diff --git a/hipaasat/solvers.py b/hipaasat/solvers.py
new file mode 100644
index 0000000..9944cbc
--- /dev/null
+++ b/hipaasat/solvers.py
@@ -0,0 +1,51 @@
+from abc import ABC, abstractmethod
+import sys
+
+from .cnf import check_consistency, Clause, CNF, Literal, simplify
+
+from typing import Optional, Tuple
+
+class SATSolver(ABC):
+    """Abstract class that solves boolean satisfyibility problems."""
+
+    @abstractmethod
+    def solve(self, cnf: CNF) -> Tuple[bool, Optional[CNF]]:
+        ...
+
+class DPLL(SATSolver):
+    """Davis–Putnam–Logemann–Loveland (DPLL) boolean satisfyiblity solver."""
+
+    def solve(self, cnf: CNF) -> Tuple[bool, Optional[CNF]]:
+        consistent = check_consistency(cnf)
+        if consistent is not None:
+            return consistent, cnf
+        simplified_cnf = simplify(cnf)
+        if simplified_cnf is None:
+            return False, cnf
+        consistent = check_consistency(simplified_cnf)
+        if consistent is not None:
+            return consistent, cnf
+
+        # Grab unassigned variable from shortest clause
+        shortest_clause = self._find_shortest_nonempty_clause(cnf)
+        assert shortest_clause
+        lit = self._get_unassigned_literal(shortest_clause)
+
+        solved, result_cnf = self.solve(cnf.assign(lit.name, True))
+        if not solved:
+            solved, result_cnf = self.solve(cnf.assign(lit.name, False))
+        
+        return solved, result_cnf
+
+    def _find_shortest_nonempty_clause(self, cnf: CNF) -> Optional[Clause]:
+        shortest_clause = None
+        shortest_clause_length = sys.maxsize # hopefully there's not a clause with 2^32 or 2^64 literals...
+        for c in cnf:
+            if c.unassigned_literal_count() < shortest_clause_length and c.unassigned_literal_count() > 0:
+                shortest_clause = c
+                shortest_clause_length = c.unassigned_literal_count()
+        return shortest_clause
+
+    def _get_unassigned_literal(self, clause: Clause) -> Literal:
+        literals = clause.get_unassigned_literals()
+        return literals[0]
diff --git a/tests/test_dpll.py b/tests/test_dpll.py
new file mode 100644
index 0000000..49b1c11
--- /dev/null
+++ b/tests/test_dpll.py
@@ -0,0 +1,151 @@
+import pytest
+
+from hipaasat.cnf import CNF, Clause, ClauseType, Literal
+from hipaasat.solvers import DPLL
+
+def test_single_literal():
+    solver = DPLL()
+    cnf = CNF([
+        Clause(ClauseType.OR, [
+            Literal("test")
+        ]),
+    ])
+    solved, result_cnf = solver.solve(cnf)
+    assert solved
+    assert result_cnf.assigned_literal_count() == result_cnf.unique_literal_count()
+
+def test_single_literal_multiple_clauses():
+    solver = DPLL()
+    cnf = CNF([
+        Clause(ClauseType.OR, [
+            Literal("test")
+        ]),
+        Clause(ClauseType.OR, [
+            Literal("test")
+        ]),
+        Clause(ClauseType.OR, [
+            Literal("test")
+        ]),
+    ])
+    solved, result_cnf = solver.solve(cnf)
+    assert solved
+    assert result_cnf.assigned_literal_count() == result_cnf.unique_literal_count()
+
+def test_single_literal_multiple_clauses_unsolvable():
+    solver = DPLL()
+    cnf = CNF([
+        Clause(ClauseType.OR, [
+            Literal("test")
+        ]),
+        Clause(ClauseType.OR, [
+            Literal("test", negated=True)
+        ]),
+        Clause(ClauseType.OR, [
+            Literal("test")
+        ]),
+    ])
+    solved, _ = solver.solve(cnf)
+    assert not solved
+
+def test_multiple_literals_single_clause():
+    solver = DPLL()
+    cnf = CNF([
+        Clause(ClauseType.OR, [
+            Literal("test"), Literal("test2", negated=True), Literal("test3")
