Detecting equivalent propositional variables in SAT-solver

Clauses added to SAT-solver commonly contains cycles, like [¬p ∨ q, ¬q ∨ p] or [¬p ∨ q, ¬q ∨ r, ¬r ∨ s, ¬s ∨ p]. Such cycles correspond to effect equivalence constraints, and all variables on such a cycle must have the same value. The SAT-solver could detect such situations and collapse all variables on a cycle. Currently, there is some infrastructure for collapsing variables (there is `SameAs` constructor in the type representing values of propositional variables) that can be used.

It seems that cycles with different polarity of variables like [p ∨ q, ¬p ∨ ¬q] don't appear in the wild (I didn't find any), so we don't have to care about them.

Begin at the SAT-solver entry point and inspect the existing SameAs constructor in the value representation. Trace how implication clauses are processed, then determine how equivalent-variable cycles should be collapsed and how completion can be verified for both direct and multi-step cycles.

Written by the indexing model from the issue text.