Journal of Automated Reasoning

, Volume 53, Issue 2, pp 141-172

First online:

Machine Learning for First-Order Theorem Proving

Learning to Select a Good Heuristic
  • James P. BridgeAffiliated withComputer Laboratory, University of Cambridge
  • , Sean B. HoldenAffiliated withComputer Laboratory, University of Cambridge Email author 
  • , Lawrence C. PaulsonAffiliated withComputer Laboratory, University of Cambridge

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We applied two state-of-the-art machine learning techniques to the problem of selecting a good heuristic in a first-order theorem prover. Our aim was to demonstrate that sufficient information is available from simple feature measurements of a conjecture and axioms to determine a good choice of heuristic, and that the choice process can be automatically learned. Selecting from a set of 5 heuristics, the learned results are better than any single heuristic. The same results are also comparable to the prover’s own heuristic selection method, which has access to 82 heuristics including the 5 used by our method, and which required additional human expertise to guide its design. One version of our system is able to decline proof attempts. This achieves a significant reduction in total time required, while at the same time causing only a moderate reduction in the number of theorems proved. To our knowledge no earlier system has had this capability.


Automatic theorem proving Machine learning First-order logic with equality Feature selection Support vector machines Gaussian processes