This final report is provided to satisfy a contract deliverable. We summarize here our results in automated reasoning under this contract. Many of these words are taken from past reports to ONR.The development of the Boyer-Moore "Nqthm" theorem prover was supported in part for approximately 20 years by the Office of Naval Research. The long range objective of this research has been to enable programmers to produce software that is mathematically proven to meet its specifications by using mechanical theorem-proving programs that check proofs.We begin this report with a section listing scme accomplishments under this contract related to Nqthm. In particular, the evolution of that system culminated in the release in January, 1994, of the final versions of Nqthm and Pc-Nqthm; see Subsection 1.2 below. Included mAe rcsul" zonq=',-ted during this contract whose work was supported during i our preceding ONR contract.The second section pertains to the main focus of this contract: A Computational Logic for Applicative Common Lisp, or Acl2, which is a theorem proving system that is the successor to Nqthm. The section begins with some background on Acl2, with words describing the Acl2 project from a time shortly before the beginning of this contract. Much progress has been made since that time, which we summarize in the second section of this report, deferring many more details to an Appendix.The third section lists publications, reports, presentations, and awards and honors, as drawn from previous ONR annual reports. We conclude with the Appendix mentio,,ed above,