Editing First-order logic (section)

===Tableaux method===
[[File:Prop-tableau-4.svg|thumb|right|150px|A tableaux proof for the [[propositional logic|propositional]] formula {{nowrap|1=((a ∨ ¬b) ∧  b) → a}}]]

{{Further | Method of analytic tableaux}}

Unlike the methods just described the derivations in the tableaux method are not lists of formulas. Instead, a derivation is a tree of formulas. To show that a formula A is provable, the tableaux method attempts to demonstrate that the negation of A is unsatisfiable. The tree of the derivation has <math>\lnot A</math> at its root; the tree branches in a way that reflects the structure of the formula. For example, to show that <math>C \lor D</math> is unsatisfiable requires showing that C and D are each unsatisfiable; this corresponds to a branching point in the tree with parent <math>C \lor D</math> and children C and D.