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Below, a stands for full-name quantifier, e stands for existential quantifier, and ┐ stands for negative conjunction.
Let f (x): x be afraid of difficulties, g (x): x succeed, and h (x): x fail.
Premises: Ax(F(x)→┐G(x), ax (Hercus), Ex(┐H(x).
Conclusion: Ex(┐F(x))
Prove:
1 Ex(┐H(x))
2 ┐H(c)
3 Ax(G(x)∨H(x))
4 grams (degrees Celsius) ∨ hour (degrees Celsius)
5 grams (Celsius)
6 Ax(F(x)→┐G(x))
7 F(c)→┐G(c)
8 ┐F(c)
9 Ex(┐F(x))