Sindbad~EG File Manager

Length of proof is 21.  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).
14 [] -E(xa,xb,xc,xd)|E(xc,xd,xa,xb).
21 [] -E(xb,xc,xa,xa)|xb=xc.
24 [] T(xa,xb,xb).
25 [] -T(xa,xb,xc)|T(xc,xb,xa).
26 [] T(xa1,xa1,xb1).
27 [] -T(xa,xb,xc)| -T(xb,xa,xc)|xa=xb.
29 [] -T(xa,xb,xc)| -T(xa,xc,xd)|T(xb,xc,xd).
30 [] -T(xa,xb,xc)| -T(xb,xc,xd)|xb=xc|T(xa,xc,xd).
37 [] T(xa,xb,ext(xa,xb,alpha,gamma)).
38 [] xb!=ext(xa,xb,alpha,gamma).
52 [] Col(xa,xb,xa).
69 [] -le(xa,xb,xc,xd)| -le(xc,xd,xa,xb)|E(xa,xb,xc,xd).
71 [] le(xa,xa,xc,xd).
83 [] sameside(xa,xp,xb)|xa=xp|xb=xp|xc=xp| -T(xa,xp,xc)| -T(xb,xp,xc).
86 [] sameside(xa,xp,xb)| -Col(xa,xp,xb)|T(xa,xp,xb).
88 [] -sameside(xa,xp,xb)|sameside(xb,xp,xa).
90 [] insert(xa,xb,xa1,xc1)=ext(ext(xc1,xa1,alpha,gamma),xa1,xa,xb).
120 [] -T(xc,y,xd)| -E(xa,xb,xc,y)|le(xa,xb,xc,xd).
122 [] -sameside(xa,xp,xb)|xb!=xp.
126 [] r!=a.
127 [] b!=c.
128 [] -sameside(insert(b,c,a,r),a,r)| -E(a,insert(b,c,a,r),b,c).
129 [] q=ext(r,a,alpha,gamma).
130 [] c1=ext(q,a,b,c).
131 [] ext(r,a,alpha,gamma)=q.
132 [] ext(q,a,b,c)=c1.
140 [binary,126.1,83.2] sameside(r,a,x)|x=a|y=a| -T(r,a,y)| -T(x,a,y).
161 [ur,30,26,37,126,demod,131] T(r,a,q).
211 [binary,127.1,21.2] -E(b,c,x,x).
246 [binary,128.1,88.2] -E(a,insert(b,c,a,r),b,c)| -sameside(r,a,insert(b,c,a,r)).
259 [para_from,129.1.2,90.1.2.1] insert(x,y,a,r)=ext(q,a,x,y).
260 [para_from,129.1.2,38.1.2] a!=q.
268 [para_from,130.1.2,5.1.2] E(a,c1,b,c).
269 [para_from,130.1.2,4.1.3] T(q,a,c1).
339 [ur,27,24,260] -T(q,a,q).
805 [binary,269.1,25.1] T(c1,a,q).
1025 [binary,339.1,86.3,unit_del,52] sameside(q,a,q).
2013 [binary,1025.1,122.1] q!=a.
3087 [binary,211.1,69.3,unit_del,71] -le(b,c,x,x).
3223 [binary,268.1,14.1] E(b,c,a,c1).
6392 [ur,120,3223,3087] -T(a,c1,a).
6417 [ur,29,26,6392] -T(c1,a,c1).
6603 [binary,6417.1,86.3,unit_del,52] sameside(c1,a,c1).
6784 [binary,6603.1,122.1] c1!=a.
6878 [ur,140,6784,2013,161,805] sameside(r,a,c1).
12817 [para_into,246.2.3,90.1.1,demod,131,132,unit_del,6878] -E(a,insert(b,c,a,r),b,c).
14370 [para_from,259.1.2,5.1.2] E(a,insert(x,y,a,r),x,y).
14371 [binary,14370.1,12817.1] $F.