Sindbad~EG File Manager

Length of proof is 26.  Level of proof is 10.

---------------- PROOF ----------------

1 [] E(x,y,y,x).
14 [] -E(xa,xb,xc,xd)|E(xc,xd,xa,xb).
24 [] T(xa,xb,xb).
25 [] -T(xa,xb,xc)|T(xc,xb,xa).
26 [] T(xa1,xa1,xb1).
28 [] -T(xa,xb,xd)| -T(xb,xc,xd)|T(xa,xb,xc).
45 [] -T(xa,xb,xc)| -E3(xa,xb,xc,xa1,xb1,xc1)|T(xa1,xb1,xc1).
49 [] -Col(xa,xb,xc)|Col(xb,xa,xc).
50 [] -Col(xa,xb,xc)|Col(xa,xc,xb).
61 [] -le(xa,xb,xc,xd)|T(xa,xb,ins(xc,xd,xa,xb)).
65 [] -le(xa,xb,xc,xd)| -E(xa,xb,xa1,xb1)| -E(xc,xd,xc1,xd1)|le(xa1,xb1,xc1,xd1).
68 [] -le(xa,xb,xc,xd)| -le(xc,xd,xa,xb)|E(xa,xb,xc,xd).
71 [] -Col(xa,xb,xc)| -T(xa,xb,xc)|le(xa,xb,xa,xc).
72 [] -Col(xa,xb,xc)| -T(xa,xb,xc)|le(xb,xc,xa,xc).
73 [] -T(xa,xb,xc)| -E(xa,xc,xa,xb)|xc=xb.
92 [] -E(xa1,xa2,xb1,xb2)| -E(xa1,xa3,xb1,xb3)| -E(xa2,xa3,xb2,xb3)|E3(xa1,xa2,xa3,xb1,xb2,xb3).
93 [] -Col(xa,xb,xc)|T(xa,xb,xc)|T(xb,xc,xa)|T(xc,xa,xb).
103 [] -le(xa,xb,xc,xd)|E(xa,xb,xc,insert(xa,xb,xc,xd)).
104 [] -T(xc,y,xd)| -E(xa,xb,xc,y)|le(xa,xb,xc,xd).
105 [] Col(a,b,c).
106 [] -T(a,b,c).
107 [] le(a,b,a,c).
108 [] le(b,c,a,c).
112 [binary,105.1,50.1] Col(a,c,b).
113 [binary,105.1,49.1] Col(b,a,c).
123 [binary,106.1,45.3] -T(x,y,z)| -E3(x,y,z,a,b,c).
129 [binary,106.1,28.3] -T(a,b,x)| -T(b,c,x).
130 [binary,106.1,25.2] -T(c,b,a).
147 [binary,107.1,103.1] E(a,b,a,insert(a,b,a,c)).
150 [binary,107.1,68.1] -le(a,c,a,b)|E(a,b,a,c).
163 [binary,108.1,68.2] -le(a,c,b,c)|E(a,c,b,c).
164 [binary,108.1,68.1] -le(a,c,b,c)|E(b,c,a,c).
355 [binary,112.1,93.1,unit_del,130] T(a,c,b)|T(b,a,c).
1627 [binary,355.2,72.2,unit_del,113] T(a,c,b)|le(a,c,b,c).
1894 [binary,147.1,14.1] E(a,insert(a,b,a,c),a,b).
1898 [hyper,104,24,147] le(a,b,a,insert(a,b,a,c)).
2136 [binary,150.1,71.3,unit_del,112] E(a,b,a,c)| -T(a,c,b).
28114 [hyper,65,1898,1,1894] le(b,a,a,b).
28127 [hyper,65,28114,1,1] le(a,b,b,a).
28140 [binary,28127.1,61.1] T(a,b,ins(b,a,a,b)).
29073 [binary,28140.1,129.1] -T(b,c,ins(b,a,a,b)).
32849 [binary,2136.1,73.2,factor_simp] -T(a,c,b)|b=c.
32935 [para_from,32849.2.1,29073.1.1,unit_del,26] -T(a,c,b).
32939 [binary,32935.1,1627.1] le(a,c,b,c).
32944 [binary,32935.1,355.1] T(b,a,c).
33065 [binary,32944.1,123.1] -E3(b,a,c,a,b,c).
34603 [binary,32939.1,164.1] E(b,c,a,c).
34604 [binary,32939.1,163.1] E(a,c,b,c).
34782 [hyper,92,1,34603,34604] E3(b,a,c,a,b,c).
34783 [binary,34782.1,33065.1] $F.

------------ end of proof -------------