Processing math: 100%

$1:2:5:6:7$	$\to 〈 V P^{5} V 〉 Δ E_{1} Δ E_{3} {(Δ E_{1})}^{2}$	$\to S_{1} S_{3} S_{1}^{2} = (2)$
$1:3:4:5:7$	$\to 〈 V P^{5} V 〉 Δ E_{2} {(Δ E_{1})}^{2} Δ E_{2}$	$\to S_{2} S_{1}^{3} S_{2} = (1)$
$1:3:4:6:7$	$\to 〈 V P^{5} V 〉 Δ E_{2} Δ E_{1} Δ E_{2} Δ E_{1}$	$\to S_{2} S_{1} S_{2} S_{1} = (1)$
$1:3:5:6:7$	$\to 〈 V P^{5} V 〉 {(Δ E_{2})}^{2} {(Δ E_{1})}^{2}$	$\to S_{2}^{2} S_{1}^{2} = (1)$
$1:4:5:6:7$	$\to 〈 V P^{5} V 〉 Δ E_{3} {(Δ E_{1})}^{3}$	$\to S_{3} S_{1}^{3} = (2)$
$1:2:3:4:5:7$	$\to - 〈 V P^{6} V 〉 {(Δ E_{1})}^{4} Δ E_{2}$	$\to S_{1}^{4} S_{2} = (1)$
$1:2:3:4:6:7$	$\to - 〈 V P^{6} V 〉 {(Δ E_{1})}^{3} Δ E_{2} Δ E_{1}$	$\to S_{1}^{3} S_{2} S_{1} = (1)$
$1:2:3:5:6:7$	$\to - 〈 V P^{6} V 〉 {(Δ E_{1})}^{2} Δ E_{2} {(Δ E_{1})}^{2}$	$\to S_{1}^{2} S_{2} S_{1}^{2} = (1)$
$1:2:4:5:6:7$	$\to - 〈 V P^{6} V 〉 Δ E_{1} Δ E_{2} {(Δ E_{1})}^{3}$	$\to S_{1} S_{2} S_{1}^{3} = (1)$
$1:3:4:5:6:7$	$\to - 〈 V P^{6} V 〉 Δ E_{2} {(Δ E_{1})}^{4}$	$\to S_{2} S_{1}^{4} = (1)$
$1:2:3:4:5:6:7$	$\to 〈 V P^{7} V 〉 {(Δ E_{1})}^{6}$	$\to S_{1}^{6} = (1)$