We describe a flexible approach to automated reasoning, where non-theorems can be automatically altered to produce proved results which are related to the original. This is achieve...
In this paper, we formalize and prove the statement that coincidences cannot be accidental, a statement that underlies many useful heuristics in mathematics and physics. Our proof...
This paper proposes an extension to theorem proving interfaces for use with proofdirected debugging and other disproof-based applications. The extension is based around tracking a...
Sometimes it is pragmatically useful to prove a theorem by contradiction rather than finding a direct proof. Some reductio ad absurdum arguments have made mathematical history and ...
Mechanized reasoning systems and computer algebra systems have different objectives. Their integration is highly desirable, since formal proofs often involve both of the two differ...