Not quite correct. Actually Calvinists believe in the will of man. That will is held hostage, unable to acknowledge God. God must set that person free.
As Ireaneus points out, and one that I would agree with, man is certainly most ungrateful if he cannot acknowledge what God has done. That being said, I would also add that it is impossible for man NOT to acknowledge what God has done for them.
Do you think a saved individual cannot acknowledge God's gift? Do you think an unsaved individual can acknowledge God's gift?
Are you saying that man has no free will UNTIL the Holy Spirit comes into him? So the majority of men have no free will? Can you back this up biblically?
St. Irenaeus did not say CANNOT. He is not saying anything close to the Calvinist position. He is saying IF he DOES NOT. There is no cannot involved. Therefore your commentary on Irenaeus seems a tad off.
I’d say that the acknowledgement of God’s Grace is probably tantamount to accepting it, but that it can be rejected by the choice of the individual at some point in time. I’m not sure that the reverse is true.
We do have different definitions of ‘saved’. We look at ‘saved’ at the Judgement, not here in life, where it is possible to backslide. The Reformed view is that there is a point in time during life where the saving occurs. We may be talking past each other if we continue to use different definitions.