Journal of Automated Reasoning

, Volume 47, Issue 2, pp 111–132

Automated Inference of Finite Unsatisfiability


DOI: 10.1007/s10817-010-9216-8

Cite this article as:
Claessen, K. & Lillieström, A. J Autom Reasoning (2011) 47: 111. doi:10.1007/s10817-010-9216-8


We present Infinox, an automated tool for analyzing first-order logic problems, aimed at showing finite unsatisfiability, i.e., the absence of models with finite domains. Finite satisfiability is not a decidable problem (only semi-decidable), which means that such a tool can never be complete. Nonetheless, our hope is that Infinox be a useful complement to finite model finders in practice. Infinox uses several different proof techniques for showing infinity of a set, each of which requires the identification of a function or a relation with particular properties. Infinox enumerates candidates to such functions and relations, and subsequently uses an automated theorem prover as a sub-procedure to try to prove the resulting proof obligations. We have evaluated Infinox on the relevant problems from the TPTP benchmark suite, and we are able to automatically show finite unsatisfiability for over 25% of these problems.


Finite unsatisfiability Automated theorem proving Automated reasoning 

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Chalmers University of TechnologyGothenburgSweden

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