on real CPU time limits. This work is an extended version of our ICMS 2018 paper [2]. In comparison with that work, the relaxed WPO, efficient implementation, and a more extensive evaluation including an evaluation based on CPU time limit are the main new contributions presented first-time in this paper.…”