  We introduce a refutation graph calculus for classical first-order predicate
logic, which is an extension of previous ones for binary relations. One reduces
logical consequence to establishing that a constructed graph has empty
extension, i. e. it represents bottom. Our calculus establishes that a graph
has empty extension by converting it to a normal form, which is expanded to
other graphs until we can recognize conflicting situations (equivalent to a
formula and its negation).
