Relation mining of multivariant categorical timeseries without excluding the temporal nature
This problem is one of estimating the lag. Once that is estimated, you could create additional features representing the lagged values and move forward with "sequence mining" as you have already suggested in the question itself. 

For each variable, Var_i, you will have to estimate its lag l_i. This lag can be calculated by estimating the order of a Markov chain with seven symbols (you could use either BIC or AIC to estimate this order; both would require calculating likelihood of candidate orders and pick the order that maximizes either of these criteria). Once you are done calculating the order of the Markov chain for each of the variables, then you could represent your dataset such that each row will have the current value of Var_i and its preceding values, all the way back to its estimated lag l_i. While this methodology is laborious, it pays rich dividends as its automated and parsimonious way of representing the necessary information.