If he ... (compare) the facts, he would conclude that I was right.

I don't know what tense you want this verb to be used, but you could do

Past Tense: If he had compared the facts, he would have concluded that I was right.

Future Tense: If he compares the facts, he will conclude that I am right.

Present Tense: He's comparing the facts so that he can conclude that I'm right.