Metis 2.0 [Hur03] is a proof tactic used in the HOL4 interactive
theorem prover. Metis 2.0 is written in Standard ML for ease of
integration with HOL4, and keeps very detailed proof information to
simplify the task of translating first order refutations to higher
order logic proofs. There is a strict adherence to standards: problems
are input in the TPTP format; and statuses and proofs are output in
the SZS and TSTP formats. Metis 2.0 implements a complete ordered
resolution and ordered paramodulation calculus, and uses a fixed
strategy on every input problem. In addition to standard size and
distance measures, finite models are used to weight clauses, although
by necessity in the CASC competition the finite models were
constructed by randomly interpreting all functions and relations
(except equality). No version of Metis had previously been entered
into CASC, and for its inaugural competition Metis 2.0 was entered
into every division of CASC 21. Its performance was worse than
expected---previous versions of Metis have out-performed the baseline
Otter entry---but one pleasant surprise was that its CNF normalization
was powerful enough to completely solve 28 of the FOF competition
problems.
References
[Hur03] Hurd J. (September 2003), First-Order Proof Tactics in
Higher-Order Logic Theorem Provers, Archer M., Di Vito B., Muņoz C.,
Design and Application of Strategies/Tactics in Higher Order Logics
(STRATA 2003) (Rome, Italy), pp.56-68, NASA Technical Report
CP-2003-212448, NASA.