Rewrite-based Equational Theorem Proving with Selection and Simplification

Rewrite-Based Equational Theorem Proving with Selection and Simplification

We present various refutationally complete calculi for first-order clauses with equality that allow for arbitrary selection of negative atoms in clauses. Refutation completeness is established via the use of well-founded orderings on clauses for defining a Herbrand model for a consistent set of clauses. We also formulate an abstract notion of redundancy and show that the deletion of redundant c...

Equational Reasoning in Saturation-Based Theorem Proving

5 Rewriting Techniques for Equational Reasoning 9 5.1 Knuth-Bendix Completion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5.1.1 Basic Concepts in Term Rewriting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 5.1.2 The Completion Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 5.1.3 Ordered Rewriting . . . . . . . . ....

Advances in Equational Theorem Proving

time wall-clock time [d] m em or y [G B y te ] Figure 7.7: Memory requirements over time for ROB001-1: bottom axis denotes abstract time, top axis denotes wall-clock time in days 7.4 Further benefits Besides the smaller memory footprint and some simplifications (e. g. for interreduction) there are some other benefits of the new loop design that are worth discussing. Not all of them are complete...

Distributing Equational Theorem Proving 1

In this paper we show that distributing the theorem proving task to several experts is a promising idea. We describe the team work method which allows the experts to compete for a while and then to cooperate. In the cooperation phase the best results derived in the competition phase are collected and the less important results are forgotten. We describe some useful experts and explain in detail...

WALDMEISTER: High Performance Equational Theorem Proving