The error in Jan von Platos presentation (Was: Minimal Logics in the 2020's: A Meteoric Rise)

The sad news is, the book is only
worth some fire wood.
Plato (p. 83 of Elements of Logical Reasoning
Interestingly the book uses non-classical
logic, since it says:
 > Sequent calculus offers a good possibility for
 > exhaustive proof search in propositional logic:
 > We can check through all the possibilities for
 > malking a derivation. If none of them worked,
 > i.e., if each had at least one branch in which
 > no rule applied and no initial sequent was reached,
 > the given sequent is underivable. The
 > symbol |/-, is used for underivability.
And then it has unprovable:
c. |/- A v ~A
d. |/- ~~A => A
But mostlikely the book has a blind spot, some
serious errors, or totally unfounded claims, since
for example with such a calculus, the unprovability
of Peirce’s Law cannot be shown so easily.
Exhaustive proof search will usually not terminate.
There are some terminating calculi, like Dyckhoffs
LJT, but a naive calculus based on Gentzens take
will not terminate.