Conventional unit tests validate single input-output pairs, leaving most inputs of an execution path untested. Property-based testing addresses this shortcoming by generating multiple inputs satisfying properties but requires significant manual effort to define properties and their constraints. We propose a semantics-based approach that automatically transforms unit tests into property-based tests by extracting specifications from implementations via single-path symbolic analysis. We demonstrate this approach through Teralizer, a prototype for Java that transforms JUnit tests into property-based jqwik tests. Unlike prior work that generalizes from input-output examples, Teralizer derives specifications from program semantics. We evaluated Teralizer on three progressively challenging datasets. On EvoSuite-generated tests for EqBench and Apache Commons utilities, Teralizer improved mutation scores by 1-4 percentage points. Generalization of mature developer-written tests from Apache Commons utilities showed only 0.05-0.07 percentage points improvement. Analysis of 632 real-world Java projects from RepoReapers highlights applicability barriers: only 1.7% of projects completed the generalization pipeline, with failures primarily due to type support limitations in symbolic analysis and static analysis limitations in our prototype. Based on the results, we provide a roadmap for future work, identifying research and engineering challenges that need to be tackled to advance the field of test generalization. Artifacts available at: https://doi.org/10.5281/zenodo.17950381