### Abstract

This Isabelle/HOL formalization refines the abstract ordered resolution prover presented in Section 4.3 of Bachmair and Ganzinger's "Resolution Theorem Proving" chapter in the Handbook of Automated Reasoning. The result is a functional implementation of a first-order prover.

### License

BSD License

### Topics

- Logic/General logic/Mechanization of proofs

### Session Functional_Ordered_Resolution_Prover

- Weighted_FO_Ordered_Resolution_Prover
- Deterministic_FO_Ordered_Resolution_Prover
- IsaFoR_Term
- Executable_Subsumption
- Executable_FO_Ordered_Resolution_Prover

### Depends on

- First-Order Terms
- A Formalization of Knuth–Bendix Orders
- Formalization of Recursive Path Orders for Lambda-Free Higher-Order Terms
- Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals
- Open Induction
- Formalization of Bachmair and Ganzinger’s Ordered Resolution Prover
- Polynomial Factorization

### Used by

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

## Cite

×

Functional_Ordered_Resolution_Prover-AFP

    @article{Functional_Ordered_Resolution_Prover-AFP,
      author  = {Anders Schlichtkrull and Jasmin Christian Blanchette and Dmitriy Traytel},
      title   = {A Verified Functional Implementation of Bachmair and Ganzinger's Ordered Resolution Prover},
      journal = {Archive of Formal Proofs},
      month   = {November},
      year    = {2018},
      note    = {\url{https://isa-afp.org/entries/Functional_Ordered_Resolution_Prover.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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- Sep 13, 2023 : Isabelle2023
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