Intuition behind proofs by rules of inference Unfortunately I don't get the intuition behind the proofs by rules of inference.
I do understand example, however I don't see the broad picture, I simply don't understand how to reason about the solution.
Following I will show few example with my notes, which are might be incorrect, please show me what I don't get right.
Exercise 1. Prove ¬p from (p → q), (q → r) and ¬r.
We are given few assumption, (p → q) is true, (q → r) is true and ¬r is true. The question is whether ¬p is true.
If (q → r) is true and ¬r is true, then q should be false, therefore ¬q is true.
If (p → q) is true and ¬q is true that ¬p is true.
Whether the reasoning is true?

You can transform $A \to B = \neg A \vee B$. So you have the following premises:


*

*$p \to q = \neg p \vee q$ (1)

*$q \to r = \neg q \vee r$ (2)

*$\neg r$ (3)


By resolution on (2) and (3): you have $\neg q$ (4)
By resolution on (1) and (4): you have $\neg p$.
