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Disproving: If $(\Gamma\vdash(\phi\,\lor\psi))$, either $(\Gamma\vdash\phi)$ or $(\Gamma\vdash\psi)$ is true

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List Question

Are my DNF and CNF for $A \land (A \lor C) \implies (C \lor B)$ correct?

Properly Translate Propositional Statement to Discrete Math

$\alpha \to\beta$ is valid, where $\alpha$, $\beta$ share no common atomic proposition; then $\alpha$ is unsatisfiable or $\beta$ is valid, or both

How to prove $\lnot (\alpha \rightarrow \lnot \beta) \vdash \lnot (\beta \rightarrow \lnot \alpha)$ in HPC

Double negation vs. law of excluded middle?

Modus ponens as a rule of inference vs. tautology

Logical entailment in propositional logic.

logical equivalence question about contingency

$\to$ vs. $\vdash$ in logic

Syntax vs semantics in logic and metalogic

Do definitions have to fit axioms in logic?

Are the statements equal?

Valid vs. sound (and if these differences matter in syntax vs. semantics, metalogic vs. logic)

Validity and "true in every interpretation"?

Disproving: If $(\Gamma\vdash(\phi\,\lor\psi))$, either $(\Gamma\vdash\phi)$ or $(\Gamma\vdash\psi)$ is true

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