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Two CNF formulas are called ucp-equivalent, if they behave in the same waywith respect to the unit clause propagation (UCP). A formula is calleducp-irredundant, if removing any clause leads to a formula which is notucp-equivalent to the original one. As a consequence of known results, theratio of the size of a ucp-irredundant formula and the size of a smallestucp-equivalent formula is at most $n^2$, where $n$ is the number of thevariables. We demonstrate an example of a ucp-irredundant formula for asymmetric definite Horn function which is larger than a smallest ucp-equivalentformula by a factor $\Omega(n/\ln n)$ and, hence, a general upper bound on theabove ratio cannot be smaller than this.

On CNF formulas irredundant with respect to unit clause propagation