# Show that exist a finite set of clauses F in first-order logic that Res*(F) is infinite

A predicate-logic resolution derivation of a clause $$C$$ from a set of clauses $$F$$ is a sequence of clauses $$C_1,\dots,C_m$$, with $$C_m = C$$ such that each $$C_i$$ is either a clause of $$F$$ (possibly with the variables renamed) or follows by a resolution step from two preceding clauses $$C_j ,C_k$$, with $$j, k < i$$. We write $$\operatorname{Res}^*(F)$$ for the set of clauses $$C$$ such that there is a derivation of $$C$$ from $$F$$.
The question is to give an example of a finite set of clauses $$F$$ in first-order logic such that $$\operatorname{Res}^*(F)$$ is infinite.