A practically efficient and almost linear unification algorithm
Artificial Intelligence
Average case analysis of unification algorithms
STACS 91 Proceedings of the 8th annual symposium on Theoretical aspects of computer science
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
An Efficient Unification Algorithm
ACM Transactions on Programming Languages and Systems (TOPLAS)
Topological sorting of large networks
Communications of the ACM
WALDMEISTER - High-Performance Equational Deduction
Journal of Automated Reasoning
An Almost Linear Robinson Unification ALgorithm
MFCS '88 Proceedings of the Mathematical Foundations of Computer Science 1988
DISCOUNT: A SYstem for Distributed Equational Deduction
RTA '95 Proceedings of the 6th International Conference on Rewriting Techniques and Applications
On the Evaluation of Indexing Techniques for Theorem Proving
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Handbook of automated reasoning
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
The design and implementation of VAMPIRE
AI Communications - CASC
AI Communications - CASC
(Nominal) unification by recursive descent with triangular substitutions
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Efficient operations in feature terms using constraint programming
ILP'11 Proceedings of the 21st international conference on Inductive Logic Programming
First-Order theorem proving and vampire
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
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Unification is one of the key procedures in first-order theorem provers. Most first-order theorem provers use the Robinson unification algorithm. Although its complexity is in the worst case exponential, the algorithm is easy to implement and examples on which it may show exponential behaviour are believed to be atypical. More sophisticated algorithms, such as the Martelli and Montanari algorithm, offer polynomial complexity but are harder to implement. Very little is known about the practical perfomance of unification algorithms in theorem provers: previous case studies have been conducted on small numbers of artificially chosen problem and compared term-to-term unification while the best theorem provers perform set-of-terms-to-term unification using term indexing. To evaluate the performance of unification in the context of term indexing, we made large-scale experiments over the TPTP library containing thousands of problems using the COMPITmethodology. Our results confirm that the Robinson algorithm is the most efficient one in practice. They also reveal main sources of inefficiency in other algorithms. We present these results and discuss various modification of unification algorithms.