"contrary to conjecture" is correct and usable in written English.
You can use it to refer to something that is not in line with what was previously speculated or expected. For example: "The results of the experiment were contrary to conjecture, indicating that the proposed method was not as effective as initially believed."
This confirmed that, contrary to some conjecture, early hominids did not need big brains to make their way out of Africa.
Contrary to the conjecture in Malinvaud (1971) about the falsification of preferences, Laffont and Rochet (1985) proved the equivalence between price and quantity planning procedures.
In 1961 Dana Scott proved that the failure of the Axiom of Constructibility follows from the existence of a measurable cardinal, contrary to a conjecture Gödel had made in 1940.
Contrary to previous conjectures, we find a multiplicity of folding mechanisms, suggesting that Gō-like models cannot be justified by considerations of topology alone.
However, contrary to some conjectures, unrecorded consumption does not seem to be linked to more health problems than recorded consumption, if volume and patterns of drinking are controlled for (Rehm et al. 2010).
Some descriptive evidence shows that, contrary to the 'paradox' conjecture, Europe's weaknesses reside both in its system of scientific research and in a relatively weak industry.
Moreover, the results revealed that contrary to the previous conjecture, the use of soil moisture temporal anomaly did not reduce the impacts of static properties (e.g., soil properties) on soil moisture temporal dynamics.
Contrary to what previous intuition may conjecture, the degree of underreporting in our sample is higher in the years of expansion (2006 2007) than when the economy shrinks (2008 2009).
Contrary to "No to Keystone.
This is contrary to my experience.
