Sindbad~EG File Manager

Length of proof is 127.  Level of proof is 23.
 
---------------- 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).
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).
18 [] E(xa,xa,xb,xb).
19 [] -T(xa,xb,xc)| -T(xa1,xb1,xc1)| -E(xa,xb,xa1,xb1)| -E(xb,xc,xb1,xc1)|E(xa,xc,xa1,xc1).
21 [] -E(xb,xc,xa,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).
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).
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).
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).
56 [] xa=xb| -Col(xa,xb,xc)| -E(xa,xp,xa,xq)| -E(xb,xp,xb,xq)|E(xc,xp,xc,xq).
58 [] -T(xa,xc,xb)| -E(xa,xc,xa,xc1)| -E(xb,xc,xb,xc1)|xc=xc1.
73 [] -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).
77 [] -E(xa1,xa2,xb1,xb2)| -E(xa1,xa3,xb1,xb3)| -E(xa2,xa3,xb2,xb3)|E3(xa1,xa2,xa3,xb1,xb2,xb3).
79 [] Col(xa,xb,xc)| -T(xa,xb,xc).
80 [] Col(xa,xb,xc)| -T(xb,xc,xa).
81 [] Col(xa,xb,xc)| -T(xc,xa,xb).
90 [] a!=b.
91 [] T(a,b,c).
92 [] T(a,b,d).
93 [] -T(a,c,d).
94 [] -T(a,d,c).
95 [] c1=ext(a,d,c,d).
96 [] d1=ext(a,c,c,d).
97 [] p=ext(c1,c,c,d).
98 [] r=ext(d1,c,c,e).
99 [] q=ext(p,r,r,p).
100 [] b1=ext(a,c1,c,b).
101 [] b2=ext(a,d1,d,b).
102 [] e=ip(c1,d,b,d1,c).
103 [] d1=e|d1!=e.
104 [] c=c1|c!=c1.
112 [] ip(c1,d,b,d1,c)=e.
275 [hyper,29,91,4] T(b,c,ext(a,c,x,y)).
296 [binary,92.1,25.1] T(d,b,a).
304 [hyper,29,92,4] T(b,d,ext(a,d,x,y)).
358 [para_from,95.1.2,5.1.2] E(d,c1,c,d).
359 [para_from,95.1.2,4.1.3] T(a,d,c1).
361 [para_from,96.1.2,5.1.2] E(c,d1,c,d).
362 [para_from,96.1.2,4.1.3] T(a,c,d1).
364 [para_from,97.1.2,5.1.2] E(c,p,c,d).
365 [para_from,97.1.2,4.1.3] T(c1,c,p).
367 [para_from,98.1.2,5.1.2] E(c,r,c,e).
368 [para_from,98.1.2,4.1.3] T(d1,c,r).
370 [para_from,99.1.2,5.1.2] E(r,q,r,p).
371 [para_from,99.1.2,4.1.3] T(p,r,q).
373 [para_from,100.1.2,5.1.2] E(c1,b1,c,b).
374 [para_from,100.1.2,4.1.3] T(a,c1,b1).
376 [para_from,101.1.2,5.1.2] E(d1,b2,d,b).
377 [para_from,101.1.2,4.1.3] T(a,d1,b2).
379 [para_from,102.1.2,9.3.2] -T(c1,d,b)| -T(d1,c,b)|T(c,e,c1).
381 [para_from,104.1.1,94.1.3,unit_del,359] c!=c1.
388 [para_into,275.1.3,96.1.2] T(b,c,d1).
418 [binary,304.1,25.1] T(ext(a,d,x,y),d,b).
419 [para_into,304.1.3,95.1.2] T(b,d,c1).
420 [binary,358.1,77.2] -E(d,x,c,y)| -E(x,c1,y,d)|E3(d,x,c1,c,y,d).
422 [binary,358.1,17.1] E(d,c1,d,c).
430 [hyper,2,358,1] E(c,d,c1,d).
458 [binary,359.1,25.1] T(c1,d,a).
463 [hyper,32,92,359] T(a,b,c1).
477 [binary,361.1,16.1] E(d1,c,c,d).
478 [binary,361.1,14.1] E(c,d,c,d1).
484 [hyper,2,361,1] E(c,d,d1,c).
486 [binary,362.1,81.2] Col(c,d1,a).
504 [hyper,32,91,362] T(a,b,d1).
515 [ur,28,362,93] -T(c,d,d1).
520 [binary,364.1,15.1] -E(c,d,x,y)|E(c,p,x,y).
526 [hyper,2,364,1] E(c,d,p,c).
543 [binary,365.1,79.2] Col(c1,c,p).
568 [binary,367.1,22.1] E(r,c,e,c).
571 [binary,367.1,14.1] E(c,e,c,r).
579 [binary,368.1,81.2] Col(c,r,d1).
592 [binary,368.1,25.1] T(r,c,d1).
611 [binary,370.1,14.1] E(r,p,r,q).
646 [binary,373.1,22.1] E(b1,c1,b,c).
669 [binary,374.1,25.1] T(b1,c1,a).
686 [binary,376.1,22.1] E(b2,d1,b,d).
722 [hyper,32,362,377] T(a,c,b2).
725 [hyper,29,362,377] T(c,d1,b2).
735 [binary,379.1,25.2,unit_del,419] -T(d1,c,b)|T(c,e,c1).
747 [binary,388.1,81.2] Col(c,d1,b).
760 [binary,388.1,25.1] T(d1,c,b).
796 [para_into,418.1.1,95.1.2] T(c1,d,b).
825 [binary,422.1,14.1] E(d,c,d,c1).
841 [hyper,15,361,430] E(c,d1,c1,d).
862 [hyper,31,458,296] T(c1,b,a).
