In symbolic regression with formal constraints, the conventional formulation of regression problem is extended with desired properties of the target model, like symmetry, monotonicity, or convexity. We present a genetic programming algorithm that solves such problems using a Satisfiability Modulo Theories solver to formally verify the candidate solutions. The essence of the method consists in collecting the counterexamples resulting from model verification and using them to improve search guidance. The method is exact: upon successful termination, the produced model is guaranteed to meet the specified constraints. We compare the effectiveness of the proposed method with standard constraint-agnostic machine learning regression algorithms on a range of benchmarks, and demonstrate that it outperforms them on several performance indicators.