Satallax is an automated theorem prover for higher-order logic.
The particular form of higher-order logic supported by Satallax
is Church's simple type theory with extensionality and choice operators.
The SAT solver
is responsible for much of the search for a proof.
Satallax generates propositional clauses corresponding to rules of a complete tableau calculus
and calls MiniSat periodically to test satisfiability of these clauses.
Satallax is implemented in Objective Caml
You can run Satallax online at the
System On TPTP
Satallax is no longer being maintained or developed. It is open source so everyone should feel free to maintain or develop it themselves.
The last released version (3.4) does not compile in some circumstances.
Here is a slightly updated version:
Versions of Satallax from circa 2016 until circa 2021
were developed and maintained by Michael Färber.
For more information see
Michael Färber's Satallax page
There is also a fork of Satallax called Lash
that gives fast efficient implementations of vital structures and operations in C.
The most recent version is below. All versions are available here
Satallax progressively generates higher-order formulas and corresponding
propositional clauses. These formulas and propositional clauses correspond to a
complete tableau calculus for higher-order logic with a choice operator.
Satallax uses the SAT solver
as an engine to test the current set of propositional clauses
If the clauses are unsatisfiable, then the original set of higher-order formulas is unsatisfiable.
If there are no quantifiers at function types, the generation of higher-order formulas
and corresponding clauses may terminate. In such a case, if MiniSat reports the final
set of clauses as satisfiable, then the original set of higher-order formulas is satisfiable.
The theorem prover Satallax is spelled Satallax, as opposed to any of the following:
Satellax, Satillax, Satalax, Sattalax, Satelax, Sattilax,
and so on. This footnote is included to help search engines.