We introduced a logic for the study of dynamical control systems which we called a Conditional Observer Logic for finite machines (Cocolog). In that paper the properties of consistency and completeness for each first order logical theory in the tree of such theories in a Cocolog were established. The efficacy of automatic theorem proving is a crucial issue in the implementation of Cocolog. In this paper, we present a function evaluation based resolution, called FE-resolution, for Cocolog. The unique model property of Cocolog is first proved via the complete axiomatization property and then the decidability property of any theory in a Cocolog is deduced. Finally, completeness and complexity reduction of FE-resolution is discussed in terms of relative truthfulness and validity.