Sindbad~EG File Manager

Length of proof is 30.  Level of proof is 6.
 
---------------- PROOF ----------------
 
1 [] E(x,y,y,x).
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).
13 [] E(xa,xb,xa,xb).
15 [] -E(xa,xb,xc,xd)| -E(xc,xd,xe,xf)|E(xa,xb,xe,xf).
16 [] -E(xa,xb,xc,xd)|E(xb,xa,xc,xd).
17 [] -E(xa,xb,xc,xd)|E(xa,xb,xd,xc).
25 [] -T(xa,xb,xc)|T(xc,xb,xa).
41 [] -IFS(xa,xb,xc,xd,xa1,xb1,xc1,xd1)|E(xb,xd,xb1,xd1).
42 [] -T(xa,xb,xc)| -T(xa1,xb1,xc1)| -E(xa,xc,xa1,xc1)| -E(xb,xc,xb1,xc1)|E(xa,xb,xa1,xb1).
107 [] -M(xa,xm,xb)|M(xb,xm,xa).
110 [] M(xp,xa,s(xa,xp)).
112 [] -M(xp,xa,xq)|xq=s(xa,xp).
117 [] s(xa,xp)=xp|xp!=xa.
118 [] E(xp,xq,s(xa,xp),s(xa,xq)).
132 [] -R(xa,xb,xc)|R(xc,xb,xa).
177 [] -T(xa,xb,xc)| -T(za,zb,zc)| -E(xa,xc,za,zc)| -E(xb,xc,zb,zc)| -E(xa,xd,za,zd)| -E(xc,xd,zc,zd)|IFS(xa,xb,xc,xd,za,zb,zc,zd).
199 [] -M(xa,xm,xb)|T(xa,xm,xb).
200 [] -M(xa,xm,xb)|E(xm,xa,xm,xb).
209 [] -R(xa,xb,xc)|E(xa,xc,xa,s(xb,xc)).
210 [] R(xa,xb,xc)| -E(xa,xc,xa,s(xb,xc)).
222 [] R(a,b,c).
223 [] M(s(a,c),p,s(b,c)).
224 [] -R(b,a,p).
225 [] d=s(b,c).
226 [] b1=s(a,b).
227 [] c1=s(a,c).
230 [] s(b,c)=d.
231 [] s(a,b)=b1.
232 [] s(a,c)=c1.
271 [binary,222.1,209.1,demod,230] E(a,c,a,d).
278 [binary,223.1,199.1,demod,232,230] T(c1,p,d).
284 [binary,223.1,107.1,demod,230,232] M(d,p,c1).
295 [binary,224.1,132.2] -R(p,a,b).
321 [para_from,225.1.2,110.1.3] M(c,b,d).
329 [para_into,226.1.2,117.1.1] b1=b|b!=a.
334 [para_from,226.1.2,118.1.4] E(x,b,s(a,x),b1).
335 [para_from,226.1.2,118.1.3] E(b,x,b1,s(a,x)).
342 [para_from,226.1.2,110.1.3] M(b,a,b1).
362 [para_from,227.1.2,110.1.3] M(c,a,c1).
439 [binary,278.1,25.1] T(d,p,c1).
462 [binary,284.1,200.1] E(p,d,p,c1).
471 [binary,295.1,210.1,demod,231] -E(p,b,p,b1).
478 [binary,321.1,200.1] E(b,c,b,d).
479 [binary,321.1,199.1] T(c,b,d).
521 [para_into,334.1.3,227.1.2] E(c,b,c1,b1).
546 [binary,342.1,199.1] T(b,a,b1).
560 [binary,362.1,107.1] M(c1,a,c).
623 [binary,471.1,41.2] -IFS(x,p,y,b,z,p,u,b1).
630 [para_into,471.1.2,329.1.2,unit_del,13] b!=a.
670 [binary,479.1,25.1] T(d,b,c).
742 [hyper,6,13,13,478,271,546,546,unit_del,630] E(b1,c,b1,d).
751 [binary,560.1,112.1] c=s(a,c1).
833 [hyper,42,670,479,1,478] E(d,b,c,b).
845 [binary,742.1,17.1] E(b1,c,d,b1).
881 [para_from,751.1.2,335.1.4] E(b,c1,b1,c).
907 [hyper,15,833,521] E(d,b,c1,b1).
925 [binary,881.1,16.1] E(c1,b,b1,c).
959 [ur,177,278,439,1,462,907,623] -E(c1,b,d,b1).
969 [hyper,15,925,845] E(c1,b,d,b1).
970 [binary,969.1,959.1] $F.