Incorrect type inferred with -fwarn-missing-signatures and a type class

The inferred type using -fwarn-missing-signatures and a type class is too general for top-level values.

Here is a simplified example:

{-# OPTIONS -Wall #-}

class C a where c :: a

instance C Int where c = 37

def = c

use :: Int
use = def

The inferred type reported by GHCi when -fwarn-missing-signatures is enabled is:

Ex.hs:7:0:
    Warning: Definition but no type signature for `def'
             Inferred type: def :: a

The most general possible type here is C a => a. When asking GHCi for the type of def, it reports Int.

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