Definitions

A k-SAT formula is a Boolean expression in conjunctive normal form.

$$(A+B+C)(\overline{A}+\overline{B}) (\overline{B}+\overline{C}) (\overline{A}+B+\overline{C})$$ (1)

In this case, n=3, m=4, and k=3. For $k \geq 3$, this class of problems is known to be NP-hard.

When the partial truth assignment [A=1, C=1] is applied to formula 1, it becomes

$$(\textbf{T}+B+\textbf{T}) (\textbf{F}+\overline{B}) (\overline{B}+\textbf{F}) (\textbf{F}+B+\textbf{F})$$ (3)

and causes transitive implications B=0 and B=1. Since this is a contradiction, the partial truth assignment [A=1, C=1] cannot be part of any satisfying assignment.