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The inference rules work on <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\beta \\eta $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u03b2<\/mml:mi>\n                    <mml:mi>\u03b7<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-equivalence classes of <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\lambda $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03bb<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-terms and rely on higher-order unification to achieve refutational completeness. We implemented the calculus in the Zipperposition prover and evaluated it on TPTP and Isabelle benchmarks. 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