Techniques are presented for identifying blockable subsets. Blockable subsets can increase the efficiency by which solutions to a constraint set representation (CSR) can be found. Nodes of a blockable subset can be marked as "blocked" and learning or implication procedures, used as part of a CSR solving process, can be designed to skip nodes marked as blocked. The identification of a particular blockable subset is typically associated with certain conditions being true. If and when the conditions no longer hold, the nodes of the blockable subset need to be unblocked. One type of blockable subset can be identified during the operation of an implication engine (IE) by a technique called justified node blocking (JNB). Another type of blockable subset can be identified by a technique called pivot node learning (PNL). PNL can be applied in-between application of an IE and application of case-based learning.