+        ]),
+    ])
+    solved, result_cnf = solver.solve(cnf)
+    assert solved
+    assert result_cnf.assigned_literal_count() == 1
+
+def test_multiple_literals_multiple_clauses_1():
+    solver = DPLL()
+    cnf = CNF([
+        Clause(ClauseType.OR, [
+            Literal("a", negated=True), Literal("b"), Literal("c"),
+        ]),
+        Clause(ClauseType.OR, [
+            Literal("a"), Literal("c"), Literal("d"),
+        ]),
+        Clause(ClauseType.OR, [
+            Literal("a"), Literal("c"), Literal("d", negated=True),
+        ]),
+        Clause(ClauseType.OR, [
+            Literal("a"), Literal("c", negated=True), Literal("d"),
+        ]),
+        Clause(ClauseType.OR, [
+            Literal("a"), Literal("c", negated=True), Literal("d", negated=True),
+        ]),
+        Clause(ClauseType.OR, [
+            Literal("b", negated=True), Literal("c", negated=True), Literal("d"),
+        ]),
+        Clause(ClauseType.OR, [
+            Literal("a", negated=True), Literal("b"), Literal("c", negated=True),
+        ]),
+        Clause(ClauseType.OR, [
+            Literal("a", negated=True), Literal("b", negated=True), Literal("c")
+        ]),
+    ])
+    solved, result_cnf = solver.solve(cnf)
+    assert solved
+    assert result_cnf.assigned_literal_count() == result_cnf.unique_literal_count()
+    
+    a = result_cnf.get_literal("a")
+    b = result_cnf.get_literal("b")
+    c = result_cnf.get_literal("c")
+    d = result_cnf.get_literal("d")
+
+    assert a and a.assignment == True
+    assert b and b.assignment == True
+    assert c and c.assignment == True
+    assert d and d.assignment == True
+
+def test_multiple_literals_multiple_clauses_2():
+    solver = DPLL()
+    cnf = CNF([
+        Clause(ClauseType.OR, [
+            Literal("lib-1"), Literal("lib-2"), Literal("prog-1", negated=True),
+        ]),
+        Clause(ClauseType.OR, [
+            Literal("lib-2"), Literal("prog-2", negated=True),
+        ]),
+        Clause(ClauseType.OR, [
+            Literal("python-2"), Literal("lib-1", negated=True),
+        ]),
+        Clause(ClauseType.OR, [
+            Literal("python-3"), Literal("lib-2", negated=True),
+        ]),
+        Clause(ClauseType.OR, [
+            Literal("python-3", negated=True)
+        ]),
+        Clause(ClauseType.OR, [
+            Literal("prog-1"), Literal("prog-2"),
+        ]),
+        Clause(ClauseType.AT_MOST_ONE, [
+            Literal("prog-1"), Literal("prog-2"),
+        ]),
+        Clause(ClauseType.AT_MOST_ONE, [
+            Literal("lib-1"), Literal("lib-2"),
+        ]),
+        Clause(ClauseType.AT_MOST_ONE, [
+            Literal("python-2"), Literal("python-3"),
+        ]),
+    ])
+
+    solved, result_cnf = solver.solve(cnf)
+    assert solved
+    assert result_cnf.assigned_literal_count() == result_cnf.unique_literal_count()
+
+    prog1 = result_cnf.get_literal("prog-1")
+    prog2 = result_cnf.get_literal("prog-2")
+    lib1 = result_cnf.get_literal("lib-1")
+    lib2 = result_cnf.get_literal("lib-2")
+    python2 = result_cnf.get_literal("python-2")
+    python3 = result_cnf.get_literal("python-3")
+
+    assert prog1 and prog1.assignment == True
+    assert prog2 and prog2.assignment == False
+    assert lib1 and lib1.assignment == True
+    assert lib2 and lib2.assignment == False
+    assert python2 and python2.assignment == True
+    assert python3 and python3.assignment == False
diff --git a/tests/test_hipaasat.py b/tests/test_hipaasat.py
deleted file mode 100644
index 01c2d71..0000000
--- a/tests/test_hipaasat.py
+++ /dev/null
@@ -1,5 +0,0 @@
-from hipaasat import __version__
-
-
-def test_version():
-    assert __version__ == '0.1.0'