diff --git a/ksmt-bitwuzla/src/main/kotlin/io/ksmt/solver/bitwuzla/KBitwuzlaContext.kt b/ksmt-bitwuzla/src/main/kotlin/io/ksmt/solver/bitwuzla/KBitwuzlaContext.kt
index f1999be24..5fb618e35 100644
--- a/ksmt-bitwuzla/src/main/kotlin/io/ksmt/solver/bitwuzla/KBitwuzlaContext.kt
+++ b/ksmt-bitwuzla/src/main/kotlin/io/ksmt/solver/bitwuzla/KBitwuzlaContext.kt
@@ -298,7 +298,9 @@ open class KBitwuzlaContext(val ctx: KContext) : AutoCloseable {
     }
 
     override fun close() {
+        if (isClosed) return
         isClosed = true
+
         sorts.clear()
         bitwuzlaSorts.clear()
 
diff --git a/ksmt-cvc5/src/main/kotlin/io/ksmt/solver/cvc5/KCvc5Context.kt b/ksmt-cvc5/src/main/kotlin/io/ksmt/solver/cvc5/KCvc5Context.kt
index 5edfa4f53..0368b6118 100644
--- a/ksmt-cvc5/src/main/kotlin/io/ksmt/solver/cvc5/KCvc5Context.kt
+++ b/ksmt-cvc5/src/main/kotlin/io/ksmt/solver/cvc5/KCvc5Context.kt
@@ -351,6 +351,7 @@ class KCvc5Context(
 
 
     override fun close() {
+        if (isClosed) return
         isClosed = true
 
         currentScopeExpressions.clear()
diff --git a/ksmt-test/src/test/kotlin/io/ksmt/test/CheckWithAssumptionsTest.kt b/ksmt-test/src/test/kotlin/io/ksmt/test/CheckWithAssumptionsTest.kt
index 162d82e05..a7e6ea033 100644
--- a/ksmt-test/src/test/kotlin/io/ksmt/test/CheckWithAssumptionsTest.kt
+++ b/ksmt-test/src/test/kotlin/io/ksmt/test/CheckWithAssumptionsTest.kt
@@ -38,6 +38,18 @@ class CheckWithAssumptionsTest {
     @Test
     fun testUnsatCoreGenerationCvc() = testUnsatCoreGeneration { KCvc5Solver(it) }
 
+    @Test
+    fun testTrivialUnsatCoreZ3() = testTrivialUnsatCore { KZ3Solver(it) }
+
+    @Test
+    fun testTrivialUnsatCoreBitwuzla() = testTrivialUnsatCore { KBitwuzlaSolver(it) }
+
+    @Test
+    fun testTrivialUnsatCoreYices() = testTrivialUnsatCore { KYicesSolver(it) }
+
+    @Test
+    fun testTrivialUnsatCoreCvc() = testTrivialUnsatCore { KCvc5Solver(it) }
+
     private fun testComplexAssumption(mkSolver: (KContext) -> KSolver<*>) = with(KContext()) {
         mkSolver(this).use { solver ->
             val a by bv32Sort
@@ -76,4 +88,15 @@ class CheckWithAssumptionsTest {
             assertTrue(e3 in core)
         }
     }
+
+    private fun testTrivialUnsatCore(mkSolver: (KContext) -> KSolver<*>) = with(KContext()) {
+        mkSolver(this).use { solver ->
+            val status = solver.checkWithAssumptions(listOf(falseExpr))
+            assertEquals(KSolverStatus.UNSAT, status)
+
+            val core = solver.unsatCore()
+            assertEquals(1, core.size)
+            assertTrue(falseExpr in core)
+        }
+    }
 }
diff --git a/ksmt-z3/src/main/kotlin/io/ksmt/solver/z3/KZ3Context.kt b/ksmt-z3/src/main/kotlin/io/ksmt/solver/z3/KZ3Context.kt
index 8ce96406e..f4eae36e9 100644
--- a/ksmt-z3/src/main/kotlin/io/ksmt/solver/z3/KZ3Context.kt
+++ b/ksmt-z3/src/main/kotlin/io/ksmt/solver/z3/KZ3Context.kt
@@ -261,6 +261,7 @@ class KZ3Context(
     }
 
