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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))