$1:2:5:6:7$ $\to 〈V{P}^{5}V〉\Delta {E}_{1}\Delta {E}_{3}{\left(\Delta {E}_{1}\right)}^{2}$ $\to {S}_{1}{S}_{3}{S}_{1}^{2}=\left(2\right)$ $1:3:4:5:7$ $\to 〈V{P}^{5}V〉\Delta {E}_{2}{\left(\Delta {E}_{1}\right)}^{2}\Delta {E}_{2}$ $\to {S}_{2}{S}_{1}^{3}{S}_{2}=\left(1\right)$ $1:3:4:6:7$ $\to 〈V{P}^{5}V〉\Delta {E}_{2}\Delta {E}_{1}\Delta {E}_{2}\Delta {E}_{1}$ $\to {S}_{2}{S}_{1}{S}_{2}{S}_{1}=\left(1\right)$ $1:3:5:6:7$ $\to 〈V{P}^{5}V〉{\left(\Delta {E}_{2}\right)}^{2}{\left(\Delta {E}_{1}\right)}^{2}$ $\to {S}_{2}^{2}{S}_{1}^{2}=\left(1\right)$ $1:4:5:6:7$ $\to 〈V{P}^{5}V〉\Delta {E}_{3}{\left(\Delta {E}_{1}\right)}^{3}$ $\to {S}_{3}{S}_{1}^{3}=\left(2\right)$ $1:2:3:4:5:7$ $\to -〈V{P}^{6}V〉{\left(\Delta {E}_{1}\right)}^{4}\Delta {E}_{2}$ $\to {S}_{1}^{4}{S}_{2}=\left(1\right)$ $1:2:3:4:6:7$ $\to -〈V{P}^{6}V〉{\left(\Delta {E}_{1}\right)}^{3}\Delta {E}_{2}\Delta {E}_{1}$ $\to {S}_{1}^{3}{S}_{2}{S}_{1}=\left(1\right)$ $1:2:3:5:6:7$ $\to -〈V{P}^{6}V〉{\left(\Delta {E}_{1}\right)}^{2}\Delta {E}_{2}{\left(\Delta {E}_{1}\right)}^{2}$ $\to {S}_{1}^{2}{S}_{2}{S}_{1}^{2}=\left(1\right)$ $1:2:4:5:6:7$ $\to -〈V{P}^{6}V〉\Delta {E}_{1}\Delta {E}_{2}{\left(\Delta {E}_{1}\right)}^{3}$ $\to {S}_{1}{S}_{2}{S}_{1}^{3}=\left(1\right)$ $1:3:4:5:6:7$ $\to -〈V{P}^{6}V〉\Delta {E}_{2}{\left(\Delta {E}_{1}\right)}^{4}$ $\to {S}_{2}{S}_{1}^{4}=\left(1\right)$ $1:2:3:4:5:6:7$ $\to 〈V{P}^{7}V〉{\left(\Delta {E}_{1}\right)}^{6}$ $\to {S}_{1}^{6}=\left(1\right)$