If in all satisfying assignments all pair of variables can take all possible values is this tautology?
The VC dimension of a set $S \in \{0,1\}^n$ is the maximal $d$ such that for all $i_1 &lt; \cdots &lt; i_d \in \{1,\ldots,n\}$ and all $b_1,\ldots,b_d \in \{0,1\}$, there is a point $x \in S$ such that $x_{i_1} = b_1,\ldots,x_{i_d} = b_d$. Your condition states that the VC dimension of the set of satisfying assignment of a formula is at least $2$. The formula is a tautology if the VC dimension is $n$. There are sets of arbitrary VC dimension, so even if you replace pairs by larger tuples, your conclusion would still be wrong.