L. Bachmair, N. Dershowitz, and D. A. Plaisted, Completion without Failure, Rewriting Techniques-resolution of Equations in Algebraic Structures, vol.2, pp.1-30, 1989.

L. Bachmair and H. Ganzinger, Resolution Theorem Proving, Handbook of Automated Reasoning, pp.19-99, 2001.

. Jasmin-christian-blanchette, Formalizing the Metatheory of Logical Calculi and Automatic Provers in Isabelle/HOL (Invited Paper), 2019.

S. Jasmin-christian-blanchette, M. Böhme, S. J. Fleury, A. Smolka, and . Steckermeier, Semi-intelligible Isar Proofs from Machine-Generated Proofs, J. Autom. Reasoning, vol.56, pp.155-200, 2016.

A. Jasmin-christian-blanchette, A. Bouzy, A. Lochbihler, D. Popescu, and . Traytel, Friends with Benefits: Implementing Corecursion in Foundational Proof Assistants, ESOP 2017, Hongseok Yang, vol.10201, pp.111-140, 2017.

M. Jasmin-christian-blanchette, P. Fleury, C. Lammich, and . Weidenbach, A Verified SAT Solver Framework with Learn, Forget, Restart, and Incrementality, J. Autom. Reasoning, vol.61, pp.333-365, 2018.

F. Bobot, J. Filliâtre, C. Marché, and A. Paskevich, Why3: Shepherd Your Herd of Provers, pp.53-64, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00790310

K. Claessen and N. Smallbone, Efficient Encodings of First-Order Horn Formulas in Equational Logic, IJCAR 2018, Didier Galmiche, vol.10900, pp.388-404, 2018.

L. Cruz-filipe, J. H. Marijn, W. A. Heule, M. Hunt, P. Kaufmann et al., Efficient Certified RAT Verification, LNCS, vol.10395, pp.220-236, 2017.

M. Fleury, J. C. Blanchette, and P. Lammich, A Verified SAT Solver with Watched Literals using Imperative HOL, CPP 2018, pp.158-171, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01904647

F. Haftmann and T. Nipkow, Code Generation via Higher-Order Rewrite Systems, FLOPS 2010, vol.6009, pp.103-117, 2010.

T. Hillenbrand, A. Buch, R. Vogt, and B. Löchner, WALDMEISTER-High-Performance Equational Deduction, J. Autom. Reasoning, vol.18, pp.265-270, 1997.

N. Hirokawa, A. Middeldorp, C. Sternagel, and S. Winkler, Infinite Runs in Abstract Completion, LIPIcs, vol.84, p.16, 2017.

L. Hupel and T. Nipkow, A Verified Compiler from Isabelle/HOL to CakeML, LNCS, vol.10801, pp.999-1026, 2018.

J. Hurd, First-Order Proof Tactics in Higher-Order Logic Theorem Provers, Design and Application of Strategies/Tactics in Higher Order Logics (STRATA), pp.56-68, 2003.

A. Birch-jensen, J. B. Larsen, A. Schlichtkrull, and J. Villadsen, Programming and Verifying a Declarative First-Order Prover in Isabelle/HOL, AI Commun, vol.31, pp.281-299, 2018.

C. Kaliszyk and J. Urban, PRocH: Proof Reconstruction for HOL Light, LNCS, vol.7898, pp.267-273, 2013.

D. Kapur and P. Narendran, NP-Completeness of the Set Unification and Matching Problems, LNCS, vol.230, pp.489-495, 1986.

D. E. Knuth and P. B. Bendix, Simple Word Problems in Universal Algebras, Computational Problems in Abstract Algebra, John Leech, pp.263-297, 1970.

L. Kovács and A. Voronkov, Finding Loop Invariants for Programs over Arrays using a Theorem Prover, SYNASC 2009, Stephen M. Watt, Viorel Negru, p.10, 2009.

L. Kovács and A. Voronkov, First-Order Theorem Proving and Vampire, LNCS, vol.8044, pp.1-35, 2013.

A. Krauss, Partial Recursive Functions in Higher-Order Logic, 2006.

, LNCS, vol.4130, pp.589-603

A. Krauss, Recursive Definitions of Monadic Functions, EPTCS, vol.43, pp.1-13, 2010.

R. Kumar, R. Arthan, M. O. Myreen, and S. Owens, Self-Formalisation of Higher-Order Logic: Semantics, Soundness, and a Verified Implementation, J. Autom. Reasoning, vol.56, pp.221-259, 2016.

P. Lammich, Automatic Data Refinement, 2013.

, LNCS, vol.7998, pp.84-99

P. Lammich, The GRAT Tool Chain-Efficient (UN)SAT Certificate Checking with Formal Correctness Guarantees, LNCS, vol.10491, pp.457-463, 2017.

S. Lescuyer, Formalizing and Implementing a Reflexive Tactic for Automated Deduction in Coq, Ph.D. Dissertation, 2011.
URL : https://hal.archives-ouvertes.fr/tel-00713668

F. Mari?, Formal Verification of Modern SAT Solvers. Archive of Formal Proofs, Formal Proof Development, 2008.

F. Mari?, Formal Verification of a Modern SAT Solver by Shallow Embedding into Isabelle/HOL, Theoret. Comput. Sci, vol.411, pp.4333-4356, 2010.

