User talk:2601:184:4081:1CBE:BCCD:9145:66F5:A63E

The example does not follow the form of logic and resolution in particular. wiki resolution: “produces a new clause implied by two clauses containing complementary literals” e.g. “avb, ~avc => bvc”.

14 Resolve(12,1): 1 and 12 are not of the form avb and do not contain complementary literals. Likewise for 15, 17, 18.

16: 16 is derived from 3 and 15. But if y=x then 15 is true but 16 is false. 16 contradicts 15.

19: 19 (true) is derived from 18 and 16, i.e. x <= y and ~(x <= y). If this is Resolution then we would derive false. Please explain how the expression x<y ? y : x is derived from these two contradictory expressions e.g. if we have x=y and ~(x=y) what expression do we derive? In general, from expressions P and ~P what do we derive?

The reference by Volkstorf is straightforward and contains numerous simple, complete examples. I would suggest that a much better example can be found there.