Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Automated Theory Formation in Pure Mathematics
Automated Theory Formation in Pure Mathematics
Vampire 1.1 (System Description)
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
The IJCAR-2004 automated theorem proving competition
AI Communications
Mathematical applications of inductive logic programming
Machine Learning
Applying SAT Solving in Classification of Finite Algebras
Journal of Automated Reasoning
AI Communications - CASC
Automatic Construction and Verification of Isotopy Invariants
Journal of Automated Reasoning
A Rational Reconstruction of a System for Experimental Mathematics
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
SRASS - A Semantic Relevance Axiom Selection System
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Cooperating reasoning processes: more than just the sum of their parts
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
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We extend our previous study of the automatic construction of isomorphic classification theorems for algebraic domains by considering the isotopy equivalence relation, which is of more importance than isomorphism in certain domains. This extension was not straightforward, and we had to solve two major technical problems, namely generating and verifying isotopy invariants. Concentrating on the domain of loop theory, we have developed three novel techniques for generating isotopic invariants, by using the notion of universal identities and by using constructions based on substructures. In addition, given the complexity of the theorems which verify that a conjunction of the invariants form an isotopy class, we have developed ways of simplifying the problem of proving these theorems. Our techniques employ an intricate interplay of computer algebra, model generation, theorem proving and satisfiability solving methods. To demonstrate the power of the approach, we generate an isotopic classification theorem for loops of size 6, which extends the previously known result that there are 22. This result was previously beyond the capabilities of automated reasoning techniques.