I am trying to solve problems such as the following:
Find real numbers $a_1,a_2,a_3, b_1,b_2,b_3$ such that all following expressions are true:
- $a_1>0$ or $b_1>0$
- $a_1+a_2>0$ or $b_1+b_2<0$
The constraints are all additive, in the form: "sum-of-variables < or = or > 0". Some constraints are a disjunction of two such inequalities.
Is there an automatic tool or mathematical software that can solve such systems easily?