Solution of the Robbins Problem

@article{McCune1997SolutionOT,
  title={Solution of the Robbins Problem},
  author={William McCune},
  journal={Journal of Automated Reasoning},
  year={1997},
  volume={19},
  pages={263-276},
  url={https://api.semanticscholar.org/CorpusID:30847540}
}
This article shows that the three equations known as commutativity, association, and the Robbins equation are a basis for the variety oflean algebras and presents the proof and the search strategies that enabled the program EQP to find the proof.

A Complete Proof of the Robbins Conjecture

The document gives a formalization of the proof of the Robbins conjecture, following A. Mann, A Complete Proof of the Robbins Conjecture, 2003.

Computer Solutions of Problems in Inverse Semigroups

The main goal of this article is to use automated reasoning to solve problems regarding the axiomatic definition of inverse semigroups and provide a single identity for groups in terms of two binary operations.

Using Automated Theorem Provers in Nonassociative Algebra

We present a case study on how mathematicians use automated t heorem provers to solve open problems in (non-associative) algebra.

Automated Deduction in Ring Theory

Various possibilities of using Prover9 in ring theory and semiring theory, in particular, associative rings, rings with involutions, semirings with cancellation laws and near-rings are explored.

Superposition-based Equality Handling for Analytic Tableaux

We present a variant of the basic ordered superposition rules to handle equality in an analytic free-variable tableau calculus. We prove completeness of this calculus by an adaptation of the model…

Proof Development with Ωmega: The Irrationality of \(\sqrt 2\)

The well-known theorem asserting the irrationality of \(\sqrt 2\) was proposed as a case study for a comparison of fifteen (interactive) theorem proving systems [Wiedijk, 2002]. This represents an…

Automated theorem proving in quasigroup and loop theory

This work surveys all known results in the area of quasigroup and loop theory to have been obtained with the assistance of automated theorem provers, and compares the performance of selected state-of-the art first order theorem prover on them.

A Model Generation Style Completeness Proof for Constraint Tableaux with Superposition

We present a calculus that integrates equality handling by superposition into a free variable tableau calculus. We prove completeness of this calculus by an adaptation of the model generation [2,15]…

Journal of Formalized Mathematics

In the early 1930s, Huntington proposed several axiom systems for Boolean algebras. Robbins slightly changed one of them and asked if the resulted system is still a basis for variety of Boolean…

Theorem roving Software, Based on Method of Positively-Constructed Formulae

The language of positively constructed formulae and its calculus are described in this paper. The results o f a software system development for automated theorem proving in the calculus are…
...

Robbins algebra: Conditions that make a near-boolean algebra boolean

A number of properties that, if adjoined to those of a Robbins algebra, guarantee that the algebra is Boolean are presented, and it is shown how an automated reasoning program was used to obtain the corresponding proofs.

A Unification Algorithm for Associative-Commutative Functions

An algorithm which unifies terms whose function is associative and commutative is presented here and termmaaon, soundness, and completeness of the algorithm have been proved for a subclass of the general case.

Canonical Forms and Unification

The relations between narrowing and unification are studied and a new version of Fay's algorithm is given and it is shown how to eliminate many redundancies in this algorithm and give a sufficient condition for the termination of the algorithm.

Basic Paramodulation and Superposition

It is proved that refutational completeness in the context of deletion rules, such as simplification by rewriting (demodulation) and subsumption, and of techniques for eliminating redundant inferences, is correct.

Undecidable properties of finite sets of equations

The task of this paper is to expose techniques and theorems that can be used to establish that many collections of finite sets of equations characterized by common algebraic or logical properties fail to be recursive.

New sets of independent postulates for the algebra of logic, with special reference to Whitehead and Russell’s Principia mathematica

Three sets of independent postulates for the algebra of logic, or Boolean algebra, were published by the present writer in 1904. The first set, based on the treatment in Whitehead's Universal…

Simple Word Problems in Universal Algebras

An algorithm is described which is capable of solving certain word problems: i.e. of deciding whether or not two words composed of variables and operators can be proved equal as a consequence of a…

Theorem Proving with Ordering and Equality Constrained Clauses

This work gives simple conditions for a constraint strategy to be complete (refutationally and in the sense of Knuth-Bendix-like completion) and allows to prove in a uniform way the completeness of several instantiations of the framework with concrete strategies.

A Boolean Algebra

Before starting on what follows, the reader is advised to turn back to the Preface for suggestions on how much of this chapter to read, and how many of the examples to do.