I have to point this out to you because I do in fact think that 'faith' (the supernatural ability to know the gospel really is true) comes from God, not us. But no one ever got saved by simply knowing and agreeing that the gospel really is true (even the demons know that), but only those who then place their trust in what they now know to be true about the gospel are saved. And, as I've shown, Paul calls the trusting we do 'not working'.
Agreed
Faith is the supernatural ability to know the gospel really is true, and is graciously given by God to everyone who he calls.
I think this is officially called "prevenient grace", though you have not embraced term. You are substituting FAITH for "prevenient grace" IMO. This is 'free willers' doctrine that explains how man can overcome the depravity of man (verses like NO ONE SEEKS GOD).
'Believing/trusting' is man's response to God's gracious gift faith, the supernatural gift of 'knowing'.
Dictionary definition of FAITH: complete trust or confidence in someone or something.
Similar: Trust, belief, conviction, hope
Thus, I don't except your differentiation of the words FAITH and BELIEF and cite the dictionary as my authority.
I think most Arminians would rephrase your thinking as:
'Believing/trusting' is man's response to God's gracious gift
faith "prevenient grace", the supernatural gift of 'knowing'.
I think I understand you. Your terminology of FAITH is not equal BELIEF is foreign, that's all.
Aside: "prevenient grace" is not found in the Bible IMO, though proponents would site John 1:9, Titus 2:11, John 12:32, Romans 2:4, 1 Tim. 2:4
Aside2: "prevenient grace" definition: the gift of God to allow men to 'freely' decide to believe or not. (which you are calling faith IMO)