The semantic foundations of logic: predicate logic
The semantic foundations of logic: predicate logic
Efficiency and Completeness of the Set of Support Strategy in Theorem Proving
Journal of the ACM (JACM)
The Concept of Demodulation in Theorem Proving
Journal of the ACM (JACM)
A fascinating country in the world of computing: your guide to automated reasoning
A fascinating country in the world of computing: your guide to automated reasoning
Ivy: a preprocessor and proof checker for first-order logic
Computer-Aided reasoning
Solution of the Robbins Problem
Journal of Automated Reasoning
Journal of Automated Reasoning
A Legacy Recalled and a Tradition Continued
Journal of Automated Reasoning
Distributivity in Łℵ0 and Other Sentential Logics
Journal of Automated Reasoning
Solving Open Questions and Other Challenge Problems Using Proof Sketches
Journal of Automated Reasoning
Conquering the Meredith Single Axiom
Journal of Automated Reasoning
A Milestone Reached and a Secret Revealed
Journal of Automated Reasoning
A Legacy Recalled and a Tradition Continued
Journal of Automated Reasoning
Conquering the Meredith Single Axiom
Journal of Automated Reasoning
Hilbert's Twenty-Fourth Problem
Journal of Automated Reasoning
Hi-index | 0.00 |
For close to a century, despite the efforts of fine minds that include Hilbert and Ackermann, Tarski and Bernays, Łukasiewicz, and Rose and Rosser, various proofs of a number of significant theorems have remained missing – at least not reported in the literature – amply demonstrating the depth of the corresponding problems. The types of such missing proofs are indeed diverse. For one example, a result may be guaranteed provable because of being valid, and yet no proof has been found. For a second example, a theorem may have been proved via metaargument, but the desired axiomatic proof based solely on the use of a given inference rule may have eluded the experts. For a third example, a theorem may have been announced by a master, but no proof was supplied. The finding of missing proofs of the cited types, as well as of other types, is the focus of this article. The means to finding such proofs rests with heavy use of McCune's automated reasoning program OTTER, reliance on a variety of powerful strategies this program offers, and employment of diverse methodologies. Here we present some of our successes and, because it may prove useful for circuit design and program synthesis as well as in the context of mathematics and logic, detail our approach to finding missing proofs. Well-defined and unmet challenges are included.