### Abstract

This Isabelle/HOL formalization is the companion of the technical report “A comprehensive framework for saturation theorem proving”, itself companion of the eponym IJCAR 2020 paper, written by Uwe Waldmann, Sophie Tourret, Simon Robillard and Jasmin Blanchette. It verifies a framework for formal refutational completeness proofs of abstract provers that implement saturation calculi, such as ordered resolution or superposition, and allows to model entire prover architectures in such a way that the static refutational completeness of a calculus immediately implies the dynamic refutational completeness of a prover implementing the calculus using a variant of the given clause loop. The technical report “A comprehensive framework for saturation theorem proving” is available on the Matryoshka website. The names of the Isabelle lemmas and theorems corresponding to the results in the report are indicated in the margin of the report.

### License

BSD License

### Topics

- Logic/General logic/Mechanization of proofs

### Session Saturation_Framework

- Calculus
- Intersection_Calculus
- Calculus_Variations
- Lifting_to_Non_Ground_Calculi
- Labeled_Lifting_to_Non_Ground_Calculi
- Given_Clause_Architectures

### Depends on

- Formalization of Recursive Path Orders for Lambda-Free Higher-Order Terms
- Formalization of Bachmair and Ganzinger’s Ordered Resolution Prover
- Well-Quasi-Orders

### Used by

- A Formalization of the SCL(FOL) Calculus: Simple Clause Learning for First-Order Logic
- Given Clause Loops
- Extensions to the Comprehensive Framework for Saturation Theorem Proving

### Auto-related entries

- Given Clause Loops

## Cite

×

Saturation_Framework-AFP

    @article{Saturation_Framework-AFP,
      author  = {Sophie Tourret},
      title   = {A Comprehensive Framework for Saturation Theorem Proving},
      journal = {Archive of Formal Proofs},
      month   = {April},
      year    = {2020},
      note    = {\url{https://isa-afp.org/entries/Saturation_Framework.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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Older releases:

- Sep 13, 2023 : Isabelle2023
- Oct 27, 2022 : Isabelle2022
- Dec 14, 2021 : Isabelle2021-1
- Feb 23, 2021 : Isabelle2021
- Apr 20, 2020 : Isabelle2020
- Apr 10, 2020 : Isabelle2019