 Schönfinkel introduced a new logical constant \(U\), that expresses the disjointness of two classes. For instance, \(UPQ\) may be written in usual FOL notation as \(\lnot\exists x(Px\land Qx)\), when \(P\) and \(Q\)  are one-place predicates. (The formula may be thought to formalize, for instance, the natural language sentence “No parrots are quiet.”) In the process of the elimination of the bound variables, \(UXY\) is obtained from an expression that contains ‘\(Xx\)’ and ‘\(Yx\)’, where \(x\) does not occur in \(X\) or \(Y\). For example, if \(X\) and \(Y\) happen to be \(n\)-ary predicates with \(n\ge2\), then \(x\) occurs only in their last argument places. “Nobody reads Aristotle and Plato” can be formalized as \(\lnot\exists x(Rxa\land Rxp)\), where \(a\) and \(p\) are name constants that stand for “Aristotle” and “Plato,” respectively. This formula cannot be written as \(U(Ra)(Rp)\). On the other hand, “There is nobody whom both Russell and Wittgenstein read,” that is, \(\lnot\exists x(Rrx\land Rwx)\) turns into \(U(Rr)(Rw)\), where the parentheses delineate the arguments of \(U\). Often, the expressions \(X\) and \(Y\) (in \(UXY\)) consist of predicates (and name constants) together  with combinators and other \(U\)s.