Sindbad~EG File Manager

Length of proof is 114.  Level of proof is 25.
 
---------------- 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).
8 [] -T(xa,xp,xc)| -T(xb,xq,xc)|T(xp,ip(xa,xp,xc,xb,xq),xb).
9 [] -T(xa,xp,xc)| -T(xb,xq,xc)|T(xq,ip(xa,xp,xc,xb,xq),xa).
13 [] E(xa,xb,xa,xb).
14 [] -E(xa,xb,xc,xd)|E(xc,xd,xa,xb).
16 [] -E(xa,xb,xc,xd)|E(xb,xa,xc,xd).
18 [] E(xa,xa,xb,xb).
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).
26 [] T(xa1,xa1,xb1).
28 [] -T(xa,xb,xd)| -T(xb,xc,xd)|T(xa,xb,xc).
29 [] -T(xa,xb,xc)| -T(xa,xc,xd)|T(xb,xc,xd).
31 [] -T(xa,xb,xd)| -T(xb,xc,xd)|T(xa,xc,xd).
32 [] -T(xa,xb,xc)| -T(xa,xc,xd)|T(xa,xb,xd).
33 [] -T(xa,xb,xc)| -T(xb,xc,xd)|xb=xc|T(xa,xb,xd).
37 [] T(xa,xb,ext(xa,xb,alpha,gamma)).
38 [] xb!=ext(xa,xb,alpha,gamma).
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).
43 [] -T(xa,xb,xc)| -E(xa,xc,xa1,xc1)|T(xa1,insert(xa,xb,xa1,xc1),xc1).
46 [] -Col(xa,xb,xc)|Col(xb,xc,xa).
47 [] -Col(xa,xb,xc)|Col(xc,xa,xb).
48 [] -Col(xa,xb,xc)|Col(xc,xb,xa).
49 [] -Col(xa,xb,xc)|Col(xb,xa,xc).
50 [] -Col(xa,xb,xc)|Col(xa,xc,xb).
52 [] Col(xa,xb,xa).
53 [] -Col(xa,xb,xc)| -E3(xa,xb,xc,xa1,xb1,xc1)|Col(xa1,xb1,xc1).
58 [] -T(xa,xc,xb)| -E(xa,xc,xa,xc1)| -E(xb,xc,xb,xc1)|xc=xc1.
60 [] xa=xb| -T(xa,xb,xc)| -T(xa,xb,xd)|T(xb,xc,xd)|T(xb,xd,xc).
98 [] xp=xq|xp=xr| -T(xq,xp,xr)|xa!=xp|Col(xa,xp,xq).
102 [] xp=xq| -Col(xp,xq,xr)|Col(xq,xp,xr).
104 [] xa=xb|xp=xq| -Col(xa,xb,xc)| -Col(xp,xq,xc)| -Col(xa,xb,xd)| -Col(xp,xq,xd)|xc=xd| -Col(xa,xb,xe)|Col(xp,xq,xe).
107 [] -M(xa,xm,xb)|M(xb,xm,xa).
112 [] -M(xp,xa,xq)|xq=s(xa,xp).
117 [] s(xa,xp)=xp|xp!=xa.
126 [] -Col(xa,xm,xb)| -E(xm,xa,xm,xb)|xa=xb|M(xa,xm,xb).
127 [] Col(xa,xb,xc)|xb=xd| -E(xa,xb,xc,xd)| -E(xb,xc,xd,xa)| -Col(xa,xp,xc)| -Col(xb,xp,xd)|M(xa,xp,xc).
131 [] insert(xa,xb,xa1,xc1)=ext(ext(xc1,xa1,alpha,gamma),xa1,xa,xb).
145 [] -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).
148 [] -E3(xa1,xa2,xa3,xb1,xb2,xb3)|E(xa2,xa3,xb2,xb3).
149 [] -E(xa1,xa2,xb1,xb2)| -E(xa1,xa3,xb1,xb3)| -E(xa2,xa3,xb2,xb3)|E3(xa1,xa2,xa3,xb1,xb2,xb3).
150 [] -Col(xa,xb,xc)|T(xa,xb,xc)|T(xb,xc,xa)|T(xc,xa,xb).
151 [] Col(xa,xb,xc)| -T(xa,xb,xc).
152 [] Col(xa,xb,xc)| -T(xb,xc,xa).
153 [] Col(xa,xb,xc)| -T(xc,xa,xb).
