c_1, x_1, x_10, x_11, x_12, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, 
x_10^2*x_5^2-x_10*x_11*x_5*x_6-2*x_10*x_12*x_4*x_5+x_10*x_12*x_6^2+x_11^2*x_4*x_5-x_11*x_12*x_4*x_6+x_12^2*x_4^2
-x_1^2*x_12^2+2*x_1*x_10*x_12*x_3-x_1*x_11^2*x_3+x_1*x_11*x_12*x_2-x_10^2*x_3^2+x_10*x_11*x_2*x_3-x_10*x_12*x_2^2+1
-x_4^2*x_9^2+2*x_4*x_5*x_7*x_9-x_4*x_5*x_8^2+x_4*x_6*x_8*x_9-x_5^2*x_7^2+x_5*x_6*x_7*x_8-x_6^2*x_7*x_9+1
-x_1^2*x_9^2+x_1*x_2*x_8*x_9+2*x_1*x_3*x_7*x_9-x_1*x_3*x_8^2-x_2^2*x_7*x_9+x_2*x_3*x_7*x_8-x_3^2*x_7^2-c_1^2
-2*x_1^2*x_12*x_9+2*x_1*x_10*x_3*x_9+x_1*x_11*x_2*x_9-2*x_1*x_11*x_3*x_8+x_1*x_12*x_2*x_8+2*x_1*x_12*x_3*x_7-x_10*x_2^2*x_9+x_10*x_2*x_3*x_8-2*x_10*x_3^2*x_7+x_11*x_2*x_3*x_7-x_12*x_2^2*x_7
2*x_1*x_10*x_12*x_5-x_1*x_11^2*x_5+x_1*x_11*x_12*x_6-2*x_1*x_12^2*x_4-2*x_10^2*x_3*x_5+x_10*x_11*x_2*x_5+x_10*x_11*x_3*x_6-2*x_10*x_12*x_2*x_6+2*x_10*x_12*x_3*x_4-x_11^2*x_3*x_4+x_11*x_12*x_2*x_4
-2*x_1*x_4*x_9^2+2*x_1*x_5*x_7*x_9-x_1*x_5*x_8^2+x_1*x_6*x_8*x_9+x_2*x_4*x_8*x_9+x_2*x_5*x_7*x_8-2*x_2*x_6*x_7*x_9+2*x_3*x_4*x_7*x_9-x_3*x_4*x_8^2-2*x_3*x_5*x_7^2+x_3*x_6*x_7*x_8
2*x_10*x_4*x_5*x_9-2*x_10*x_5^2*x_7+x_10*x_5*x_6*x_8-x_10*x_6^2*x_9-2*x_11*x_4*x_5*x_8+x_11*x_4*x_6*x_9+x_11*x_5*x_6*x_7-2*x_12*x_4^2*x_9+2*x_12*x_4*x_5*x_7+x_12*x_4*x_6*x_8-x_12*x_6^2*x_7
-2*x_1*x_10*x_5*x_9+2*x_1*x_11*x_5*x_8-x_1*x_11*x_6*x_9+4*x_1*x_12*x_4*x_9-2*x_1*x_12*x_5*x_7-x_1*x_12*x_6*x_8-x_10*x_2*x_5*x_8+2*x_10*x_2*x_6*x_9-2*x_10*x_3*x_4*x_9+4*x_10*x_3*x_5*x_7-x_10*x_3*x_6*x_8-x_11*x_2*x_4*x_9-x_11*x_2*x_5*x_7+2*x_11*x_3*x_4*x_8-x_11*x_3*x_6*x_7-x_12*x_2*x_4*x_8+2*x_12*x_2*x_6*x_7-2*x_12*x_3*x_4*x_7
