Line	Rule	$C_i$	$M_i$	Query
$L_1$	axiom	$\{w,x\}$	$1\mapsto \overline{u}$
$L_2$	axiom	$\{\overline{w},x\}$	$2\mapsto u$
$L_3$	$\text{res}(L_1,L_2,w)$	$\{x\}$	$\text{merge}(M_1,M_2,3,w)$	$3\mapsto (w,1,2)$
$L_4$	axiom	$\{\overline{x},y\}$	$4\mapsto \overline{u}$
$L_5$	$\text{res}(L_3,L_4,x)$	$\{y\}$	$\text{merge}(M_3,M_4,5,x)$	$5\mapsto (x,3,4)$
$L_6$	axiom	$\{v,\overline{y}\}$	$6\mapsto \ast$
$L_7$	$\text{res}(L_5,L_6,y)$	$\{v\}$	$\text{select}(M_5,M_6)=M_5$
$L_8$	axiom	$\{\overline{x},z\}$	$8\mapsto \ast$
$L_9$	$\text{res}(L_3,L_8,x)$	$\{z\}$	$\text{select}(M_3,M_8)=M_3$
$L_{10}$	axiom	$\{\overline{v},\overline{z}\}$	$10\mapsto \ast$
$L_{11}$	$\text{res}(L_9,L_{10},z)$	$\{\overline{v}\}$	$\text{select}(M_9,M_{10})=$
			$\text{select}(M_3,M_{10})=M_3$
$L_{12}$	$\text{res}(L_7,L_{11},v)$	$\{\}$	$\text{merge}(M_7,M_{11},12,v)$	$12\mapsto (v,5,3)$
			$=\text{merge}(M_5,M_3,12,v)$