169 [] -T(xa,xm,xb)| -E(xm,xa,xm,xb)|M(xa,xm,xb).
178 [] E(c,a,c,b).
179 [] -M(a,x,b).
180 [] p=ext(c,a,a,c).
181 [] q=ext(c,b,a,p).
182 [] r=ip(p,a,c,q,b).
184 [] r1=insert(b,r,a,q).
189 [] ip(b,r,p,c,a)=cx.
314 [binary,178.1,169.2,unit_del,179] -T(a,c,b).
315 [binary,178.1,126.2,unit_del,179] -Col(a,c,b)|a=b.
317 [binary,178.1,58.3] -T(x,a,c)| -E(x,a,x,b)|a=b.
318 [binary,178.1,22.1] E(a,c,b,c).
321 [binary,178.1,14.1] E(c,b,c,a).
324 [hyper,149,178,178,18] E3(c,a,a,c,b,b).
334 [binary,179.1,107.2] -M(b,x,a).
335 [ur,169,26,179] -E(a,a,a,b).
342 [para_from,180.1.2,5.1.2] E(a,p,a,c).
343 [para_from,180.1.2,4.1.3] T(c,a,p).
349 [para_from,181.1.2,5.1.2] E(b,q,a,p).
350 [para_from,181.1.2,4.1.3] T(c,b,q).
356 [para_from,182.1.2,9.3.2] -T(p,a,c)| -T(q,b,c)|T(b,r,p).
357 [para_from,182.1.2,8.3.2] -T(p,a,c)| -T(q,b,c)|T(a,r,q).
370 [para_into,184.1.2,131.1.1] r1=ext(ext(q,a,alpha,gamma),a,b,r).
371 [para_from,184.1.2,43.3.2] -T(b,r,x)| -E(b,x,a,q)|T(a,r1,q).
382 [binary,314.1,25.2] -T(b,c,a).
422 [binary,318.1,14.1] E(b,c,a,c).
457 [binary,334.1,169.3] -T(b,x,a)| -E(x,b,x,a).
462 [binary,335.1,148.2] -E3(x,a,a,y,a,b).
467 [ur,42,26,13,318,335] -T(a,b,c).
509 [binary,343.1,25.1] T(p,a,c).
519 [hyper,29,343,4] T(a,p,ext(c,p,x,y)).
534 [binary,349.1,14.1] E(a,p,b,q).
564 [binary,350.1,25.1] T(q,b,c).
580 [ur,28,350,314] -T(a,c,q).
584 [binary,356.1,25.2,unit_del,564,343] T(b,r,p).
586 [binary,356.3,152.2,unit_del,509,564] Col(p,b,r).
602 [binary,356.3,25.1,unit_del,509,564] T(p,r,b).
607 [binary,357.3,151.2,unit_del,509,564] Col(a,r,q).
623 [para_from,370.1.2,5.1.2] E(a,r1,b,r).
645 [ur,28,343,382] -T(b,c,p).
661 [para_into,324.1.5,317.3.2,unit_del,462] -T(x,a,c)| -E(x,a,x,b).
663 [para_into,324.1.5,315.2.2,unit_del,462] -Col(a,c,b).
700 [binary,509.1,169.1,unit_del,342] M(p,a,c).
733 [ur,29,509,314] -T(p,c,b).
740 [binary,534.1,22.1] E(p,a,q,b).
786 [ur,31,564,467] -T(a,q,c).
828 [hyper,9,584,343,demod,189] T(a,cx,b).
829 [hyper,8,584,343,demod,189] T(r,cx,c).
891 [binary,607.1,50.1] Col(a,q,r).
907 [hyper,2,623,1] E(b,r,r1,a).
934 [ur,29,564,645] -T(q,c,p).
940 [binary,661.1,509.1] -E(p,a,p,b).
948 [binary,663.1,153.1] -T(b,a,c).
952 [binary,663.1,49.2] -Col(c,a,b).
953 [binary,663.1,48.2] -Col(b,c,a).
955 [binary,663.1,46.2] -Col(b,a,c).
959 [binary,700.1,112.1] c=s(a,p).
1023 [binary,786.1,25.2] -T(c,q,a).
1051 [binary,828.1,151.2] Col(a,cx,b).
1066 [binary,828.1,25.1] T(b,cx,a).
1129 [binary,907.1,16.1] E(r,b,r1,a).
1174 [ur,42,509,13,318,940] -T(p,b,c).
1207 [ur,31,509,948] -T(b,p,c).
