I have a very large number (670 billion) of systems of inequalities of the form:

$C_1 - C_2 < C_4 - C_3 \wedge C_3 - C_2 < C_5 - C_3 \wedge ...$

where the $C_i > 0$. Ie. each system of inequalities consists of the comparisons of differences between positive real numbers which must all be true at the same time.

Now I want to find the subset of systems which are consistent, ie. there exists a choice of $C_i$ such that all inequalities are satisfied.

Given the the large number of systems this method would have to be automated. Therefore my question is:

Is there an algorithm to decide whether a system of inequalities of the form described above is consistent?