The standard NP-hard SAT problem is the problem of Boolean satisfiability of conjunctions of clauses, where clauses are disjunctions of literals.
I am interested in the problem of the Boolean satisfiability of conjunctions of exclusive clauses, where exclusive clauses is an exclusive disjunction of multiple literals. By exclusive disjunction of literals, I do not mean $l_1 \oplus \ldots \oplus l_n$, which would require an odd number of literals to be true; I mean that the clause is true iff exactly one literal of the clause is true. (Of course, the literals can be positive or negative, i.e., $l = x$ or $l = \neg x$.)
Is there a reference to justify that it is also NP-hard, or a straightforward reduction to prove it?
I had a look in Wikipedia and in the Garey-Johnson, to no avail. Thanks in advance for your help!