Sledgehammer is a tool that increases the level of automation in the Isabelle/HOL proof assistant by asking external automatic theorem provers (ATPs), including SMT solvers, to prove the current goal. When the external ATP succeeds it must provide enough evidence that the goal holds for Isabelle to be able to reprove it internally based on that evidence. In particular, Isabelle can do this by replaying fine-grained proof certificates from proof-producing SMT solvers as long as they are expressed in the Alethe format, which until now was supported only by the veriT SMT solver. We report on our experience adding proof reconstruction support for the cvc5 SMT solver in Isabelle by extending cvc5 to produce proofs in the Alethe format and then adapting Isabelle to reconstruct those proofs. We discuss several difficulties and pitfalls we encountered and describe a set of tools and techniques we developed to improve the process. A notable outcome of this effort is that Isabelle can now be used as an independent proof checker for SMT problems written in the SMT-LIB standard. We evaluate cvc5’s integration on a set of SMT-LIB benchmarks originating from Isabelle as well as on a set of Isabelle proofs. Our results confirm that this integration complements and improves Sledgehammer’s capabilities.

Abstract Proofs from SMT solvers ensure correctness independently from implementation, which is often a requirement when solvers are used in safety-critical applications or proof assistants. Alethe is an established SMT proof format generated by the solvers veriT and cvc5, with reconstruction support in the proof assistants Isabelle/HOL and Coq. The format is close to SMT-LIB and allows both coarse- and fine-grained steps, facilitating proof production. However, it lacks a stand-alone checker, which harms its usability and hinders its adoption. Moreover, the coarse-grained steps can be too expensive to check and lead to verification failures. We present Carcara , an independent proof checker and elaborator for Alethe, implemented in Rust. It aims to increase the adoption of the format by providing push-button proof-checking for Alethe proofs, focusing on efficiency and usability; and by providing elaboration for coarse-grained steps into fine-grained ones, increasing the potential success rate of checking Alethe proofs in performance-critical validators, such as proof assistants. We evaluate Carcara over a large set of Alethe proofs generated from SMT-LIB problems and show that it has good performance and its elaboration techniques can make proofs easier to check.