diff --git a/src/solve_algorithms.cpp b/src/solve_algorithms.cpp
index cd48e5d..a12c509 100644
--- a/src/solve_algorithms.cpp
+++ b/src/solve_algorithms.cpp
@@ -288,7 +288,7 @@ void SolveAlgorithm::detach() {
 			s->popRootLevel(s->rootLevel());
 			core_ = new LitVec();
 			for (LitVec::const_iterator it = path_->begin(); it != path_->end(); ++it) {
-				if (isSentinel(*it) || s->isTrue(*it) || *it == ctx_->stepLiteral() || !ctx_->varInfo(it->var()).input())
+				if (s->isTrue(*it) || *it == ctx_->stepLiteral())
 					continue;
 				core_->push_back(*it);
 				if (!s->pushRoot(*it)) {
diff --git a/tests/facade_test.cpp b/tests/facade_test.cpp
index 5b44897..d0ab78d 100644
--- a/tests/facade_test.cpp
+++ b/tests/facade_test.cpp
@@ -215,6 +215,33 @@ TEST_CASE("Facade", "[facade]") {
 		libclasp.prepare();
 		REQUIRE(libclasp.solve().unsat());
 	}
+
+	SECTION("testUnsatCore") {
+		config.solve.numModels = 0;
+		Clasp::Asp::LogicProgram& asp = libclasp.startAsp(config, true);
+		int expect = 0;
+		std::string prg;
+		SECTION("AssumeFalse") {
+			prg = "a.\n#assume{not a}.";
+			expect = -1;
+		}
+		SECTION("AssumeTrue") {
+			prg = "a :- b.\nb :- a.\n#assume{a}.";
+			expect = 1;
+		}
+		INFO(prg);
+		lpAdd(asp, prg.c_str());
+		libclasp.prepare();
+		REQUIRE(libclasp.solve().unsat());
+		const LitVec* core = libclasp.summary().unsatCore();
+		REQUIRE(core);
+		CHECK(core->size() == 1);
+		Potassco::LitVec out;
+		CHECK(asp.extractCore(*core, out));
+		CHECK(out.size() == 1);
+		CHECK(out[0] == expect);
+	}
+
 	SECTION("testComputeBrave") {
 		config.solve.numModels = 0;
 		config.solve.enumMode = EnumOptions::enum_brave;