Sindbad~EG File Manager

Length of proof is 13.  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).
7 [] -T(x,y,x)|x=y.
8 [] -T(xa,xp,xc)| -T(xb,xq,xc)|T(xp,ip(xa,xp,xc,xb,xq),xb).
9 [] -T(xa,xp,xc)| -T(xb,xq,xc)|T(xq,ip(xa,xp,xc,xb,xq),xa).
12 [] -E(xa,xb,xc,xd)| -E(xc,xd,xe,xf)|E(xa,xb,xe,xf).
14 [] -E(xa,xb,xc,xd)|E(xa,xb,xd,xc).
15 [] E(xa,xa,xb,xb).
16 [] -T(xa,xb,xc)| -T(xa1,xb1,xc1)| -E(xa,xb,xa1,xb1)| -E(xb,xc,xb1,xc1)|E(xa,xc,xa1,xc1).
18 [] -E(xb,xc,xa,xa)|xb=xc.
20 [] T(a,b,c).
21 [] T(A,B,C).
22 [] E(a,b,B,C).
23 [] E(b,c,A,B).
24 [] -E(a,c,A,C).
25 [] d=ext(a,b,b,b).
42 [binary,22.1,14.1] E(a,b,C,B).
47 [binary,23.1,14.1] E(b,c,B,A).
52 [binary,24.1,14.2] -E(a,c,C,A).
57 [para_from,25.1.2,5.1.2] E(b,d,b,b).
63 [ur,16,20,42,47,52] -T(C,B,A).
67 [hyper,12,57,15] E(b,d,x,x).
71 [hyper,12,5,67] E(x,ext(y,x,b,d),z,z).
73 [binary,71.1,18.1] x=ext(y,x,b,d).
75 [para_from,73.1.2,4.1.3] T(x,y,y).
76 [hyper,9,75,21] T(B,ip(x,C,C,A,B),x).
77 [hyper,8,75,21] T(C,ip(x,C,C,A,B),A).
78 [binary,76.1,7.1] B=ip(B,C,C,A,B).
79 [para_from,78.1.1,63.1.2] -T(C,ip(B,C,C,A,B),A).
80 [binary,79.1,77.1] $F.