This open access set, LNAI 16688-16689, constitutes the proceedings of the 13th International Joint Conference, IJCAR 2026, held in Lisbon, Portugal, during July 26–29, 2026.

The 41 full research papers and 8 short papers included in these two volumes were carefully reviewed and selected from 112 submissions. The papers cover the following topical sections:

Part I: Theorem Proving and Automation; SAT, SMT, and Verification; Intuitionistic, Modal, and Temporal Logics;

Part II: Calculi, Proof Theory, and Decision Procedures; and Unification, Rewriting, and Computational Models.