Prover9 Manual  Version 200902A 
The following tables list the supported symbols for integer arithmetic.
Operations  Relations  



Note that  cannot be used as a binary subtraction operation (because LADR does not allow arityoverloading of symbols). Instead of xy, one must write x+ y.
Recall that when Mace4 is searching for a model of size n, it is using the set {0,1,...,n1} as the underlying domain of the model. When set(arithmetic) is in effect, the integer operations and relations are applied to the elements of the domain. However, when evaluating integer expressions, Mace4 is free to go outside of the domain, including negative integers. For example, the constraint A+ B = C+ D has A=C=1, B=D=3 as a solution (among many others), and the constraint A + B = 10 is valid for domain sizes less than 10.
However, when assigning possible values to uninterpreted functions and constants (e.g., unknowns A and B), Mace4 will use members of the domain only. For example, given the constraint A + B = 10 with a domain size of 8, Mace4 will not give the solution A=9, B=1.
Case 1: some other subexpression validates a formula; for example, 3/0 = 2  1+4=5 is valid.
Case 2: instances of x = x; for example, 3/0 = 3/0 is valid. Given an arithmetic equality alpha = beta involving division by zero, Mace4 will simplify it by using ring theory identities, and if simplify(alpha) is identical to simplify(beta), the equation evaluates to TRUE. The simplification procedure is not guaranteed to produce a unique canonical form such that the simplified expressions are identical if alpha = beta. Thus, Mace4 can be incompelte for constraints involving division by zero; that is, it might say that there are no solutions when there are valid solutions. However, we believe that Mace4 is sound; that is, all solutions that it gives are valid.
op(490, infix_right, "+"). op(470, infix_right, "*"). op(460, infix, "/"). op(460, infix, "mod"). op(390, prefix, "").These declarations allow, for example, the expression (a * (b * c)) + (d + e) to be written as a * b * c + d + e. When in doubt, include parentheses and observe how Mace4 echoes the formulas in the output file.
mace4 n8 f queens1.in > queens1.out
mace4 n8 f queens2.in > queens2.out
mace4 f sendmoney.in > sendmoney.out
mace4 f zebra2.in > zebra2.out
mace4 f kenken6.in > kenken6.out