This two-volume set LNAI 12166 and 12167 constitutes the refereed proceedings of the 10th International Joint Conference on Automated Reasoning, IJCAR 2020, held in Paris, France, in July 2020.* In 2020, IJCAR was a merger of the following leading events, namely CADE (International Conference on Automated Deduction), FroCoS (International Symposium on Frontiers of Combining Systems), ITP (International Conference on Interactive Theorem Proving), and TABLEAUX (International Conference on Analytic Tableaux and Related Methods).The 46 full research papers, 5 short papers, and 11 system descriptions presented together with two invited talks were carefully reviewed and selected from 150 submissions. The papers focus on the following topics:Part I: SAT; SMT and QBF; decision procedures and combination of theories; superposition; proof procedures; non classical logicsPart II: interactive theorem proving/ HOL; formalizations; verification; reasoning systems and tools*The conference was held virtually due to the COVID-19 pandemic.Chapter ‘Constructive Hybrid Games’ is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.