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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

Problem data bases

  • TPTP: Thousands of Problems for Theorem Provers
  • TGTP: Thousand of Geometric Problems for Geometric Theorem Provers

Proof data bases

Proof data bases tools

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.
  • Eldarica: SMT solver for problems in the constrained Horn fragment. Can output models of Horn clauses in SMT-LIB, and proofs of unsatisfiability in several formats.
  • Larus: Larus is a theorem prover for coherent logic that uses SAT/SMT provers to construct proofs. Larus can generate natural language proofs (in LaTeX) and machine checkable proofs (Coq/Isabelle/Mizar).
  • Leo-III: ATP for (polymorphic) higher-order logic, providing proofs in TPTP format.
  • Princess: ATP and SMT solver for first-order logic modulo various theories, with support for outputting proofs in different formats.
  • 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).