Polysat: conflict resolution updates (#5534)

* variable elimination / saturation sketch

* conflict resolution updates

src/math/polysat/saturation.h

@@ -0,0 +1,58 @@
+/*++
+Copyright (c) 2021 Microsoft Corporation
+
+Module Name:
+
+    Polysat core saturation
+
+Author:
+
+    Nikolaj Bjorner (nbjorner) 2021-03-19
+    Jakob Rath 2021-04-6
+
+--*/
+#pragma once
+#include "math/polysat/conflict_core.h"
+
+namespace polysat {
+
+    class solver;
+    class constraint_manager;
+
+    class inference_engine {
+        friend class conflict_core;
+        solver* m_solver = nullptr;
+        void set_solver(solver& s) { m_solver = &s; }
+    protected:
+        solver& s() { return *m_solver; }
+        constraint_manager& cm();
+    public:
+        virtual ~inference_engine() {}
+        /** Try to apply an inference rule.
+         *  Derive new constraints from constraints containing the variable v (i.e., at least one premise must contain v).
+         *  Returns true if a new constraint was added to the core.
+         */
+        virtual bool perform(pvar v, conflict_core& core) = 0;
+    };
+
+    class inf_polynomial_superposition : public inference_engine {
+    public:
+        bool perform(pvar v, conflict_core& core) override;
+    };
+
+    // TODO: other rules
+    // clause_ref by_ugt_x();
+    // clause_ref by_ugt_y();
+    // clause_ref by_ugt_z();
+    // clause_ref y_ule_ax_and_x_ule_z();
+
+    /*
+     * TODO: we could resolve constraints in cjust[v] against each other to
+     * obtain stronger propagation. Example:
+     *  (x + 1)*P = 0 and (x + 1)*Q = 0, where gcd(P,Q) = 1, then we have x + 1 = 0.
+     * We refer to this process as narrowing.
+     * In general form it can rely on factoring.
+     * Root finding can further prune viable.
+     */
+
+}