The phrase "inconsistent with both" is grammatically correct and can be used in written English.
It is typically used to describe something that does not align or agree with two different things. Example: The evidence presented by the prosecution was inconsistent with both witness testimonies, casting doubt on the reliability of their claims.
"This incident was inconsistent with both international law and standards of professionalism for conduct between navies at sea," the statement by Cook said.
Cary Sherman, the president of the recording association, said that the case "is inconsistent with both the views of Congress and the findings of the district court".
Mr. Oxendine rejected that reasoning, saying it was inconsistent with both Georgia court decisions and the insurer's own financial statements and sales materials.
In his ruling, Griffith said Wilson's position is "inconsistent with both the letter and spirit" of the state's open records act, which only allows public records to be kept secret in very specific circumstances.
On the other side of this debate we have a president who wraps himself in the flag and invokes the name of God in support of policies that seem inconsistent with both American and Christian values.
"Sport England refused to recognise bridge as a sport, a position which the EBU believes to be inconsistent with both the wishes of Parliament, and the opinion of significant international sporting organisations," said an EBU spokesman.
Weiquan lawyers, along with international human rights organizations, have argued that the provisions against subversion are inconsistent both with China's own constitution and with international human rights standards, particularly in light of the lack of transparency and clear guidelines used in applying the laws.
In 2012 a fundraiser hosted by Pope John XXIII High School where Capuano and fellow Massachusetts Congressman Ed Markey were to receive awards was cancelled due to their "positions [being] inconsistent with church doctrine;" both were humble in response to the news.
Previous epidemiological data on the relation between physical activity (exercise) and pulmonary embolism are inconsistent, with studies reporting both increased and decreased risk.
Data examining the interaction of diabetes and metabolic syndrome are limited, and these data are inconsistent with respect to both results and quality.
However, the evidence does not entirely support that conclusion; the epidemiological literature is inconsistent with respect to both late-life and midlife blood pressure effects.
