Is there any smart way to check if certain statements are not provable in any of these proof systems?
Like for example the following task:
Prove or disprove the following statements:
- $\vDash \exists x(\neg A(x) \lor \forall x A(x))$
- $(\exists x A(x) \rightarrow \exists x B(x)) \vDash \forall x(A(x) \rightarrow B(x))$