def propositional_prove(formula: str, assumptions: List[str]):
from propositions.syntax import Formula
from propositions.tautology import proof_or_counterexample, prove_in_model, evaluate, all_models
from propositions.tautology import prove_tautology, encode_as_formula
from propositions.proofs import InferenceRule
f = Formula.parse(formula)
if f is None:
print_error('Could not parse the given formula')
return None
collected_assumptions = []
for assumption in assumptions:
a = Formula.parse(assumption)
if a is None:
print_error('Could not parse the given assumption')
return None
collected_assumptions.append(a)
f = encode_as_formula(InferenceRule(collected_assumptions, f))
valid_proofs = []
for model in all_models(list(f.variables())):
if not evaluate(f, model):
valid_proofs.append(prove_in_model(f, model))
if len(valid_proofs) > 0:
print_result('Found valid proof:\n' + str(valid_proofs))
return True
print_result('No valid proof.\n' + str(proof_or_counterexample(f)))
return False
def test_prove_from_encoding(debug=True):
from propositions.some_proofs import prove_and_commutativity
from propositions.tautology import encode_as_formula
for p in [
DISJUNCTION_COMMUTATIVITY_PROOF,
prove_and_commutativity(), DISJUNCTION_RIGHT_ASSOCIATIVITY_PROOF
]:
for r in p.rules:
if (debug):
print("\nTesting prove_from_encoding on:", r)
pp = prove_from_encoding(r)
if (debug):
print("Got:", pp)
assert pp.statement == r
newrule = InferenceRule([], encode_as_formula(r))
assert pp.rules == {newrule, MP}
assert pp.is_valid(), offending_line(pp)