  Given the intractably large size of the space of proofs, any model that is
capable of general deductive reasoning must generalize to proofs of greater
complexity. Recent studies have shown that large language models (LLMs) possess
some abstract deductive reasoning ability given chain-of-thought prompts.
However, they have primarily been tested on proofs using modus ponens or of a
specific size, and from the same distribution as the in-context examples. To
measure the general deductive reasoning ability of LLMs, we test on a broad set
of deduction rules and measure their ability to generalize to more complex
proofs from simpler demonstrations from multiple angles: depth-, width-, and
compositional generalization. To facilitate systematic exploration, we
construct a new synthetic and programmable reasoning dataset that enables
control over deduction rules and proof complexity. Our experiments on four LLMs
of various sizes and training objectives show that they are able to generalize
to compositional proofs. However, they have difficulty generalizing to longer
proofs, and they require explicit demonstrations to produce hypothetical
subproofs, specifically in proof by cases and proof by contradiction.
