### Abstract

This Isabelle/HOL formalization extends the AFP entry Saturation_Framework with the following contributions:

- an application of the framework to prove Bachmair and Ganzinger's resolution prover RP refutationally complete, which was formalized in a more ad hoc fashion by Schlichtkrull et al. in the AFP entry Ordered_Resultion_Prover;
- generalizations of various basic concepts formalized by Schlichtkrull et al., which were needed to verify RP and could be useful to formalize other calculi, such as superposition;
- alternative proofs of fairness (and hence saturation and ultimately refutational completeness) for the given clause procedures GC and LGC, based on invariance.

### License

BSD License

### Topics

- Logic/General logic/Mechanization of proofs

### Session Saturation_Framework_Extensions

- Soundness
- Standard_Redundancy_Criterion
- Clausal_Calculus
- FO_Ordered_Resolution_Prover_Revisited
- Given_Clause_Architectures_Revisited

### Depends on

- First-Order Terms
- Formalization of Bachmair and Ganzinger’s Ordered Resolution Prover
- A Comprehensive Framework for Saturation Theorem Proving
- Well-Quasi-Orders

### Used by

- A Formalization of the SCL(FOL) Calculus: Simple Clause Learning for First-Order Logic

### Auto-related entries

- Clique is not solvable by monotone circuits of polynomial size
- Formalization of Concurrent Revisions
- Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals
- Pseudo Hoops

## Cite

×

Saturation_Framework_Extensions-AFP

    @article{Saturation_Framework_Extensions-AFP,
      author  = {Jasmin Christian Blanchette and Sophie Tourret},
      title   = {Extensions to the Comprehensive Framework for Saturation Theorem Proving},
      journal = {Archive of Formal Proofs},
      month   = {August},
      year    = {2020},
      note    = {\url{https://isa-afp.org/entries/Saturation_Framework_Extensions.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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Older releases:

- Sep 13, 2023 : Isabelle2023
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