Here are the premises/conclusion, and where I've gotten so far.
$1.$ $(W\wedge E)\rightarrow (P\vee L)$ (PR)
$2.$ $(W\wedge \neg E)\wedge R))\rightarrow (P\vee D)$ (PR)
$3.$ $((W\wedge \neg E)\wedge \neg R))\rightarrow (U\wedge \neg F)$ (PR)
$-.$ $(W\wedge F)\rightarrow (L\vee D)\vee P$ (CO)
$4.$ $\neg(U\wedge \neg F)\rightarrow \neg(W\wedge(\neg E\wedge \neg R))$ From $3$ transposition
$5.$ $(\neg U\vee \neg \neg F)\rightarrow \neg(W\wedge(\neg E\wedge \neg R))$ From $4$ DeM
$6.$ $(\neg U\vee F)\rightarrow \neg(W\wedge(\neg E\wedge \neg R))$ From $5$ Double negation
$7.$ $(\neg U\vee F) \rightarrow (\neg W\vee \neg (\neg E\wedge \neg R))$ From $6$ DeM
$8.$ $(\neg U \vee F)\rightarrow(\neg W\vee(\neg \neg E\vee \neg \neg R))$ From $7$ DeM
$9.$ $(\neg U \vee F)\rightarrow (\neg W \vee (E\vee R))$ From $8$ double negation
Here is where my conditional proof starts.
$10.$ $W\wedge F$ (Provisional assumption)
$11.$ $W$ From $10$ conjunction elimination (CE)
$12.$ $F$ From $10$ CE
$13.$ $\neg U \vee F$ From $12$ disjunctive addition (DA)
$14.$ $(\neg W\vee (E\vee R))$ From $9$, $13$ Modus Ponens
$15.$ $E\vee R$ From $14$, $11$ Disjunctive syllogism
At this point I'm lost. I've tried assuming several negations for reductio (contradiction) but I haven't gotten the desired result. Any ideas?