Formal software verification is an important task for ensuring software correctness, especially in safety-critical systems. One method of formal verification is automated theorem proving, where one defines their program as a set of axioms and its correctness criteria as conjectures. We investigated the suitability of Vampire, an automated theorem prover, for formal verification by analyzing the logical foundations and performing case studies. In these case studies, we implemented Selection Sort and a Key-Value Store to observe what could be represented and proven. We were unable to prove the correctness of Selection Sort, but were able to prove most properties of a Key-Value Store. We discuss the capabilities and limitations of Vampire for formal software verification, namely that it is able to prove many properties of the functions we defined, unless they are heavily reliant on inductive definitions or too general with respect to the axioms. We believe that Vampire's inductive capabilities are currently insufficient for our use case. We reflect on the experience of using Vampire from the perspective of the average computer scientist and give suggestions for further documentation. We then discuss related work, including using Isabelle, another ATP and proof assistant, to reason about sorting algorithms and a Key-Value Store. Finally, we give suggestions for future work, such as rewriting the Key-Value Store in SMT-LIB, a language used as input for SMT solvers.