Tree automata turned out to be a very convenient framework for modeling and proving properties on infinite systems like communication protocols, Java programs and also in the context of XML programming. Unfortunately, these works are not always supported by efficient verification and validation tools. This paper investigates the use of two SAT solvers --- minisat and picosat--- to evaluate queries over tree automata with global equality and disequality constraints (TAGED s for short). Unlike general tree automata, TAGED s allow to express constraints useful for e.g., evaluating queries over XML documents, like "in the document, two nodes do not have the same key". These queries being based on the membership problem which is NP-complete for TAGEDs, we propose an efficient SAT encoding of the membership problem for TAGEDs and we show its correctness and soundness. The paper reports on the experimental results, and implementation details are given.