I'm stuck on what how to continue. I know I'm missing a few steps but this is what I have so far. Thank you in advance!
- ¬Cube(b) → Small(b)
- Small(c) → (Small(d) ∨ Small(e))
- Small(d) → ¬Small(c)
Cube(b) → ¬Small(e)
Small(c)
- ¬Small(b)
- ¬Cube(b)
- Small(b) (→ Elim 1,7)
- ⊥ (⊥intro 6, 8)
10.Cube(b) (¬Intro 7-9)
- ¬Small(e) (→ Elim 4,10)
- ¬Small(b)
Goal: Small(c) → Small(b)
$\qquad \qquad Small(d) \vee Small(e)$ ($\rightarrow $ Elim 2,5)
$\qquad \qquad \qquad Small(d)$
$\qquad \qquad \qquad Small(e)$
$\qquad \qquad \qquad \bot$ ($\bot$ Intro 11,14)
$\qquad \qquad\qquad Small(d)$ ($\bot $ Elim 15)
$\qquad \qquad Small(d)$ ($\vee $ Elim 12, 13-13, 14-16)
$\qquad \qquad \neg Small(c)$ ($\rightarrow$ Elim 17, 3)
$\qquad \qquad \bot $ ($\bot $ Intro 5,18)
$\qquad \neg \neg Small(b)$ ($\neg$ Intro 6-19)
$\qquad Small(b)$ ($\neg $ Elim 20)
$Small(b) \rightarrow Small(c)$ ($\rightarrow $ Intro 5-21)