T. Nipkow, L. C. Paulson, and M. Wenzel, Isabelle/HOL: A Proof Assistant for Higher-Order Logic, LNCS, vol.2283, 2002.

D. Oe, A. Stump, C. Oliver, and K. Clancy, versat: A Verified Modern SAT Solver, LNCS, vol.7148, pp.363-378, 2012.

C. Lawrence, J. C. Paulson, and . Blanchette, Three Years of Experience with Sledgehammer, a Practical Link Between Automatic and Interactive Theorem Provers, EPiC Series in Computing, vol.2, pp.1-11, 2012.

N. Peltier, A Variant of the Superposition Calculus, Formal Proof Development, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01383903

G. Reger and M. Suda, Checkable Proofs for First-Order Theorem Proving, EPiC Series in Computing, vol.51, pp.55-63, 2017.
DOI : 10.29007/s6d1

URL : https://easychair.org/publications/open/5W2B

T. Ridge and J. Margetson, A Mechanically Verified, Sound and Complete Theorem Prover for First Order Logic, LNCS, vol.3603, pp.294-309, 2005.
DOI : 10.1007/11541868_19

A. Schlichtkrull, Formalization of Logic in the Isabelle Proof Assistant, 2018.

A. Schlichtkrull, Formalization of the Resolution Calculus for First-Order Logic, J. Autom. Reasoning, vol.61, pp.455-484, 2018.

A. Schlichtkrull, J. C. Blanchette, and D. Traytel, A Verified Functional Implementation of Bachmair and Ganzinger's Ordered Resolution Prover. Archive of Formal Proofs, Formal Proof Development, 2018.

A. Schlichtkrull, J. C. Blanchette, D. Traytel, and U. Waldmann, Formalization of Bachmair and Ganzinger's Ordered Resolution Prover. Archive of Formal Proofs, Formal Proof Development, 2018.

A. Schlichtkrull, J. C. Blanchette, D. Traytel, and U. Waldmann, Formalizing Bachmair and Ganzinger's Ordered Resolution Prover, IJCAR 2018, Didier Galmiche, vol.10900, pp.89-107, 2018.
DOI : 10.29007/pn71

URL : https://easychair.org/publications/preprint_open/6PPM

S. Schulz, Simple and Efficient Clause Subsumption with Feature Vector Indexing, Automated Reasoning and Mathematics, vol.7788, pp.45-67, 2013.
DOI : 10.1007/978-3-642-36675-8_3

S. Schulz, System Description: E 1.8. In LPAR-19, vol.8312, pp.735-743, 2013.
DOI : 10.1007/978-3-642-45221-5_49

S. Schulz and M. Möhrmann, Performance of Clause Selection Heuristics for Saturation-Based Theorem Proving, LNCS, vol.9706, pp.330-345, 2016.

N. Shankar and M. Vaucher, The Mechanical Verification of a DPLL-Based Satisfiability Solver, Electr. Notes Theor. Comput. Sci, vol.269, pp.3-17, 2010.

A. Steen and C. Benzmüller, The Higher-Order Prover Leo-III, IJCAR 2018, Didier Galmiche, vol.10900, pp.108-116, 2018.
DOI : 10.1007/978-3-319-94205-6_8

URL : http://christoph-benzmueller.de/papers/C70.pdf

C. Sternagel and R. Thiemann, Formalizing Knuth-Bendix Orders and Knuth-Bendix Completion, RTA 2013, Femke van Raamsdonk, vol.21, pp.287-302, 2013.

C. Sternagel and R. Thiemann, First-Order Terms. Archive of Formal Proofs, Formal Proof Development, 2018.

G. Sutcliffe, The TPTP Problem Library and Associated Infrastructure: From CNF to TH0, J. Autom. Reasoning, vol.59, pp.483-502, 2017.

T. Tammet, Towards Efficient Subsumption, LNCS, vol.1421, pp.427-441, 1998.
DOI : 10.1007/bfb0054276

R. Thiemann, Extending a Verified Simplex Algorithm, 2018.
DOI : 10.29007/5vlq

URL : https://easychair.org/publications/open/6JF3

R. Thiemann and C. Sternagel, Certification of Termination Proofs using CeTA, LNCS, vol.5674, pp.452-468, 2009.

A. Voronkov, AVATAR: The Architecture for First-Order Theorem Provers, LNCS, vol.8559, pp.696-710, 2014.
DOI : 10.1007/978-3-319-08867-9_46

C. Weidenbach, D. Dimova, A. Fietzke, R. Kumar, M. Suda et al., SPASS Version 3.5, LNCS, vol.5663, pp.140-145, 2009.
DOI : 10.1007/978-3-642-02959-2_10

M. Wenzel, Isabelle/jEdit-a Prover IDE within the PIDE Framework, CICM 2012, vol.7362, pp.468-471, 2012.

N. Wirth, Program Development by Stepwise Refinement, Commun. ACM, vol.14, p.4, 1971.