A Modern View on MCSat

2026-07-04

AI Summary

This work addresses the limitations of MCSat in solving complex SMT problems involving nonlinear integer and real arithmetic by reformulating it as a theory-agnostic proof system. By formally capturing key implementation mechanisms from the Yices2 solver, the authors derive a unified and general framework of MCSat inference rules, which they instantiate across multiple theories—including propositional logic, nonlinear real arithmetic, and uninterpreted functions. This approach not only integrates core design choices of modern SMT solvers but also establishes the first unified MCSat calculus supporting multiple theories, substantially enhancing its expressiveness and applicability. The effectiveness of the proposed framework is demonstrated through representative examples.

Abstract

The Model Constructing Satisfiability (MCSat) approach has shown strong performance in solving complex SMT problems, in particular in algebraic SMT theories such as non-linear integer and real arithmetic. In this paper we revisit the theory-independent MCSat framework as a proof system to provide a modern perspective that refines the original formulation of MCSat. By closely formalizing the implementation of MCSat within the Yices2 SMT solver, we incorporate design decisions that diverge from those in the seminal MCSat paper and thereby capture the current state-of-the-art in MCSat-based SMT reasoning. We present a general, theory-agnostic rule scheme for MCSat and instantiate it for several theories, including propositional logic, non-linear real arithmetic, and uninterpreted functions. We provide several detailed examples to illustrate the applicability of the presented calculus.

Problem

• MCSat
• SMT
• proof system
• theory-agnostic
• formalization

Innovation

• MCSat
• SMT solving
• theory-agnostic framework
• proof system
• non-linear arithmetic