This states that a quadratic attains negative values:

This gives explicit conditions on real parameters:

Test whether one region is included in another:

This states that there are points satisfying

and not

:

The statement is false, hence the region defined by

is included in the region defined by

:

Plot the relationship:

Test geometric conjectures:

This states that there is a triangle for which the conjecture is not true:

The statement is true, hence the conjecture is not true for arbitrary triangles:

This states that there is an acute triangle for which the conjecture is not true:

The statement is false, hence the conjecture is true for all acute triangles:

Prove that a statement is a tautology:

This proves that there are no values of

for which the statement is not true:

This can be proven with

TautologyQ as well: