This new paper A Lower Bound for Boolean Satisfiability on Turing Machines by Hsieh asserts an exponential lower bound for a TM time complexity on a problem of finding whether a solution exists to a conjunction of boolean formulas. obviously this problem is not in NP, or it would be a P≠NP proof. But the paper does not give its known complexity class.
What time complexity class is this problem of finding solutions to conjunctions of boolean formulas in?
Also looking for any other context wrt known theory to place this paper result in, i.e. How does it mesh with other known results etc.