  We present the problem of selecting relevant premises for a proof of a given
statement. When stated as a binary classification task for pairs (conjecture,
axiom), it can be efficiently solved using artificial neural networks. The key
difference between our advance to solve this problem and previous approaches is
the use of just functional signatures of premises. To further improve the
performance of the model, we use dimensionality reduction technique, to replace
long and sparse signature vectors with their compact and dense embedded
versions. These are obtained by firstly defining the concept of a context for
each functor symbol, and then training a simple neural network to predict the
distribution of other functor symbols in the context of this functor. After
training the network, the output of its hidden layer is used to construct a
lower dimensional embedding of a functional signature (for each premise) with a
distributed representation of features. This allows us to use 512-dimensional
embeddings for conjecture-axiom pairs, containing enough information about the
original statements to reach the accuracy of 76.45% in premise selection task,
only with simple two-layer densely connected neural networks.
