Sindbad~EG File Manager

Length of proof is 8.  Level of proof is 3.
 
---------------- PROOF ----------------
 
1 [] E(x,y,y,x).
5 [] E(y,ext(x,y,w,v),w,v).
13 [] E(xa,xb,xa,xb).
32 [] -T(xa,xb,xc)| -T(xa,xc,xd)|T(xa,xb,xd).
62 [] -le(xa,xb,xc,xd)|T(xa,xb,ins(xc,xd,xa,xb)).
63 [] -le(xa,xb,xc,xd)|E(xa,ins(xc,xd,xa,xb),xc,xd).
65 [] le(xa,xb,xc,xd)| -T(xa,xb,xe)| -E(xa,xe,xc,xd).
66 [] -le(xa,xb,xc,xd)| -E(xa,xb,xa1,xb1)| -E(xc,xd,xc1,xd1)|le(xa1,xb1,xc1,xd1).
68 [] insert(xa,xb,xa1,xc1)=ext(ext(xc1,xa1,alpha,gamma),xa1,xa,xb).
96 [] -le(xa,xb,xc,xd)|T(xc,insert(xa,xb,xc,xd),xd).
99 [] le(a,b,c,d).
100 [] le(c,d,e,f).
101 [] -le(a,b,e,f).
103 [binary,99.1,96.1] T(c,insert(a,b,c,d),d).
115 [hyper,66,100,13,1] le(c,d,f,e).
125 [ur,66,5,1,101] -le(x,ext(y,x,a,b),f,e).
204 [binary,115.1,63.1] E(c,ins(f,e,c,d),f,e).
205 [binary,115.1,62.1] T(c,d,ins(f,e,c,d)).
304 [para_into,103.1.2,68.1.1] T(c,ext(ext(d,c,alpha,gamma),c,a,b),d).
9258 [ur,65,125,204] -T(c,ext(x,c,a,b),ins(f,e,c,d)).
22005 [hyper,32,304,205] T(c,ext(ext(d,c,alpha,gamma),c,a,b),ins(f,e,c,d)).
22006 [binary,22005.1,9258.1] $F.