Sindbad~EG File Manager

Length of proof is 25.  Level of proof is 11.
 
---------------- PROOF ----------------
 
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).
18 [] E(xa,xa,xb,xb).
20 [] xq=xa| -T(xq,xa,xd)| -E(xa,xd,xb,xc)|xd=ext(xq,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).
41 [] -IFS(xa,xb,xc,xd,xa1,xb1,xc1,xd1)|E(xb,xd,xb1,xd1).
45 [] -T(xa,xb,xc)| -E3(xa,xb,xc,xa1,xb1,xc1)|T(xa1,xb1,xc1).
69 [] -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).
70 [] -E3(xa1,xa2,xa3,xb1,xb2,xb3)|E(xa1,xa2,xb1,xb2).
71 [] -E3(xa1,xa2,xa3,xb1,xb2,xb3)|E(xa1,xa3,xb1,xb3).
72 [] -E3(xa1,xa2,xa3,xb1,xb2,xb3)|E(xa2,xa3,xb2,xb3).
73 [] -E(xa1,xa2,xb1,xb2)| -E(xa1,xa3,xb1,xb3)| -E(xa2,xa3,xb2,xb3)|E3(xa1,xa2,xa3,xb1,xb2,xb3).
74 [] -Col(xa,xb,xc)|T(xa,xb,xc)|T(xb,xc,xa)|T(xc,xa,xb).
78 [] -FS(xa,xb,xc,xd,xa1,xb1,xc1,xd1)|Col(xa,xb,xc).
79 [] -FS(xa,xb,xc,xd,xa1,xb1,xc1,xd1)|E3(xa,xb,xc,xa1,xb1,xc1).
80 [] -FS(xa,xb,xc,xd,xa1,xb1,xc1,xd1)|E(xa,xd,xa1,xd1).
81 [] -FS(xa,xb,xc,xd,xa1,xb1,xc1,xd1)|E(xb,xd,xb1,xd1).
83 [] FS(a,b,c,d,a1,b1,c1,d1).
84 [] a!=b.
85 [] -E(c,d,c1,d1).
113 [binary,83.1,81.1] E(b,d,b1,d1).
114 [binary,83.1,80.1] E(a,d,a1,d1).
115 [binary,83.1,79.1] E3(a,b,c,a1,b1,c1).
116 [binary,83.1,78.1] Col(a,b,c).
126 [ur,20,84,24,18] b=ext(a,b,x,x).
190 [binary,115.1,72.1] E(b,c,b1,c1).
191 [binary,115.1,71.1] E(a,c,a1,c1).
192 [binary,115.1,70.1] E(a,b,a1,b1).
195 [binary,116.1,74.1] T(a,b,c)|T(b,c,a)|T(c,a,b).
205 [para_from,126.1.1,84.1.2] a!=ext(a,b,x,x).
230 [binary,191.1,22.1] E(c,a,c1,a1).
257 [binary,192.1,22.1] E(b,a,b1,a1).
292 [hyper,45,195,115] T(b,c,a)|T(c,a,b)|T(a1,b1,c1).
359 [hyper,73,190,257,230] E3(b,c,a,b1,c1,a1).
360 [hyper,73,257,190,191] E3(b,a,c,b1,a1,c1).
427 [hyper,6,192,190,114,113,195,292,unit_del,84,85,factor_simp,factor_simp] T(b,c,a)|T(c,a,b).
429 [binary,359.1,45.2] -T(b,c,a)|T(b1,c1,a1).
431 [binary,360.1,45.2] -T(b,a,c)|T(b1,a1,c1).
435 [binary,427.2,25.1] T(b,c,a)|T(b,a,c).
2028 [binary,435.2,431.1] T(b,c,a)|T(b1,a1,c1).
4971 [hyper,6,257,191,113,114,435,2028,unit_del,85,factor_simp] T(b,c,a)|b=a.
4976 [para_from,4971.2.1,126.1.1,unit_del,205] T(b,c,a).
4978 [binary,4976.1,429.1] T(b1,c1,a1).
5062 [hyper,69,4976,4978,257,230,113,114] IFS(b,c,a,d,b1,c1,a1,d1).
11399 [binary,5062.1,41.1] E(c,d,c1,d1).
11400 [binary,11399.1,85.1] $F.