"The house is all blue(B), and the house is all white(W)"
Those statements are, ostensibly, not of the form p ⋀ ¬p. However, they do seem to entail p ⋀ ¬p. For example "The house is all blue" entails that the house is not any other colour, including white. So the example entails B ⋀ ¬W ⋀ W ⋀ ¬B.
I can't think of any contrary statement that does not entail something self-referential. Is a self-reference necessary for a contradiction?