YOU SAID:

I did not have sexual relations with that horsey

INTO JAPANESE

私はあの馬とは性的関係がありませんでした

BACK INTO ENGLISH

I had no sexual relations with that horse

INTO JAPANESE

その馬と性的関係はありませんでした

BACK INTO ENGLISH

There was no sexual relationship with that horse

INTO JAPANESE

その馬との性的関係はありませんでした

BACK INTO ENGLISH

There was no sexual relationship with that horse