  In theorem proving, the task of selecting useful premises from a large
library to unlock the proof of a given conjecture is crucially important. This
presents a challenge for all theorem provers, especially the ones based on
language models, due to their relative inability to reason over huge volumes of
premises in text form. This paper introduces Thor, a framework integrating
language models and automated theorem provers to overcome this difficulty. In
Thor, a class of methods called hammers that leverage the power of automated
theorem provers are used for premise selection, while all other tasks are
designated to language models. Thor increases a language model's success rate
on the PISA dataset from $39\%$ to $57\%$, while solving $8.2\%$ of problems
neither language models nor automated theorem provers are able to solve on
their own. Furthermore, with a significantly smaller computational budget, Thor
can achieve a success rate on the MiniF2F dataset that is on par with the best
existing methods. Thor can be instantiated for the majority of popular
interactive theorem provers via a straightforward protocol we provide.
