A family of satisfiable benchmark instances in conjunctive normal form is introduced. The instances are constructed by transforming a random regular graph into a system of linear equations followed by clausification. Schemes for introducing nonlinearity to the instances are developed, making the instances suitable for benchmarking solvers with equivalence reasoning techniques. An extensive experimental evaluation shows that state-of-the-art solvers scale exponentially in the instance size. Compared with other well-known families of satisfiable benchmark instances, the present instances are among the hardest.