1229 [para_into,959.1.2,117.1.1] c=p|p!=a.
1283 [binary,1051.1,48.1] Col(b,cx,a).
1285 [binary,1066.1,457.1] -E(cx,b,cx,a).
1373 [binary,1174.1,25.2] -T(c,b,p).
1393 [ur,31,564,1174] -T(p,q,c).
1408 [binary,1207.1,150.3,unit_del,1373,733] -Col(c,b,p).
1454 [para_from,1229.1.1,1207.1.3,unit_del,24] p!=a.
1474 [binary,1285.1,41.2] -IFS(x,cx,y,b,z,cx,u,a).
1506 [ur,31,343,1373] -T(a,b,p).
1558 [binary,1408.1,48.2] -Col(p,b,c).
1593 [ur,60,1454,509,467,314] -T(p,a,b).
1594 [ur,33,509,1454,1207] -T(b,p,a).
1609 [ur,145,829,829,13,13,321,1474] -E(r,b,r,a).
1615 [binary,1506.1,150.4,unit_del,1594,1593] -Col(b,p,a).
1617 [binary,1506.1,150.2,unit_del,1594,1593] -Col(a,b,p).
1731 [binary,1615.1,48.2] -Col(a,p,b).
1732 [ur,98,1454,38,519,1615] b!=p.
1766 [ur,98,1732,38,37,1617] a!=b.
1767 [ur,98,1732,38,37,1408] c!=b.
1826 [ur,98,1766,38,37,952] c!=a.
1857 [ur,98,1767,38,37,663] a!=c.
1900 [ur,98,1826,38,37,953] b!=c.
1928 [ur,6,178,534,321,1,343,350,1826] E(p,b,q,a).
1938 [ur,98,1857,38,37,955] b!=a.
1983 [ur,98,1900,38,37,1558] p!=b.
2010 [binary,1928.1,22.1] E(b,p,a,q).
2035 [ur,127,1938,1,18,1051,1283,179] Col(a,b,b).
2058 [ur,58,564,321,1938] -E(q,b,q,a).
2068 [ur,98,1983,38,37,1731] a!=p.
2096 [binary,2010.1,371.2,unit_del,584] T(a,r1,q).
2097 [binary,2010.1,14.1] E(a,q,b,p).
2138 [ur,42,564,13,422,2058] -T(q,a,c).
2183 [binary,2096.1,153.2] Col(r1,q,a).
2200 [binary,2096.1,25.1] T(q,r1,a).
2253 [binary,2138.1,150.2,unit_del,580,1023] -Col(q,a,c).
2260 [binary,2138.1,25.2] -T(c,a,q).
2316 [binary,2183.1,48.1] Col(a,q,r1).
2345 [hyper,42,602,2200,1928,1129] E(p,r,q,r1).
2372 [binary,2253.1,50.2] -Col(q,c,a).
2373 [binary,2253.1,49.2] -Col(a,q,c).
2375 [ur,98,1857,2068,343,2253] q!=a.
2411 [ur,32,343,2260] -T(c,p,q).
2448 [binary,2345.1,22.1] E(r,p,r1,q).
2465 [ur,98,1826,38,37,2372] q!=c.
2501 [ur,102,2375,52] Col(a,q,q).
2544 [binary,2411.1,150.4,unit_del,1393,934] -Col(p,q,c).
2586 [hyper,145,584,2096,2010,2448,349,1] IFS(b,r,p,q,a,r1,q,p).
2587 [hyper,145,584,2096,2010,2448,1,740] IFS(b,r,p,a,a,r1,q,b).
2623 [ur,98,2465,38,37,2373] a!=q.
2685 [ur,98,2465,38,37,2544] p!=q.
2695 [binary,2586.1,41.1] E(r,q,r1,p).
2718 [binary,2587.1,41.1] E(r,a,r1,b).
2769 [ur,127,1731,2685,534,1928,2035,179] -Col(p,b,q).
2860 [binary,2718.1,22.1] E(a,r,b,r1).
2910 [hyper,149,2860,2097,2695] E3(a,r,q,b,r1,p).
2930 [binary,2910.1,53.2,unit_del,607] Col(b,r1,p).
2938 [binary,2930.1,47.1] Col(p,b,r1).
2956 [hyper,104,891,586,2316,2938,2501,unit_del,2623,1983,2769] r=r1.
2997 [para_from,2956.1.1,1609.1.3] -E(r,b,r1,a).
2998 [binary,2997.1,1129.1] $F.