Encoding TLA+ set theory into many-sorted first-order logic

We present an encoding of Zermelo-Fraenkel set theory into many-sorted first-order logic, the input language of state-of-the-art SMT solvers. This translation is the main component of a back-end prover based on SMT solvers in the TLA+ Proof System.

[1]  Josef Urban Translating Mizar for First Order Theorem Provers , 2003, MKM.

[2]  María Manzano,et al.  Extensions of First-Order Logic , 1996 .

[3]  David Delahaye,et al.  Tableaux Modulo Theories Using Superdeduction - An Application to the Verification of B Proof Rules with the Zenon Automated Theorem Prover , 2012, IJCAR.

[4]  Damien Doligez,et al.  Zenon Modulo: When Achilles Outruns the Tortoise Using Deduction Modulo , 2013, LPAR.

[5]  Lawrence C. Paulson,et al.  Extending Sledgehammer with SMT Solvers , 2011, Journal of Automated Reasoning.

[6]  Tobias Nipkow,et al.  Term rewriting and all that , 1998 .

[7]  Stephan Merz,et al.  Automatic Verification of TLA + Proof Obligations with SMT Solvers , 2012, LPAR.

[8]  Pascal Fontaine,et al.  SMT Solvers for Rodin , 2012, ABZ.

[9]  Jeremy Avigad Eliminating definitions and Skolem functions in first-order logic , 2003, TOCL.

[10]  Stephan Merz,et al.  Harnessing SMT Solvers for TLA+ Proofs , 2012, Electron. Commun. Eur. Assoc. Softw. Sci. Technol..

[11]  Stephan Merz,et al.  Refinement Types for tla + , 2014, NASA Formal Methods.

[12]  Leslie Lamport,et al.  Specifying Systems: The TLA+ Language and Tools for Hardware and Software Engineers [Book Review] , 2002, Computer.

[13]  Damien Doligez,et al.  Zenon : An Extensible Automated Theorem Prover Producing Checkable Proofs , 2007, LPAR.

[14]  Jonathan M. McCune,et al.  Memoir---Formal Specs and Correctness Proofs , 2011 .

[15]  Claude Marché,et al.  Discharging Proof Obligations from Atelier B Using Multiple Automated Provers , 2012, ABZ.