  Consider a following NP-problem DOUBLE CLIQUE (abbr.: CLIQ$_{2}$): Given a
natural number $k>2$ and a pair of two disjoint subgraphs of a fixed graph $G$
decide whether each subgraph in question contains a $k$-clique. I prove that
CLIQ$_{2}$ can't be solved in polynomial time by a deterministic TM, which
infers $\mathbf{P}\neq \mathbf{NP}$. This proof upgrades the well-known proof
of polynomial unsolvability of the partial result with respect to analogous
monotone problem CLIQUE (abbr.: CLIQ) as well as my previous presentation that
used appropriate 3-value semantics. Note that problem CLIQ$_{2}$ is not
monotone and appears more complex than just iterated CLIQ, as the required
subgraphs are mutually dependent.
