Natural deduction proof of $(c ∧ n) → t, h ∧ ¬s, h ∧ ¬(s ∨ c) → p \vdash (n ∧ ¬t) → p$ I'm trying to do a question from Huth and Ryan's book Logic in Computer Science and I am stuck on the following natural deduction proof: 

Prove by natural deduction that the sequent 

$$(c ∧ n) → t, h ∧ ¬s, h ∧ ¬(s ∨ c) → p \vdash (n ∧ ¬t) → p$$ 

is valid.

I have tried assuming $n ∧ ¬t$ on line 4 after the premises, and using Modus Tollens from there to get $¬(c ∧ n)$, but I don't know what I can do after that. Any help would be appreciated.
$\begin{align}n, \neg (c\wedge n)\vdash&amp;~ \neg c \\ h\wedge \neg s\vdash&amp;~ \neg s \\ h\wedge \neg s\vdash&amp;~ h \\ \neg c, \neg s\vdash&amp;~ \neg (s\vee c)\\ h, \neg(s\vee c), h\wedge \neg (s\vee c)\to p\vdash &amp; ~ p\end{align}$

More or less.  Format and provide justifications .
Here's a proof that might help:



Here is the OP's attempt:


  I have tried assuming n∧¬t on line 4 after the premises, and using Modus Tollens from there to get $¬(c∧n)$, but I don't know what I can do after that. 


The OP reached line 6 of this proof. 

After that I used De Morgan's rules (DeM) on line 7. However, doing that left me with a disjunction. I considered the two cases of the disjunction on lines 10-14 and 15-18. They both led to $P$ which allowed me to use disjunction elimination (vE) on line 19. Line 20 used a conditional introduction to conclude the proof.

For more information about these rules or to try the proof checker see the links below.



Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/

P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/