php, 270 bytes

Result

AC

Duration

507ms

Code [DL]

<?php [$a,$b,$c]=explode(" ",fgets(STDIN));[$d,$e,$f]=explode(" ",fgets(STDIN));[$g,$h,$i]=explode(" ",fgets(STDIN));[$j,$k,$l]=explode(" ",fgets(STDIN));$g-=$a;$h-=$b;$i-=$c;$j-=$a;$k-=$b;$l-=$c;echo(($e-$b)*($i*$j-$g*$l)+($f-$c)*($g*$k-$h*$j)+($d-$a)*($h*$l-$i*$k))/6;

stdin

15 79 54
23 03 18
06 35 37
63 96 02

stdout

7946

stderr

PHP Notice:  A non well formed numeric value encountered in /volume/CODE on line 1
PHP Notice:  A non well formed numeric value encountered in /volume/CODE on line 1
PHP Notice:  A non well formed numeric value encountered in /volume/CODE on line 1
PHP Notice:  A non well formed numeric value encountered in /volume/CODE on line 1
PHP Notice:  A non well formed numeric value encountered in /volume/CODE on line 1
PHP Notice:  A non well formed numeric value encountered in /volume/CODE on line 1

strace