  We study the computational complexity of satisfiability problems for classes
of simple finite height (ortho)complemented modular lattices $L$. For single
finite $L$, these problems are shown tobe $\mc{NP}$-complete; for $L$ of height
at least $3$, equivalent to a feasibility problem for the division ring
associated with $L$. Moreover, it is shown that the equational theory of the
class of subspace ortholattices as well as endomorphism *-rings (with
pseudo-inversion) of finite dimensional Hilbert spaces is complete for the
complement of the Boolean part of the nondeterministic Blum-Shub-Smale model of
real computation without constants. This results extends to the category of
finite dimensional Hilbert spaces, enriched by pseudo-inversion.
