How can I express a chain of OR operations in an ILP, given that each operand is an inequality between two binary variables? I have asked a similar question here: Chain of Boolean ORs. In that question, I asked specifically about the scenario where the variable on the left-hand sides is always the same.
For this question, I am interested in the more general case. For example, $$(x_1 \leq x_3) \textrm{ OR } (x_2 \leq x_3) \textrm{ OR } (x_1 \leq x_4),$$ in which the left-hand sides nor the right-hand sides are always the same.
A boolean OR of just two variables can be expressed by introducing an additional variable and modifying the constraints appropriately. But how can we model the general case described above?