|These benchmarks consist of nine provable parameterized
formulas (ending with ``_p'') and nine unprovable parameterized formulas
(ending with ``_n''). For each parameterized formula A(n), the test consists
in determining the greatest natural number n <= 21 satisfying the following
Even though it has been proved that most of these tests can
be easily solved by current solvers, they are still interesting because:
the prover returns the correct result for the formulas A(1),
A(2), ..., A(n) in less than 100 seconds, and
the prover cannot do the formula A(n+1) in less than 100
seconds or n=21.
In the table, we report the CPU time requested by the system
to solve the last instance A(n). For TA, we do not take into account the
time needed to compute the first order formula A*(n) corresponding to A(n)
(which is negligible), but we do take into account the time requested by
FLOTTER to convert A*(n) into a set Cl(A*(n)) of clauses (reported in the
FLOTTER column), and the time requested by SPASS to determine the consistency
or inconsistency of Cl(A*(n)) (reported in the SPASS column). Furthermore,
we stopped TA on A(n) with n < 21, either because FLOTTER does not terminate
gracefully when computing Cl(A*(n+1)), or because SPASS or FLOTTER exceed
the 100 seconds time limit. In the table, these three cases correspond
to the rows in which the value for n/SPASS/FLOTTER respectively is underlined.
they are not extended cnf formulas, and
some of these tests have not been solved yet.