I read that truth trees are not the best way of searching for an interpretation because in some cases, the tree will always be infinite even when there is an interpretation (with a finite domain) that exists.
Why is it that truth trees can be infinite when there exists an interpretation with a finite domain? And how can I determine whether the sentences at the root of an infinite truth tree are valid or invalid, if creating a tree does not help me get closer to that goal?
An example of an infinite tree, taken from Bonevac's Deduction (pg 205 #50):
∀x(Fx→∃y(Fy∧Ryx))∃x(Fx∧Rxx)