Does a woman remain legally (religiously) married to the suitor after she says, "I have married myself to you," and he says, "I have accepted your marriage," and he has intercourse with her without penetration, and then she later denies the marriage?

Marriage has pillars without which it cannot be contracted. These are: the presence of the woman's guardian or his representative, two just witnesses, a dowry, and a formula indicating the contract. What transpired between you does not constitute a legitimate marriage, and you have committed a heinous sin and a clear transgression due to the mutual touching and the unlawful seclusion. For the Prophet, peace and blessings be upon him, said: "For one of you to be stabbed in the head with an iron needle is better for him than to touch a woman who is not lawful for him." You must leave her and avoid her, and it is not permissible for you to cling to her or correspond with her. What is incumbent upon you is sincere repentance to Allah by regretting this sin and resolving not to return to it.