From Webster's Third New International Dictionary:
disbelief : the act of disbelieving : mental refusal to accept (as a statement or proposition) as true *listened to him with shocked disbelief*
disbelieving: refusing to believe : withholding belief : UNBELIEVING
–dis-be-liev-ing-ly adverb
disbelieve: transitive verb : to hold not to be true or real : reject or withhold belief in *disbelieve his professions of sincerity* *disbelieve the existence of ghosts*
intransitive verb : to withhold or reject belief — used with in *disbelieves in the sanctity of the status quo— W.C.Brownell*
believe intransitive verb
1 a : to have a firm or wholehearted religious conviction or persuasion — usually used with in *believe in the Scriptures* and sometimes with on *and many believed on him there— Jn 10:42(Authorized Version)* b : to receive in faith or trust : ACCEPT *a story that divided the audience into those who believed and those who didn't* — often used with in *serfs incapable of believing in the sincerity of a master who desired to help them— E.J.Simmons* *because of its sincerity T this is the kind of play one would like to believe in— Punch*
2 obsolete : to give credence : TRUST — used with to *believe to your own virtues*
3 : to have a firm conviction as to the beneficial, genuine, or good quality of something — used with in *believe in physical culture*
4 : THINK, SUPPOSE *inclined to believe in accordance with her husband*
transitive verb
1 a : to take (a statement or person making a statement) as true, valid, or honest : give credence to *believe the reports* b : to accept or receive as genuine, valid, or good *a bland assumption that all scientists T decide and publish what science believes— R.M.Weaver*
2 obsolete : to assume the existence of as true or valid *believe a God*
3 : to be of the opinion : SUPPOSE, SUSPECT *believe it will rain* *the dye is believed to be a complex acid*µ‹
The following two statements are not equivalent:
I disbelieve in God.
I believe there is no God.
The first statement represents complete conviction; there is no doubt that there is no God. The second statement is a hedge at best because it could mean that you may only be inclined to believe that there is no God. The first is a statement by an atheist; the second is by an agnostic.