For the LTB divisions, a control program uses a SInE-like analysis to
extract reduced axiomatizations that are handed to several instances
of E. E will not use the on-the-fly learning introduced this year.
For CASC-25, E implements a strategy-scheduling automatic mode. The
total CPU time available is broken into 8 (unequal) time slices. For
each time slice, the problem is classified into one of several
classes, based on a number of simple features (number of clauses,
maximal symbol arity, presence of equality, presence of non-unit and
non-Horn clauses,...). For each class, a schedule of strategies is
greedily constructed from experimental data as follows: The first
strategy assigned to a schedule is the the one that solves the most
problems from this class in the first time slice. Each subsequent
strategy is selected based on the number of solutions on problems not
already solved by a preceding strategy.
About 210 different strategies have been evaluated on all untyped
first-order problems from TPTP 6.0.0, and about 180 of these
strategies are used in the automatic mode. A few new strategies may be
added.
E 1.9.1pre
Stephan Schulz
DHBW Stuttgart, Germany
Architecture
E 1.9.1pre [Sch02,Sch13] is a purely equational theorem prover for
full first-order logic with equality. It consists of an (optional)
clausifier for pre-processing full first-order formulae into clausal
form, and a saturation algorithm implementing an instance of the
superposition calculus with negative literal selection and a number of
redundancy elimination techniques. E is based on the DISCOUNT-loop
variant of the given-clause algorithm, i.e., a strict
separation of active and passive facts. No special rules for
non-equational literals have been implemented. Resolution is
effectively simulated by paramodulation and equality resolution.
Strategies
Proof search in E is primarily controlled by a literal selection
strategy, a clause evaluation heuristic, and a simplification
ordering. The prover supports a large number of pre-programmed literal
selection strategies. Clause evaluation heuristics can be constructed
on the fly by combining various parameterized primitive evaluation
functions, or can be selected from a set of predefined
heuristics. Clause evaluation heuristics are based on symbol-counting,
but also take other clause properties into account. In particular, the
search can prefer clauses from the set of support, or containing many
symbols also present in the goal. Supported term orderings are several
parameterized instances of Knuth-Bendix-Ordering (KBO) and
Lexicographic Path Ordering (LPO).
Implementation
E is build around perfectly shared terms, i.e. each distinct term is
only represented once in a term bank. The whole set of terms thus
consists of a number of interconnected directed acyclic graphs.
Term memory is managed by a simple mark-and-sweep garbage collector.
Unconditional (forward) rewriting using unit clauses is implemented
using perfect discrimination trees with size and age constraints.
Whenever a possible simplification is detected, it is added as a rewrite
link in the term bank.
As a result, not only terms, but also rewrite steps are shared.
Subsumption and contextual literal cutting (also known as subsumption
resolution) is supported using feature vector indexing [Sch04].
Superposition and backward rewriting use fingerprint indexing [Sch12],
a new technique combining ideas from feature vector indexing and path
indexing.
Finally, LPO and KBO are implemented using the elegant and efficient
algorithms developed by Bernd Löchner in [Loe06,Loe06].
The prover and additional information are available at
http://www.eprover.org
Expected Competition Performance
E 1.9.1 has only seen minor changes and inconsequential bug fixes
compared to last years version. It can produce proof objects quite
efficiently. The system is expected to perform reasonably well in most
proof classes, but will at best complement top systems in the disproof
classes.