Let$\mathbf{CNFH}=\left\{\right\}$ is a satisfiable CNF-formula where each clause contains any number of literals, but at most one negated literal}. Show that $\mathbf{CNFH}?\mathbf{P}$.

$⟨\phi ⟩$Consider the following algorithm which can be used for this language:

N= "On input where $\phi$ a Boolean formula in CNF"

If$\phi${ don't consists a unit clause} assume every literals.

Repetition performed until these exists no new $(~x)$unit clause:

If an empty clause is existing inrole="math" localid="1663228645556" $\phi$ reject.

Dependability can be viewed as:

Consider that ${\text{CNF}}_2\in \text{P}$.

Consider one more situation of $\varphi$that will be belonging to some other variable.

Consider another situation ${\text{CNF}}_3\in \text{P}$.

Consider first situation of $\varphi$and consider it belongs to some p and if there is any$p$ then reject. Consider one more situation of $\varphi$that will be belonging to some other variable, let's say $q$and$r$ here situation will rejected if there is any$-q$ otherwise accepted.

Similarly, this situation will be held true for$CN{F}_H\in P$ .