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
MiniSat 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 website.
News
May, 2016: Major new release forthcoming
June, 2013: Two versions of Satallax competed
in the
THF (higher-order) Division
of
CASC-24 and came in first and second.
Satallax-MaLeS 1.2 came in first solving 119 of 150 problems.
Satallax 2.7 (the latest "official" version available on this site) came in second solving solving 116 of 150 problems.
Satallax-MaLeS 1.2 is an alternative version of Satallax in which the strategy schedule
for was computed using machine learning techniques.
Daniel Kuehlwein is responsible for Satallax-MaLeS.
July, 2012: Satallax 2.4 came in second (or third) behind Isabelle 2012 (Sledgehammer)
in the
THF (higher-order) Division of
CASC-J6.
A demonstration system Isabelle-HOT 2012 which calls the higher-order provers Satallax and LEO (in addition to calling first-order systems and SMT solvers) was significantly better than all the other systems. Satallax 2.4 solved about 5% more problems than last year's winner, Satallax 2.1.
February, 2011: Satallax has been reimplemented in Objective Caml and released as Satallax 2.0.
July, 2010: Satallax 1.4 came in second in the higher-order THF division of
CASC-J5. (Click
here for results
and
here for detailed results.)
Satallax won the best new system award.
Downloads
The most recent version is below. All versions are available
here.
Satallax 2.8July 2015
This version includes Nik Sultana's code to construct Isabelle proofs.
Satallax 2.7April 15, 2013
Starting with this version, Satallax can call the first-order theorem prover E during search.
Also, there are many new modes and a new strategy schedule.
Satallax 2.6August 16, 2012
Fixed a bug with TPTP include directives that use full paths.
Satallax 2.4April 23, 2012
Added an implementation of higher-order preunification that is sometimes used to suggest instantiations.
Added support for demonstrating satisfiability in finite models.
Competed in CASC-J6
Satallax 2.3January 30, 2012
Upgraded to MiniSat 2.2.0.
Added code to lookup the value of propositional variables in the assignment. This can be used to guide the search.
Support for create Coq proof terms (for the simply typed fragment of Coq) has been added. This assumes Coq >= 8.4 (with eta conversion).
Satallax 2.2September 9, 2011
There is now an option for producing higher-order unsatisfiable cores.
The production of Coq proof scripts is more robust than in Satallax 2.1.
Satallax 2.1June 17, 2011
New flags and new modes have been added.
Support for producing Coq proof scripts has been added.
The code for producing proof scripts was written by Andreas Teucke.
Before producing proof scripts, PicoSAT is called to compute a minimal unsatisfiable core.
Competed in CASC-23; Winner of THF division
Satallax 2.0February 10, 2011
This is a complete reimplementation of Satallax in Objective Caml.
A foreign function interface is now used to interact with MiniSat code.
Satallax 1.4June 2, 2010
A number of extensions to the search procedure have been implemented. New modes that use these extensions have been added.
The strategy has been adjusted to use some of the new modes.
Extension 1. A preprocessing phase has been added. This splits a problem into independent problems if possible.
Extension 2. Subterms of the original problem can be preemptively used as instantiations.
Extension 3. Some modes use higher-order clauses and pattern matching during search.
Finally, bug in pattern matching from version 1.3 has been fixed.
This is the last version of Satallax coded in Lisp.
Competed in CASC-J5
Satallax 1.2January 29, 2010
Shadowing is now disallowed. A name must be declared exactly once.
Satallax 1.0January 8, 2010
There are bugs when certain command line options are used in combination (-t with -m, -t with -M). (h/t Geoff Sutcliffe)
Satallax 2.8July 2015
This version includes Nik Sultana's code to construct Isabelle proofs.
Brief Description
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
MiniSat as an engine to test the current set of propositional clauses
for unsatisfiability.
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.
