TL;DR
This work presents a proof extraction algorithm for versioned e-graphs, an extension of e-graphs that supports branching reasoning contexts and proof by cases and implements it in Vegie, a lightweight automated inductive theorem prover.
The resulting prototype reconstructs about 80% of generated proof steps automatically, making Leo-III the first higher-order automated theorem prover to support independently checkable proof reconstruction and providing a basis for cross-system reuse.
A proof checker called Nörgler is introduced that builds upon and extends the established approach pioneered by GDV and supports checking propositional, (untyped and typed) first-order, and higher-order refutations represented in TSTP.
It is shown that the epsilon calculus provides a natural framework for analyzing tolerance of falsity in proofs and for identifying conditions under which an incorrect proof can be semantically repaired.
We present a formalization in Dafny of the Omega Test, an algorithm used to decide the satisfiability of a system of inequalities. The implementation defines executable representations for rational numbers, linear expressions, inequalities, equalities, divisibility constraints, and systems of constraints, together with...
This work presents a proof trimmer for Boolean satisfiability solving, and shows how this technique can be used to reduce proof size and proof checking time for richer combinatorial paradigms.
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