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.^[1][2] It can a participate as part of an automated theorem proving system.^[2] The software is primarily written in the Haskell programming language.^[3] It is released under the terms of the GNU General Public License and is free.^[4]

Paradox

Developer(s)	Koen Lindström Claessen Niklas Sörensson
Written in	Haskell
Type	Automated theorem proving
License	GNU General Public License

Features

The Paradox developers described the software as a Mace-style method after the McCune's tool of that name.^[5][6] The Paradox introduced new techniques which help to reduce the computational complexity of the model search problem:^[5]

• term definitions, new variable reduction technique,
• incremental satisfiability checker which works with small domains first, then gradually increases the size of the domain, reusing the information it obtained from previous failed searches,
• static symmetry reduction which adds extra constraints,
• sort inference which works with unsorted problems.

Paradox was developed up to version 4, the final version being effective in model finding for Web Ontology Language OWL2.^[7]

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.^[8]