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Explanation: Just to support Palomo’s and mult47’s answers:
witnesseth is the archaic form of the third person singular:
(it) witnesseth = (it) witnesses:
This contract witnesseth that = El presente contrato hace constar que;
When it stands alone: Witnesseth (that) = Se hace constar (que).
As to Serena’s answer, I’m afraid she may be confusing “witnesseth” with “whereas” (=por cuanto; visto que).