Simplify Conjunctive Normal Form?

Question

is there any kind of general rules to follow or algorithm for trying to simplify something in conjunctive normal form? Specifically, I'm trying:
(P or Q) and P and (Q or R) and (P or notP or R) and (notQ or R)
I got that the 4th one is always true because it has complementary literals so
(P or Q) and P and (Q or R) and (notQ or R)
(P or Q) and P and (R or (Q and notQ)
(P or Q) and P and R
(P or Q) and (P or P) and R
(P or (Q and P)) and R
And then I got stuck. The answer I was supposed to get to was (P and R) so I feel like I was close but I'm not sure how to get rid of (P or Q). Are there some sort of rules to make this not-just-guess-work? (Sorry in advance, not sure how to even put in logic symbols so I figured I'd just use words)

Answer 1

From $(P\vee Q)\wedge P\wedge R$.
By the distributive law of conjunction over disjunction, $((P\wedge P)\vee (Q\wedge P))\wedge R$
By idempotency, $(P\vee (Q\wedge P))\wedge R$.
By the distributive law $(P\wedge(1 \vee Q))\wedge R$
By annihilation for 1, $(P\wedge 1)\wedge R$
By absorption for 1, $P\wedge R$

Regarding your question, there are no methodical rules to simplify boolean expressions without defining a normal form which we could identify and which would allow us to recognize when the algorithm ends.