Twee: An Equational Theorem Prover

Twee is an automated theorem prover for equational logic. It implements unfailing Knuth-Bendix completion with ground joinability testing and a connectedness-based redundancy criterion. It came second in the UEQ division of CASC-J10, solving some problems that no other system solved. This paper describes Twee’s design and implementation

Efficient Encodings of First-Order Horn Formulas in Equational Logic

We present several translations from first-order Horn formulas to equational logic. The goal of these translations is to allow equational theorem provers to efficiently reason about non-equational problems. Using these translations we were able to solve 37 problems of rating 1.0 (i.e. which had not previously been automatically solved) from the TPTP

Optimizing mkbTT

We describe performance enhancements that have been added to mkbTT, a modern completion tool combining multi-completion with the use of termination tools

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

A Phytography of WALDMEISTER

The architecture of the {Waldmeister} prover for unit equational deduction is based on a strict separation of active and passive facts. After an inspection of the system's proof procedure, the representation of each of the central data structures is outlined, namely indexing for the active facts, compression for the passive facts, successor sets for the hypotheses, and minimal recording of inference steps for the proof object. In order to cope with large search spaces, specialized redundancy criteria are employed, and the empirically gained control knowledge is integrated to ease the use of the system. The paper concludes with a quantitative comparison of the {Waldmeister} versions over the years, and a view of the future prospects