Performance impact of enabling duplicate lower-generation matches

Determine whether enabling duplicate E-matching matches with lower generation numbers in the Z3 implementation of congruence-class-tracking generation accounting would significantly affect performance.

Background

The implementation described in the paper omits propagation of generation updates that could allow duplicate matches with lower generation numbers. This omission causes the implementation to deviate slightly from the corresponding formal solver model.

The authors report that generation updates are rare in practice and therefore conjecture that enabling such duplicate matches would not significantly affect performance. The effect remains experimentally unresolved in the paper.

References

Our implementation skips this, slightly deviating from , yet still greatly improves stability. We suspect enabling such duplicate matches would not significantly affect performance for the same reason as above: generation updates are rare in practice.

— A Deeper Look at Depth: Stable Generation Accounting for Quantifier Reasoning  (2609.26345 - Cebeci et al., 22 Sep 2026) in Section 4, Z3 Implementation