Vetinari

The set of integers Z is nonempty, with two operations: + and *

There is an integer 0 such that a+0=0+a=a for all a \in Z

There is an integer 1 such that a*1=1*a=a for all a \in Z

For every a \in Z there exists b \in Z such that a+b=b+a=0

For all a, b \in Z, a+b=b+a

For all a, b, c \in Z, a+(b+c)=(a+b)+c and a*(b*c)=(a*b)*c

If a*b=0, then a=0 and/or b=0

There exists a nonempty subset of Z called N, with 1 \in N

If a is an integer, then exactly one of the following is true:

a is in N a=0 -a is in N