Let us assume we have a program of size $k$ that solves any instance of SAT of size $N < n$ in $poly(n)$ time. For every input of size $N \geq n$ the program is allowed not to solve it.
Then we might imagine an infinite sequence of programs of sizes $k_0 \leq k_1 \leq\ ...\ \leq k_i\leq\ ...$ which solves SAT up to the size $n_0<n_1<\ ...\ < n_i<\ ...$ in $poly(n):n<n_i$ time. And if an instance is solvable by $i^{th}$ program in $T_i(n)$ time, it's also solvable by $i+1^{th}$ program in at most $(1+1/\Omega(poly(n))T_i(n)$ time.
Also we assume the sequence is unbounded and no better sequence exists. $\forall m\in\mathbb N\ \exists i\in\mathbb N: k_i>m.$
Does the last statement mean $\mathsf{P\subsetneq NP}$? And what if we put other complexity classes and functions there?
P.S. I said time in first statement but regarding other complexity classes we might put space there too.