We present a broad empirical study of state-of-the-art LLMs and LRMs (Large Reasoning Models) on ProofGrid, a new battery of challenging but tractable logical inference tasks that form a domain-independent test of constraint-based reasoning. The tasks include proof writing and proof checking across propositional and equational logic. We also introduce two novel tasks: proof inpainting and proof gap-filling. Solving these problems requires tracking the global structure of a mathematical argument, writing hierarchical subproofs, maintaining coherence across nested assumptions, performing complex case analyses, applying inference rules, reasoning about identity and term rewriting, and reasoning about proofs themselves. Our experiments reveal impressive performance by top-tier models but also systematic failure modes. Along with the benchmarks, we release a new data resource comprising over 10K formal deduction problems and corresponding proofs.