Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
Concept
Prover9
Summary
Prover9 is an automated theorem prover for first-order and equational logic developed by William McCune.
Prover9 is the successor of the Otter theorem prover also developed by William McCune. Prover9 is noted for producing relatively readable proofs and having a powerful hints strategy.
Prover9 is intentionally paired with Mace4, which searches for finite models and counterexamples. Both can be run simultaneously from the same input, with Prover9 attempting to find a proof, while Mace4 attempts to find a (disproving) counter-example. Prover9, Mace4, and many other tools are built on an underlying library named LADR ("Library for Automated Deduction Research") to simplify implementation. Resulting proofs can be double-checked by Ivy, a proof-checking tool that has been separately verified using ACL2.
In July 2006 the LADR/Prover9/Mace4 input language made a major change (which also differentiates it from Otter). The key distinction between "clauses" and "formulas" completely disappeared; "formulas" can now have free variables; and "clauses" are now a subset of "formulas". Prover9/Mace4 also supports a "goal" type of formula, which is automatically negated for proof. Prover9 attempts to automatically generate a proof by default; in contrast, Otter's automatic mode must be explicitly set.
Prover9 was under active development, with new releases every month or every other month, until 2009. Prover9 is free software, and therefore, open source software; it is released under GPL version 2 or later.
The traditional "all men are mortal", "Socrates is a man", prove "Socrates is mortal" can be expressed this way in Prover9:
formulas(assumptions).
man(x) -> mortal(x). % open formula with free variable x
man(socrates).
end_of_list.
formulas(goals).
mortal(socrates).
end_of_list.
This will be automatically converted into clausal form (which Prover9 also accepts):
formulas(sos).
man(x) | mortal(x).
man(socrates).
mortal(socrates).
end_of_list.
A proof that the square root of 2 is irrational can be expressed this way:
formulas(assumptions).
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related courses (26)
MATH-205: Analysis IV
Learn the basis of Lebesgue integration and Fourier analysis
CS-101: Advanced information, computation, communication I
Discrete mathematics is a discipline with applications to almost all areas of study. It provides a set of indispensable tools to computer science in particular. This course reviews (familiar) topics a
MATH-351: Advanced numerical analysis
The student will learn state-of-the-art algorithms for solving differential equations. The analysis and implementation of these algorithms will be discussed in some detail.