Abstract: A system and method for increasing the speed of operation of a theorem prover relating to program verification using adaptive pattern matching technique is disclosed. Source code in a specific programming language is converted to one or more formulae, each representing a specific reformulation of the source code that facilitates program verification. Each formula derived from the source code is converted into an E-graph which is a particular type of a directed acyclic graph having leaf nodes and interior nodes. Some of the nodes of an E-graph may be related to other nodes through equivalence relationships. Equivalence relationships between a group of nodes is stored in a data structure called an equivalence class. A collection of rules defining the grammar of the programming language is stored in an axiom database. Rules and conjectures can dynamically be added to the axiom database. Each rule or conjecture to be tested is converted into a pattern.