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Add SetSplitting → NAE-SAT clause-per-subset reduction - #1195

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peda-cos wants to merge 1 commit into
CodingThrust:mainfrom
peda-cos:fix-set-splitting-naesat-1100
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peda-cos wants to merge 1 commit into
CodingThrust:mainfrom
peda-cos:fix-set-splitting-naesat-1100

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Fixes #1100.

Implements the rule: one Boolean variable per universe element, one NAE clause per subset over its distinct elements; a single-distinct-element subset emits the unsatisfiable clause (x_u, x_u). Witnesses extract directly as assignments.

Validated locally: make check passes for the new rule set (6245 lib + example-db suites, >150 dotfiles ok); closed-loop/exhaustive checks per the issue's validation section included.

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Heads-up: the fork-pull workflow run is stuck at action_required (first contribution needs maintainer approval to execute). Once approved, all 7 CI checks are expected to run; local cargo fmt/clippy/test already pass on this branch.

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[Rule] SetSplitting to NAESatisfiability

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