F: A string which is an S-expression of a ZOL formula. You can assume:
The operators used are IF,IFF,AND,OR,XOR,and NOT.
The NOT operator has one argument, a wff
The IF, IFF,and XOR operators have two wffs as arguments
The special = predicate takes two objects as arguments (= is in prefix form, not infix)
The AND and OR operators have two or more arguments
All predicates have zero or more arguments
All functions will have zero or more arguments
All predicate, function, and object symbols will be alphanumberic strings
All formulae are well-formed
Symbols may be overloaded---type is determined through position
Returns a list [S, P, O, Fn] where:
S is a string telling us whether F was satisfiable:
“T” – If the formula is a tautology,
“S” – If the formula is satisfiable but not a tautology,
“U” – If the formula is unsatisfiable.
P is a set of strings, where each string is one of the predicate symbols in F.
O is a set of strings, where each string is one of the object symbols in F.
Fn is a set of strings, where each string is one of the function symbols in F.
You must use the tableaux method to solve this problem.
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