Sindbad~EG File Manager

Length of proof is 44.  Level of proof is 11.
 
---------------- 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).
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).
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).
17 [] -E(xa,xb,xc,xd)|E(xa,xb,xd,xc).
18 [] E(xa,xa,xb,xb).
21 [] -E(xb,xc,xa,xa)|xb=xc.
22 [] -E(xa,xb,xc,xd)|E(xb,xa,xd,xc).
24 [] T(xa,xb,xb).
25 [] -T(xa,xb,xc)|T(xc,xb,xa).
27 [] -T(xa,xb,xc)| -T(xb,xa,xc)|xa=xb.
28 [] -T(xa,xb,xd)| -T(xb,xc,xd)|T(xa,xb,xc).
49 [] -IFS(xa,xb,xc,xd,za,zb,zc,zd)|T(xa,xb,xc).
50 [] -IFS(xa,xb,xc,xd,za,zb,zc,zd)|T(za,zb,zc).
51 [] -IFS(xa,xb,xc,xd,za,zb,zc,zd)|E(xa,xc,za,zc).
52 [] -IFS(xa,xb,xc,xd,za,zb,zc,zd)|E(xb,xc,zb,zc).
53 [] -IFS(xa,xb,xc,xd,za,zb,zc,zd)|E(xa,xd,za,zd).
54 [] -IFS(xa,xb,xc,xd,za,zb,zc,zd)|E(xc,xd,zc,zd).
69 [] IFS(a,b,c,d,a1,b1,c1,d1).
70 [] -E(b,d,b1,d1).
71 [] e=ext(a,c,a,c).
72 [] e1=ext(a1,c1,a,c).
121 [binary,69.1,54.1] E(c,d,c1,d1).
122 [binary,69.1,53.1] E(a,d,a1,d1).
123 [binary,69.1,52.1] E(b,c,b1,c1).
124 [binary,69.1,51.1] E(a,c,a1,c1).
125 [binary,69.1,50.1] T(a1,b1,c1).
126 [binary,69.1,49.1] T(a,b,c).
136 [para_from,71.1.2,5.1.2] E(c,e,a,c).
137 [para_from,71.1.2,4.1.3] T(a,c,e).
139 [para_from,72.1.2,5.1.2] E(c1,e1,a,c).
140 [para_from,72.1.2,4.1.3] T(a1,c1,e1).
159 [binary,123.1,22.1] E(c,b,c1,b1).
172 [binary,124.1,2.1] -E(a,c,x,y)|E(a1,c1,x,y).
192 [binary,125.1,25.1] T(c1,b1,a1).
209 [binary,126.1,27.1] -T(b,a,c)|a=b.
210 [binary,126.1,25.1] T(c,b,a).
216 [binary,136.1,17.1] E(c,e,c,a).
218 [binary,136.1,15.1] -E(a,c,x,y)|E(c,e,x,y).
225 [hyper,2,136,1] E(a,c,e,c).
239 [binary,137.1,25.1] T(e,c,a).
249 [binary,139.1,14.1] E(a,c,c1,e1).
269 [binary,140.1,25.1] T(e1,c1,a1).
287 [binary,172.2,21.1] -E(a,c,x,x)|a1=c1.
330 [binary,216.1,14.1] E(c,a,c,e).
339 [binary,218.2,21.1] -E(a,c,x,x)|c=e.
344 [hyper,15,139,225] E(c1,e1,e,c).
364 [hyper,28,239,210] T(e,c,b).
365 [binary,249.1,218.1] E(c,e,c1,e1).
395 [hyper,28,269,192] T(e1,c1,b1).
400 [para_from,287.2.1,192.1.3] T(c1,b1,c1)| -E(a,c,x,x).
409 [para_from,339.2.2,330.1.4] E(c,a,c,c)| -E(a,c,x,x).
420 [hyper,2,344,1] E(e,c,e1,c1).
442 [hyper,6,124,365,122,121,137,140] a=c|E(e,d,e1,d1).
466 [binary,400.1,27.1,unit_del,24] -E(a,c,x,x)|c1=b1.
479 [para_from,442.1.1,409.2.1,unit_del,18] E(c,a,c,c)|E(e,d,e1,d1).
491 [para_from,466.2.2,70.1.3] -E(b,d,c1,d1)| -E(a,c,x,x).
493 [hyper,15,479,18] E(e,d,e1,d1)|E(c,a,x,x).
495 [hyper,6,420,159,493,121,364,395,unit_del,70] E(c,a,x,x)|e=c.
499 [para_from,495.2.1,330.1.4,factor_simp] E(c,a,c,c).
503 [binary,499.1,21.1] c=a.
519 [para_from,503.1.1,491.2.2,unit_del,18] -E(b,d,c1,d1).
530 [para_from,503.1.1,287.1.2,unit_del,18] a1=c1.
537 [para_from,503.1.1,209.1.3,unit_del,24] a=b.
659 [para_from,530.1.2,519.1.3] -E(b,d,a1,d1).
687 [para_from,537.1.1,122.1.1] E(b,d,a1,d1).
688 [binary,687.1,659.1] $F.