A key step of relational learning is testing whether a candidate hypothesis covers a given example. The covering test is equivalent to a Constraint Satisfaction Problem (CSP), which shows a phase transition in correspondence of critical values of some order parameters. This paper investigates the effects of the phase transition in the covering test on the complexity and feasibility of learning in first order logic languages. Several hundreds of artificial learning problems have been generated. FOIL and other learners have been applied to these problems. The experiments show the presence of a failure region, where all considered learners systematically fail to identify the target concept. Furthermore, the phase transition region behaves as an attractor for the learning search, whatever the target concept and the search strategy be. Interpretations of these findings are proposed and discussed.