Let $p$ be a $k$-ary lattice term. A $k$-pointed lattice $L=(L;\vee ,\wedge$, $d_1,...,d_k)$ will be called a $p$-lattice (or a test lattice if $p$ is not specified), if $(L;\vee ,\wedge )$ is generated by $\{d_1,...,d_k\}$ and, in addition, for any $k$-ary lattice term $q$ satisfying $p(d_1,...,d_k)$$\le$$q(d_1$, $...,d_k)$ in $L$, the lattice identity $p\le q$ holds in all lattices. In an elementary visual way, we construct a finite $p$-lattice $L\left(p\right)$ for each $p$. If $p$ is a canonical lattice term,...