     override fun close() {
+        if (isClosed) return
         isClosed = true
 
         z3Expressions.keys.decRefAll()
diff --git a/ksmt-z3/src/main/kotlin/io/ksmt/solver/z3/KZ3Solver.kt b/ksmt-z3/src/main/kotlin/io/ksmt/solver/z3/KZ3Solver.kt
index d75ca3d37..f8bdfa43f 100644
--- a/ksmt-z3/src/main/kotlin/io/ksmt/solver/z3/KZ3Solver.kt
+++ b/ksmt-z3/src/main/kotlin/io/ksmt/solver/z3/KZ3Solver.kt
@@ -25,8 +25,12 @@ import kotlin.time.DurationUnit
 open class KZ3Solver(private val ctx: KContext) : KSolver<KZ3SolverConfiguration> {
     private val z3Ctx = KZ3Context(ctx)
     private val solver = createSolver()
+
     private var lastCheckStatus = KSolverStatus.UNKNOWN
     private var lastReasonOfUnknown: String? = null
+    private var lastModel: KZ3Model? = null
+    private var lastUnsatCore: List<KExpr<KBoolSort>>? = null
+
     private var currentScope: UInt = 0u
 
     @Suppress("LeakingThis")
@@ -104,7 +108,20 @@ open class KZ3Solver(private val ctx: KContext) : KSolver<KZ3SolverConfiguration
         ctx.ensureContextMatch(assumptions)
 
         val z3Assumptions = with(exprInternalizer) {
-            LongArray(assumptions.size) { assumptions[it].internalizeExpr() }
+            LongArray(assumptions.size) {
+                val assumption = assumptions[it]
+
+                /**
+                 * Assumptions are trivially unsat and no check-sat is required.
+                 * */
+                if (assumption == ctx.falseExpr) {
+                    lastUnsatCore = listOf(ctx.falseExpr)
+                    lastCheckStatus = KSolverStatus.UNSAT
+                    return KSolverStatus.UNSAT
+                }
+
+                assumption.internalizeExpr()
+            }
         }
 
         solver.updateTimeout(timeout)
@@ -116,19 +133,28 @@ open class KZ3Solver(private val ctx: KContext) : KSolver<KZ3SolverConfiguration
         require(lastCheckStatus == KSolverStatus.SAT) {
             "Model are only available after SAT checks, current solver status: $lastCheckStatus"
         }
-        val model = solver.model
 
-        KZ3Model(model, ctx, z3Ctx, exprInternalizer)
+        val model = lastModel ?: KZ3Model(
+            model = solver.model,
+            ctx = ctx,
+            z3Ctx = z3Ctx,
+            internalizer = exprInternalizer
+        )
+        lastModel = model
+
+        model
     }
 
     override fun unsatCore(): List<KExpr<KBoolSort>> = z3Try {
         require(lastCheckStatus == KSolverStatus.UNSAT) { "Unsat cores are only available after UNSAT checks" }
 
-        val unsatCore = solver.solverGetUnsatCore()
-
-        with(exprConverter) {
-            unsatCore.map { trackedAssertions.get(it) ?: it.convertExpr() }
+        val unsatCore = lastUnsatCore ?: with(exprConverter) {
+            val solverUnsatCore = solver.solverGetUnsatCore()
+            solverUnsatCore.map { trackedAssertions.get(it) ?: it.convertExpr() }
         }
+        lastUnsatCore = unsatCore
+
+        unsatCore
     }
 
     override fun reasonOfUnknown(): String = z3Try {
@@ -173,6 +199,8 @@ open class KZ3Solver(private val ctx: KContext) : KSolver<KZ3SolverConfiguration
     private fun invalidateSolverState() {
         lastReasonOfUnknown = null
         lastCheckStatus = KSolverStatus.UNKNOWN
+        lastModel = null
+        lastUnsatCore = null
     }
 
     private inline fun z3TryCheck(body: () -> KSolverStatus): KSolverStatus = try {