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Prover9
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.
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 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.
== Examples ==
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