875 [binary,463.1,79.2] Col(a,b,c1).
890 [hyper,32,463,374] T(a,b,b1).
931 [hyper,77,361,478,1] E3(c,d1,d,c,d,d1).
935 [hyper,15,364,478] E(c,p,c,d1).
936 [hyper,15,358,478] E(d,c1,c,d1).
937 [hyper,2,430,478] E(c1,d,c,d1).
972 [hyper,32,504,377] T(a,b,b2).
1043 [hyper,15,477,526] E(d1,c,p,c).
1051 [binary,543.1,49.1] Col(c,c1,p).
1057 [binary,568.1,14.1] E(e,c,r,c).
1117 [binary,646.1,14.1] E(b,c,b1,c1).
1149 [hyper,28,669,458] T(b1,c1,d).
1158 [binary,686.1,14.1] E(b,d,b2,d1).
1190 [hyper,29,91,722] T(b,c,b2).
1237 [binary,735.1,25.2,unit_del,388] T(c,e,c1).
1251 [binary,735.2,25.1,unit_del,760] T(c1,e,c).
1314 [hyper,8,796,760,demod,112] T(d,e,d1).
1342 [hyper,19,725,796,841,376] E(c,b2,c1,b).
1371 [hyper,28,669,862] T(b1,c1,b).
1424 [binary,931.1,45.2,unit_del,515] -T(c,d1,d).
1555 [hyper,19,1149,388,646,937] E(b1,d,b,d1).
1630 [binary,1251.1,80.2] Col(c,c1,e).
1649 [hyper,29,1251,365] T(e,c,p).
1674 [binary,1314.1,25.1] T(d1,e,d).
1728 [hyper,19,1190,1371,1117,1342] E(b,b2,b1,b).
1782 [ur,45,24,1424] -E3(x,y,y,c,d1,d).
1824 [binary,1649.1,25.1] T(p,c,e).
1883 [binary,1728.1,17.1] E(b,b2,b,b1).
1896 [binary,1782.1,420.3,unit_del,936] -E(c1,c1,d1,d).
1926 [hyper,6,1043,367,1,935,368,1824] d1=c|E(r,p,e,d1).
1952 [hyper,6,13,1883,13,13,972,890,unit_del,90] E(b2,x,b1,x).
1960 [ur,15,18,1896] -E(x,x,d1,d).
1966 [para_from,1926.1.1,1424.1.2,unit_del,26] E(r,p,e,d1).
1967 [binary,1952.1,22.1] E(x,b2,x,b1).
1984 [hyper,15,1952,1555] E(b2,d,b,d1).
2009 [binary,1966.1,22.1] E(p,r,d1,e).
2020 [hyper,15,370,1966] E(r,q,e,d1).
2021 [hyper,2,1966,611] E(e,d1,r,q).
2025 [binary,1967.1,21.1] b1=b2.
2127 [binary,2009.1,14.1] E(d1,e,p,r).
2190 [para_from,2025.1.1,1371.1.1] T(b2,c1,b).
2225 [hyper,73,1190,2190,1,1342,1158,1984] IFS(b,c,b2,d,b2,c1,b,d1).
2245 [binary,2225.1,41.1] E(c,d,c1,d1).
2267 [hyper,2,2245,484] E(c1,d1,d1,c).
2269 [hyper,2,2245,430] E(c1,d1,c1,d).
2281 [hyper,2,2267,1] E(d1,c,d1,c1).
2294 [hyper,56,1630,361,2269,unit_del,381] E(e,d1,e,d).
2299 [ur,56,381,361,2269,1960] -Col(c,c1,d1).
2309 [hyper,73,1314,1314,13,13,825,2281] IFS(d,e,d1,c,d,e,d1,c1).
2316 [ur,58,592,2281,381] -E(r,c,r,c1).
2336 [hyper,15,2020,2294] E(r,q,e,d).
2338 [hyper,2,2294,2021] E(e,d,r,q).
2348 [binary,2299.1,50.2] -Col(c,d1,c1).
2365 [para_into,2299.1.3,103.1.1,unit_del,1630] d1!=e.
2366 [binary,2309.1,41.1] E(e,c,e,c1).
2370 [binary,2316.1,22.2] -E(c,r,c1,r).
2384 [hyper,19,371,1674,2009,2336] E(p,q,d1,d).
2396 [hyper,6,2127,2338,1043,1057,1674,371,unit_del,2365] E(d,c,q,c).
2399 [binary,2348.1,79.1] -T(c,d1,c1).
2449 [hyper,15,568,2366] E(r,c,e,c1).
2463 [binary,2370.1,14.2] -E(c1,r,c,r).
2479 [ur,15,2384,1960] -E(x,x,p,q).
2485 [binary,2396.1,22.1] E(c,d,c,q).
2563 [ur,15,571,2463] -E(c1,r,c,e).
2580 [binary,2485.1,520.1] E(c,p,c,q).
2610 [ur,42,1237,1,2449,2563] -T(c1,r,c).
2620 [hyper,56,579,2580,611] c=r|E(d1,p,d1,q).
2623 [ur,56,381,1051,2580,2479] -E(c1,p,c1,q).
2716 [para_from,2620.1.1,2610.1.3,unit_del,24] E(d1,p,d1,q).
2737 [hyper,56,747,2580,2716] c=d1|E(b,p,b,q).
2738 [hyper,56,486,2580,2716] c=d1|E(a,p,a,q).
2780 [para_from,2737.1.1,2399.1.1,unit_del,26] E(b,p,b,q).
2785 [para_from,2738.1.1,2399.1.1,unit_del,26] E(a,p,a,q).
2803 [ur,56,90,875,2780,2623] -E(a,p,a,q).
2804 [binary,2803.1,2785.1] $F.