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You should better use the optional package qepcad which is much more reliable than the symbolic ring. See http://doc.sagemath.org/html/en/reference/interfaces/sage/interfaces/qepcad.html

You can install it by typing (in a terminal) sage -i qepcad

Then you can do;

sage: x,y = var('x, y')
sage: qf = qepcad_formula
sage: qf.iff(x>y,x-y>0)
[x > y <==> x - y > 0]
sage: F = qf.iff(x>y,x-y>0)
sage: qepcad(F)
TRUE

You should better use the optional package qepcad which is much more reliable than the symbolic ring. See http://doc.sagemath.org/html/en/reference/interfaces/sage/interfaces/qepcad.html

You can install it by typing (in a terminal) sage -i qepcad

Then you can do;do (in Sage):

sage: x,y = var('x, y')
sage: qf = qepcad_formula
sage: qf.iff(x>y,x-y>0)
[x > y <==> x - y > 0]
sage: F = qf.iff(x>y,x-y>0)
sage: qepcad(F)
TRUE