Sindbad~EG File Manager

Length of proof is 18.  Level of proof is 10.
 
---------------- PROOF ----------------
 
1 [] E(x,y,y,x).
2 [] -E(x,y,z,v)| -E(x,y,z2,v2)|E(z,v,z2,v2).
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).
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).
23 [] -T(xa,xb,xc)| -T(xA,xB,xC)| -E(xa,xb,xB,xC)| -E(xb,xc,xA,xB)|E(xa,xc,xA,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.
42 [] -T(xa,xb,xc)| -T(xa1,xb1,xc1)| -E(xa,xc,xa1,xc1)| -E(xb,xc,xb1,xc1)|E(xa,xb,xa1,xb1).
43 [] -T(xa,xb,xc)| -E(xa,xc,xa1,xc1)|T(xa1,insert(xa,xb,xa1,xc1),xc1).
62 [] insert(xa,xb,xa1,xc1)=ext(ext(xc1,xa1,alpha,gamma),xa1,xa,xb).
90 [] -le(xa,xb,xc,xd)|T(xc,insert(xa,xb,xc,xd),xd).
91 [] -le(xa,xb,xc,xd)|E(xa,xb,xc,insert(xa,xb,xc,xd)).
93 [] le(a,b,c,d).
94 [] -T(a,b,x)| -E(a,x,c,d)|x!=ext(a,b,insert(a,b,c,d),d).
95 [binary,93.1,91.1] E(a,b,c,insert(a,b,c,d)).
96 [binary,93.1,90.1] T(c,insert(a,b,c,d),d).
207 [binary,95.1,14.1] E(c,insert(a,b,c,d),a,b).
229 [hyper,23,4,26,95,5] E(a,ext(a,b,c,c),c,insert(a,b,c,d)).
231 [hyper,19,4,96,95,5] E(a,ext(a,b,insert(a,b,c,d),d),c,d).
232 [hyper,15,5,95] E(x,ext(y,x,a,b),c,insert(a,b,c,d)).
238 [hyper,2,95,1] E(c,insert(a,b,c,d),b,a).
12969 [hyper,15,229,207] E(a,ext(a,b,c,c),a,b).
13606 [binary,231.1,94.2,unit_del,4] ext(a,b,insert(a,b,c,d),d)!=ext(a,b,insert(a,b,c,d),d).
13824 [hyper,15,232,238] E(x,ext(y,x,a,b),b,a).
14229 [hyper,43,4,12969] T(a,insert(a,b,a,b),b).
14387 [binary,14229.1,25.1] T(b,insert(a,b,a,b),a).
15318 [para_into,13824.1.2,62.1.2] E(x,insert(a,b,x,y),b,a).
16307 [hyper,42,26,14387,15318,1] E(a,a,b,insert(a,b,a,b)).
18000 [hyper,2,16307,18] E(b,insert(a,b,a,b),x,x).
22111 [hyper,43,26,18000] T(x,insert(b,b,x,x),x).
22162 [binary,22111.1,27.2,unit_del,24] insert(b,b,x,x)=x.
22170 [para_into,22162.1.1,22162.1.1] x=x.
22171 [binary,22170.1,13606.1] $F.