¹Computer Science and Engineering Discipline, Khulna University, Khulna, Bangladesh
²Department of Mathematics, Statistics and Computer Science, St. Francis Xavier University, NS, Canada

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Abstract—Automated Theorem Proving systems are enormously powerful computer programs capable of solving immensely difficult problems. The extreme capabilities of these systems lie on some well-established proof systems, such as Semantic tableau. It is used to prove the validity of a formula by contradiction and it can produce a counterexample if it fails. It can also be used to prove whether a formula is a logical consequence of a set of formulas. Tableau can be used in propositional logic, predicate logic, modal logic, temporal logic, and in other non-classical logics. In this article, we describe a detailed implementation of a sequential tableau algorithm for propositional and firstorder logic using a procedural language rather then logic programming language. We also illustrate a tableau based proof system in a distributed environment using the Message Passing Interface. This paper also investigates two distinct approaches for parallel and distributed implementation and describes the experimental formula generation procedure. The proposed high performance approach will un-wrap an efficient paradigm for automated theorem proving.

Index Terms—Automated theorem proving, high performance computing, message passing interface, semantic tableau.

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Cite: Md Zahidul Islam, Ahmed Shah Mashiyat, Kashif Nizam Khan, S. M. Masud Karim, "A Tableau Based Automated Theorem Prover Using High Performance Computing," Journal of Computers vol. 7, no. 3, pp. 597-607, 2012.