Exercise logic.propositional.dnf
Description
Proposition to DNF
Derivation
Final term is not finished~~~(~T /\ T) /\ ~q /\ (T || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~(p /\ (~q || ~q)) /\ T) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~F || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~T /\ ~~(p /\ ~q /\ T /\ T)) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~~p || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ p /\ T /\ T /\ ~(~T /\ T /\ T)
⇒ logic.propositional.truezeroand~~~(~T /\ T) /\ ~q /\ (T || (~r /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~(p /\ (~q || ~q)) /\ T) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~F || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~T /\ ~~(p /\ ~q /\ T /\ T)) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~~p || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ p /\ T /\ T /\ ~(~T /\ T /\ T)
⇒ logic.propositional.notfalse~~~(~T /\ T) /\ ~q /\ (T || (~r /\ ~q /\ T /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~(p /\ (~q || ~q)) /\ T) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~F || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~T /\ ~~(p /\ ~q /\ T /\ T)) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~~p || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ p /\ T /\ T /\ ~(~T /\ T /\ T)
⇒ logic.propositional.truezeroand~~~(~T /\ T) /\ ~q /\ (T || (~r /\ ~q /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~(p /\ (~q || ~q)) /\ T) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~F || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~T /\ ~~(p /\ ~q /\ T /\ T)) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~~p || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ p /\ T /\ T /\ ~(~T /\ T /\ T)
⇒ logic.propositional.notnot~~~(~T /\ T) /\ ~q /\ (T || (~r /\ ~q /\ T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~(p /\ (~q || ~q)) /\ T) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~F || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~T /\ ~~(p /\ ~q /\ T /\ T)) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~~p || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ p /\ T /\ T /\ ~(~T /\ T /\ T)
⇒ logic.propositional.truezeroand~~~(~T /\ T) /\ ~q /\ (T || (~r /\ ~q /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~(p /\ (~q || ~q)) /\ T) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~F || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~T /\ ~~(p /\ ~q /\ T /\ T)) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~~p || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ p /\ T /\ T /\ ~(~T /\ T /\ T)
⇒ logic.propositional.notnot~~~(~T /\ T) /\ ~q /\ (T || (~r /\ ~q /\ p /\ ~q /\ T /\ T /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~(p /\ (~q || ~q)) /\ T) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~F || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~T /\ ~~(p /\ ~q /\ T /\ T)) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~~p || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ p /\ T /\ T /\ ~(~T /\ T /\ T)
⇒ logic.propositional.idempand~~~(~T /\ T) /\ ~q /\ (T || (~r /\ ~q /\ p /\ ~q /\ T /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~(p /\ (~q || ~q)) /\ T) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~F || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~T /\ ~~(p /\ ~q /\ T /\ T)) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~~p || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ p /\ T /\ T /\ ~(~T /\ T /\ T)
⇒ logic.propositional.truezeroand~~~(~T /\ T) /\ ~q /\ (T || (~r /\ ~q /\ p /\ ~q /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~(p /\ (~q || ~q)) /\ T) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~F || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~T /\ ~~(p /\ ~q /\ T /\ T)) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~~p || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ p /\ T /\ T /\ ~(~T /\ T /\ T)
⇒ logic.propositional.notnot~~~(~T /\ T) /\ ~q /\ (T || (~r /\ ~q /\ p /\ ~q /\ p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~(p /\ (~q || ~q)) /\ T) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~F || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~T /\ ~~(p /\ ~q /\ T /\ T)) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~~p || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ p /\ T /\ T /\ ~(~T /\ T /\ T)
⇒ logic.propositional.idempand~~~(~T /\ T) /\ ~q /\ (T || (~r /\ ~q /\ p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~(p /\ (~q || ~q)) /\ T) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~F || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~T /\ ~~(p /\ ~q /\ T /\ T)) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~~p || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ p /\ T /\ T /\ ~(~T /\ T /\ T)
⇒ logic.propositional.notnot~~~(~T /\ T) /\ ~q /\ (T || (~r /\ ~q /\ p /\ p /\ (~q || ~(q /\ T)))) /\ (q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~(p /\ (~q || ~q)) /\ T) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~F || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~T /\ ~~(p /\ ~q /\ T /\ T)) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~~p || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ p /\ T /\ T /\ ~(~T /\ T /\ T)
⇒ logic.propositional.idempand~~~(~T /\ T) /\ ~q /\ (T || (~r /\ ~q /\ p /\ (~q || ~(q /\ T)))) /\ (q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~(p /\ (~q || ~q)) /\ T) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~F || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~T /\ ~~(p /\ ~q /\ T /\ T)) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~~p || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ p /\ T /\ T /\ ~(~T /\ T /\ T)
⇒ logic.propositional.truezeroand~~~(~T /\ T) /\ ~q /\ (T || (~r /\ ~q /\ p /\ (~q || ~q))) /\ (q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~(p /\ (~q || ~q)) /\ T) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~F || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~T /\ ~~(p /\ ~q /\ T /\ T)) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~~p || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ p /\ T /\ T /\ ~(~T /\ T /\ T)
⇒ logic.propositional.idempor~~~(~T /\ T) /\ ~q /\ (T || (~r /\ ~q /\ p /\ ~q)) /\ (q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~(p /\ (~q || ~q)) /\ T) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~F || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~T /\ ~~(p /\ ~q /\ T /\ T)) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~~p || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ p /\ T /\ T /\ ~(~T /\ T /\ T)
⇒ logic.propositional.truezeroor~~~(~T /\ T) /\ ~q /\ T /\ (q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~(p /\ (~q || ~q)) /\ T) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~q || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~F || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ ((~~T /\ ~~(p /\ ~q /\ T /\ T)) || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ (~~p || (~r /\ T /\ ~q /\ ~F /\ ~~T /\ ~~(p /\ ~q /\ T /\ T) /\ ~~p /\ ~~(p /\ (~q || ~(q /\ T))))) /\ p /\ T /\ T /\ ~(~T /\ T /\ T)