I have a logical formula: (x_ {1} or x_ {2}) and (x_ {3} or x_ {4}) and ..... and (x_ {2r-1} or x_ {2r}) , where x_ {i} belongs to the set: {p_ {1}, p_ {2}, ... p_ {99}, ~ p_ {1}, ~ p_ {2}, ... ~ p_ {99}} , and I have to determine if this formula can be given for some x_ {i} values.
I know that this is generally difficult to calculate. But is there any pretty quick way to solve this particular problem? So far I have tried to backtrack - that is, in recursion, I substitute all possible values (0 or 1 so small) for each possible variable, and each variable that does not yet have a value is trivially true. Before I delve into recursion, I correct the formula (even if not every variable has a value), and if it is false, I do not go deep. But it is too slow. Any ideas? I would be very grateful for the help.
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