Sindbad~EG File Manager

Length of proof is 10.  Level of proof is 4.
 
---------------- PROOF ----------------
 
7 [] -T(x,y,x)|x=y.
13 [] E(xa,xb,xa,xb).
58 [] -T(xa,xc,xb)| -E(xa,xc,xa,xc1)| -E(xb,xc,xb,xc1)|xc=xc1.
109 [] M(xa,xm,xa)|xm!=xa.
117 [] s(xa,xp)=xp|xp!=xa.
124 [] s(xa,xp)!=s(xb,xp)|xa=xb.
172 [] -M(xa,xm,xb)|T(xa,xm,xb).
182 [] -R(xa,xb,xc)|E(xa,xc,xa,s(xb,xc)).
195 [] R(a,b,c).
196 [] R(a1,b,c).
197 [] T(a,c,a1).
198 [] b!=c.
199 [binary,195.1,182.1] E(a,c,a,s(b,c)).
204 [binary,196.1,182.1] E(a1,c,a1,s(b,c)).
291 [hyper,58,197,13,13] c=c.
420 [binary,198.1,7.2] -T(b,c,b).
486 [binary,291.1,117.2] s(c,c)=c.
918 [binary,420.1,172.2] -M(b,c,b).
1032 [hyper,58,197,199,204] c=s(b,c).
1348 [binary,918.1,109.1] c!=b.
1360 [binary,1348.1,124.2] s(c,x)!=s(b,x).
2528 [para_into,1032.1.1,486.1.2] s(c,c)=s(b,c).
2529 [binary,2528.1,1360.1] $F.