Human languages can express opposite propositions by means of the negative operator "not," which turns affirmative sentences into negative ones. Psycholinguistic research has indicated that negative meanings are formed by transiently reducing the access to mental representations of negated conceptual information. Neuroimaging studies have corroborated these findings, showing reduced activation of concept-specific embodied neural systems by negative versus affirmative sentences. This "disembodiment effect" of sentential negation should have two distinct consequences: first, the embodied systems should be computationally more free to support concurrent tasks when processing negative than affirmative sentences; second, the computational interference should only be reduced when there is a strict semantic congruency between the negated concept and the referent targeted by concurrent tasks. We tested these two predictions in two complementary experiments involving the comprehension of action-related sentences and kinematic measurements of its effects on concurrent, congruent actions. Sentences referred to actions involving either proximal or distal arm musculature. In experiment 1, requiring a proximal arm movement, we found interference reduction for negative proximal sentences. In experiment 2, requiring a distal arm movement, we found interference reduction for negative distal sentences. This dissociation provides the first conclusive evidence in support of a disembodiment theory of negation. We conclude that the computational cost resulting from the insertion of an additional lexical item ("not") in negative sentences is compensated by solely storing a concept in affirmative form in semantic memory, since its negative counterpart can be produced by transiently reducing the access to such stored semantic information.