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Type-checkers for the λΠ-calculus modulo theory

  • Dkcheck: type-checker
  • Kontroli: parallel version of dkcheck
  • Lambdapi: interactive extension of dkcheck with metavariables and tactics

Proof data bases

Proof translation tools

Interactive theorem provers

Automated theorem provers

  • ArchSAT: SMT solver generating Dedukti/FOL.
  • cvc5: efficient versatile SMT solver generating proof traces.
  • E: High-performance equational theorem prover for first-order logic (and increasingly higher-order logic), creating proof objects in TPTP format.
  • Vampire: ATP handing first-order and higher-order logic with equality and theories producing fine-grained TPTP compliant proofs.
  • veriT: SMT solver generating detailed proof traces in the Alethe format.
  • ZenonModulo: ATP generating Dedukti/FOL or Lambdapi/FOL.
  • Zipperposition: Superposition prover initially designed for prototyping ideas but increasingly powerful especially on higher-order benchmarks.
  • z3: efficient SMT solver that generates proofs (for a subset of checks, at least).