Paradox (theorem prover)

Paradox is a finite-domain model finder for pure first-order logic (FOL) with equality developed by Koen Lindström Claessen and Niklas Sörensson at the Chalmers University of Technology.<ref name="Equinox-Paradox"/><ref name="Petr-P"/> It can a participate as part of an automated theorem proving system.<ref name="Petr-P"/> The software is written mostly in the programming language Haskell.<ref name="CASC-6-Entrants"/> It is free and open-source software released under the terms of the GNU General Public License.<ref name="Paradox-home-alone"/>

Features

The Paradox developers described the software as a Models And Counter-Examples (Mace) style method after the McCune's tool of that name.<ref name="Author-paper"/><ref name="Baumgartner-slides"/> The Paradox introduced new techniques which help to reduce the computational complexity of the model search problem:<ref name="Author-paper"/>

• term definitions – new variable reduction method
• incremental satisfiability checker – works with small domains first, then gradually increases the domain size, reusing information gained from prior failed searches
• static symmetry reduction – adds extra constraints
• sort inference – works with unsorted problems

Paradox was developed up to version 4, the final version being effective in model finding for Web Ontology Language OWL2.<ref name="Hoot-too"/>

Competition

Paradox was a division winner in the annual CADE ATP System Competition, an annual contest for automated theorem proving, in the years 2003 to 2012.<ref name="CADE-comp-2018"/>