The sequent that should be proved.
An LK-Proof of the sequent, or None if not successful.
The formula that should be proved.
An LK-Proof of :- formula, or None if not successful.
The formula whose validity should be checked.
True if the formula is valid.
The formula whose validity should be checked.
True if the formula is valid.
A prover that is able to refute HOL sequents/formulas (or subsets of HOL, like propositional logic).
TODO: exceptions to indicate that a formula is not supported (e.g. for propositional provers).
Implementors may want to override isValid(seq) to avoid parsing proofs.