# Automating Satisfiability Proofs for First-Order Logic

First-order logic can be used to aximatize essentially all of math, through set theory.

Goal: a procedure such that if is a first-order formula (or an enumerable sequence of formulas i.e. sequence where we can compute -the element for each ), then we can detect in finite amount of time the case when is unsatisfiable

Observations:

• to prove is valid, we show is unsatisfiable
• to show that is true in an axiomatization given as an enumerable sequence , we check that the sequence ; is unsatisfiable
• given a well-defined mathematical statement, we can detect in finite amount of time if this statement follows from a well-defined set of axioms