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The routine returns true if the given objects are distinct; false if they are not; and FAIL if it is unable to reach a conclusion.

The command with(geom3d,AreDistinct) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{geom3d}\right)\:$

$\mathrm{sphere}\left(\mathrm{s1}\,\left[\mathrm{point}\left(\mathrm{o1}\,\left[0\,0\,0\right]\right)\,1\right]\right)$

$\mathrm{s1}$

$\mathrm{line}\left(l\,\left[\mathrm{o1}\,\mathrm{point}\left(\mathrm{o2}\,0\,0\,1\right)\right]\right)$

$l$

$\mathrm{rotation}\left(\mathrm{s2}\,\mathrm{s1}\,\frac{\mathrm{\pi }}{4}\,l\right)$

$\mathrm{s2}$

$\mathrm{rotation}\left(\mathrm{s3}\,\mathrm{s2}\,\frac{7\mathrm{\pi }}{4}\,l\right)$

$\mathrm{s3}$

$\mathrm{AreDistinct}\left(\mathrm{s1}\,\mathrm{s3}\right)$

$\mathrm{false}$