SURMISE

[verb] [T] [formal] - to guess (something), without having much or any proofAs we surmised, Duncan had not been telling the truth. [+ speech]There must be another explanation, he surmised. [+ speech]The police surmise that the robbers have fled the country. [+ that clause]Archaeologists are only able to surmise what these strange symbols might mean. [+ wh- word]