Grammatical inference is concerned with the study of algorithms for learning automata and grammars from words. We propose some models for learning Nondeterministic Finite Automaton (NFA) of size k from samples of words of the language and words not belonging to the language we want to describe. To this end, we formulate the problem as a SAT model trying to reduce the size of generated SAT instances. We propose new models to generate even smaller SAT instances. We also suggest some techniques for breaking some symmetries, hence reducing the search space, and consequently, speeding-up solving. We also achieved some experimental comparisons and we analyze our various model improvements and over-constraint propositions. Compared to [1], our models are easier and faster to solve. Compare to the parallel solver of [2], we find some new bounds for some instances for which the minimal size of NFA is not known yet.