  A predicate linear temporal logic LTL_{\lambda,=} without quantifiers but
with predicate abstraction mechanism and equality is considered. The models of
LTL_{\lambda,=} can be naturally seen as the systems of pebbles (flexible
constants) moving over the elements of some (possibly infinite) domain. This
allows to use LTL_{\lambda,=} for the specification of dynamic systems using
some resources, such as processes using memory locations, mobile agents
occupying some sites, etc. On the other hand we show that LTL_{\lambda,=} is
not recursively axiomatizable and, therefore, fully automated verification of
LTL_{\lambda,=} specifications is not, in general, possible.
