Implied Clause and Resolvent
Here is a counterexample:
$$
(a \lor y \lor s) \land (\overline{y} \lor b \lor z) \land (\overline{z} \lor c \lor d) \land (\overline{s} \lor b \lor t) \land (\overline{t} \lor c \lor d).
$$
This formula implies $a \lor b \lor c \lor d$, but only the five listed 3-clauses, no two of which resolve to $a\lor b\lor c\lor d$.