Get resolution working for real!

resolution.py

@@ -148,6 +148,14 @@ True
 False
 """
 
+false_clause: Clause = FSet()
+"""
+The clause which represents the logical condition False
+
+i.e. the empty clause
+"""
+
+
 def next_generation(
     previous_generations: KnowledgeBase_,
     current_generation: KnowledgeBase_,
@@ -204,6 +212,45 @@ def next_generation(
 	"""
 	return fset(*derive(current_generation), *derive2(current_generation, previous_generations))
 
+def derives_false(
+	knowledge_base: KnowledgeBase,
+	previous_generations: KnowledgeBase = FSet(),
+) -> bool:
+	"""
+	Determine if it is possible to derive false from a given knowledge base.
+
+	Uses any number of generations of resolution via `next_generation()` to find a
+	generation which contains the `false_clause`, indicating that the original knowledge
+	base (and all subsiquent generations) are contradictory.
+
+	`previous_generations` may be set if the current knowledge base was derived from some
+	other series of clauses using `derive()`.
+
+	>>> derives_false(fset(
+	...     fset( IRNeg(IRProp('animal', (IRProp('Kim'),)))                              ),
+	...     fset( IRNeg(IRProp('dog', (IRVar('x0'),))), IRProp('animal', (IRVar('x0'),)) ),
+	...     fset( IRNeg(IRProp('cat', (IRVar('x1'),))), IRProp('animal', (IRVar('x1'),)) ),
+	...     fset( IRProp('dog', (IRProp('Kim'),))                                        ),
+	... ))
+	True
+
+	>>> derives_false(fset(
+	...     fset( IRNeg(IRProp('animal', (IRProp('Kim'),)))                              ),
+	...     fset( IRNeg(IRProp('dog', (IRVar('x0'),))), IRProp('animal', (IRVar('x0'),)) ),
+	...     fset( IRNeg(IRProp('cat', (IRVar('x1'),))), IRProp('animal', (IRVar('x1'),)) ),
+	... ))
+	False
+	"""
+	if false_clause in knowledge_base:
+		return True
+	elif len(knowledge_base) == 0:
+		return False
+	else:
+		return derives_false(
+			next_generation(previous_generations, knowledge_base),
+			knowledge_base | previous_generations
+		)
+
 
 if __name__ == '__main__':
 	import doctest