def prove_tautology(tautology: Formula) -> Proof:
"""Proves the given predicate-logic tautology.
Parameters:
tautology: predicate-logic tautology to prove.
Returns:
A valid proof of the given predicate-logic tautology from the axioms
`PROPOSITIONAL_AXIOMATIC_SYSTEM_SCHEMAS` via only assumption lines
and MP lines.
"""
assert is_propositional_tautology(tautology.propositional_skeleton()[0])
# Task 9.12
skeleton, m = tautology.propositional_skeleton()
skeleton_proof = prove_propositional_tautology(skeleton)
return prove_from_skeleton_proof(tautology, skeleton_proof, m)
def prove_tautology(tautology: Formula) -> Proof:
"""Proves the given predicate-logic tautology.
Parameters:
tautology: predicate-logic tautology to prove.
Returns:
A valid proof of the given predicate-logic tautology from the axioms
`PROPOSITIONAL_AXIOMATIC_SYSTEM_SCHEMAS` via only assumption lines
and MP lines.
"""
assert is_propositional_tautology(tautology.propositional_skeleton()[0])
propositional_tautology, sub_map = tautology.propositional_skeleton()
proof_to_convert = prove_propositional_tautology(propositional_tautology)
proof = _prove_from_skeleton_proof(tautology, proof_to_convert, sub_map)
return proof