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Length of proof is 25.  Level of proof is 8.

---------------- PROOF ----------------

4 [] T(x,y,ext(x,y,w,v)).
5 [] E(y,ext(x,y,w,v),w,v).
6 [] -E(x,y,x1,y1)| -E(y,z,y1,z1)| -E(x,v,x1,v1)| -E(y,v,y1,v1)| -T(x,y,z)| -T(x1,y1,z1)|x=y|E(z,v,z1,v1).
13 [] E(xa,xb,xa,xb).
14 [] -E(xa,xb,xc,xd)|E(xc,xd,xa,xb).
15 [] -E(xa,xb,xc,xd)| -E(xc,xd,xe,xf)|E(xa,xb,xe,xf).
18 [] E(xa,xa,xb,xb).
19 [] -T(xa,xb,xc)| -T(xa1,xb1,xc1)| -E(xa,xb,xa1,xb1)| -E(xb,xc,xb1,xc1)|E(xa,xc,xa1,xc1).
20 [] xq=xa| -T(xq,xa,xd)| -E(xa,xd,xb,xc)|xd=ext(xq,xa,xb,xc).
21 [] -E(xb,xc,xa,xa)|xb=xc.
24 [] T(xa,xb,xb).
25 [] -T(xa,xb,xc)|T(xc,xb,xa).
29 [] -T(xa,xb,xc)| -T(xa,xc,xd)|T(xb,xc,xd).
32 [] -T(xa,xb,xc)| -T(xa,xc,xd)|T(xa,xb,xd).
37 [] T(xa,xb,ext(xa,xb,alpha,gamma)).
38 [] xb!=ext(xa,xb,alpha,gamma).
43 [] insert(xa,xb,xa1,xc1)=ext(ext(xc1,xa1,alpha,gamma),xa1,xa,xb).
61 [] -E(xa1,xa2,xb1,xb2)| -E(xa1,xa3,xb1,xb3)| -E(xa2,xa3,xb2,xb3)|E3(xa1,xa2,xa3,xb1,xb2,xb3).
71 [] T(a,b,c).
72 [] E(a,c,a1,c1).
73 [] -T(a1,insert(a,b,a1,c1),c1)| -E3(a,b,c,a1,insert(a,b,a1,c1),c1).
74 [] d1=ext(c1,a1,alpha,gamma).
75 [] b1=ext(d1,a1,a,b).
76 [] c2=ext(d1,b1,b,c).
77 [] ext(c1,a1,alpha,gamma)=d1.
78 [] ext(d1,a1,a,b)=b1.
221 [para_into,73.2.5,43.1.1,demod,77,78] -T(a1,insert(a,b,a1,c1),c1)| -E3(a,b,c,a1,b1,c1).
224 [para_from,74.1.2,43.1.2.1] insert(x,y,a1,c1)=ext(d1,a1,x,y).
225 [para_from,74.1.2,38.1.2] a1!=d1.
226 [para_from,74.1.2,37.1.3] T(c1,a1,d1).
232 [para_from,75.1.2,5.1.2] E(a1,b1,a,b).
233 [para_from,75.1.2,4.1.3] T(d1,a1,b1).
237 [para_from,76.1.2,5.1.2] E(b1,c2,b,c).
238 [para_from,76.1.2,4.1.3] T(d1,b1,c2).
254 [ur,20,225,24,18] d1=ext(a1,d1,x,x).
382 [binary,226.1,25.1] T(d1,a1,c1).
681 [hyper,32,233,238] T(d1,a1,c2).
686 [hyper,29,233,238] T(a1,b1,c2).
2535 [binary,232.1,14.1] E(a,b,a1,b1).
2576 [binary,237.1,14.1] E(b,c,b1,c2).
2597 [hyper,19,686,71,232,237] E(a1,c2,a,c).
3272 [hyper,19,71,686,2535,2576] E(a,c,a1,c2).
3334 [hyper,15,2597,72] E(a1,c2,a1,c1).
4178 [hyper,61,2535,3272,2576] E3(a,b,c,a1,b1,c2).
4308 [hyper,6,13,3334,13,13,681,382] d1=a1|E(c2,x,c1,x).
8224 [para_from,254.1.1,225.1.2] a1!=ext(a1,d1,x,x).
19790 [para_into,224.1.2,75.1.2] insert(a,b,a1,c1)=b1.
40247 [para_from,19790.1.2,686.1.2] T(a1,insert(a,b,a1,c1),c2).
79840 [para_from,4308.1.1,254.1.1,unit_del,8224] E(c2,x,c1,x).
79842 [binary,79840.1,21.1] c2=c1.
80139 [para_from,79842.1.1,4178.1.6] E3(a,b,c,a1,b1,c1).
80468 [para_from,79842.1.2,221.1.3,unit_del,40247,80139] $F.