Sindbad~EG File Manager

Length of proof is 98.  Level of proof is 24.
 
---------------- PROOF ----------------
 
2 [] -E(x,y,z,v)| -E(x,y,z2,v2)|E(z,v,z2,v2).
15 [] -E(xa,xb,xc,xd)| -E(xc,xd,xe,xf)|E(xa,xb,xe,xf).
25 [] -T(xa,xb,xc)|T(xc,xb,xa).
37 [] T(xa,xb,ext(xa,xb,alpha,gamma)).
38 [] xb!=ext(xa,xb,alpha,gamma).
39 [] -T(xa,xb,xc)| -T(xa1,xb1,xc)| -T(xa,xp,xa1)|T(xp,crossbar(xa,xb,xc,xa1,xb1,xp),xc).
40 [] -T(xa,xb,xc)| -T(xa1,xb1,xc)| -T(xa,xp,xa1)|T(xb,crossbar(xa,xb,xc,xa1,xb1,xp),xb1).
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).
50 [] -Col(xa,xb,xc)|Col(xa,xc,xb).
51 [] Col(xa,xa,xb).
52 [] Col(xa,xb,xa).
56 [] xa=xb| -Col(xa,xb,xc)| -E(xa,xp,xa,xq)| -E(xb,xp,xb,xq)|E(xc,xp,xc,xq).
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).
103 [] xa=xb|xp=xq| -Col(xp,xq,xa)| -Col(xp,xq,xb)| -Col(xp,xq,xr)|Col(xa,xb,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).
109 [] M(xa,xm,xa)|xm!=xa.
110 [] M(xp,xa,s(xa,xp)).
111 [] -M(xp,xa,xr)| -M(xp,xa,xq)|xr=xq.
112 [] -M(xp,xa,xq)|xq=s(xa,xp).
113 [] s(xa,s(xa,xp))=xp.
114 [] s(xa,xp)!=xr|s(xa,xq)!=xr|xp=xq.
115 [] s(xa,xp)!=s(xa,xq)|xp=xq.
116 [] s(xa,xp)!=xp|xp=xa.
117 [] s(xa,xp)=xp|xp!=xa.
124 [] s(xa,xp)!=s(xb,xp)|xa=xb.
126 [] -Col(xa,xm,xb)| -E(xm,xa,xm,xb)|xa=xb|M(xa,xm,xb).
131 [] -E(xc,xa,xc,xb)|M(xa,isomidpoint(xa,xb,xc),xb).
132 [] -R(xa,xb,xc)|R(xc,xb,xa).
133 [] -R(xa,xb,xc)|xa=xb| -Col(xb,xa,xa1)|R(xa1,xb,xc).
134 [] -R(xa,xb,xc)|R(xa,xb,s(xb,xc)).
142 [] -perp(xa,xb,xp,xq)|perp(xp,xq,xa,xb).
156 [] xa=xb| -Col(xa,xb,xd)| -perp(xa,xb,xc,xd)|perpAt(xa,xb,xd,xc,xd).
158 [] xa=xb| -Col(xa,xb,xp)| -Col(xa,xb,xq)|xq=xp|R(xc,xp,xq)| -perp(xa,xb,xc,xp).
159 [] xa=xb| -Col(xa,xb,xp)| -Col(xa,xb,xq)|xq=xp|perp(xa,xb,xc,xp)|Col(xa,xb,xc)| -R(xc,xp,xq).
161 [] Col(xa,xb,xc)|Col(xa,xb,foot(xa,xb,xc)).
162 [] Col(xa,xb,xc)|perp(xa,xb,xc,foot(xa,xb,xc)).
163 [] -R(xa,xb,xc)| -M(s(xa,xc),xp,s(xb,xc))|R(xb,xa,xp).
164 [] -R(xa,xb,xc)| -M(s(xa,xc),xp,s(xb,xc))|xb=xc|xa!=xp.
166 [] xa=xb|xc=xd| -Col(xa,xb,xc)| -Col(xa,xb,xd)| -Col(xc,xd,xp)|Col(xa,xb,xp).
187 [] Col(xa,xb,xc)| -T(xa,xb,xc).
188 [] Col(xa,xb,xc)| -T(xb,xc,xa).
189 [] Col(xa,xb,xc)| -T(xc,xa,xb).
203 [] -M(xa,xm,xb)|T(xa,xm,xb).
204 [] -M(xa,xm,xb)|E(xm,xa,xm,xb).
213 [] -R(xa,xb,xc)|E(xa,xc,xa,s(xb,xc)).
214 [] R(xa,xb,xc)| -E(xa,xc,xa,s(xb,xc)).
218 [] -perpAt(y,z,x,y1,z1)|y1!=z1.
219 [] -perpAt(y,z,x,y1,z1)| -Col(y,z,u)| -Col(y1,z1,v)|R(u,x,v).
225 [] s(xa,s(xa,xp))=xp.
226 [] a!=b.
227 [] -perp(a,b,x,a)| -Col(a,b,y)| -T(c,y,x).
228 [] -Col(a,b,c).
230 [] c1=s(cx,c).
231 [] a1=s(a,c).
234 [] foot(a,b,c)=cx.
235 [] s(cx,c)=c1.
236 [] s(a,c)=a1.
237 [] isomidpoint(c1,a1,a)=p.
238 [] crossbar(a1,a,c,c1,cx,p)=t.
350 [binary,226.1,115.2] s(x,a)!=s(x,b).
360 [ur,102,226,52] Col(b,a,a).
383 [binary,228.1,162.1,demod,234] perp(a,b,c,cx).
384 [binary,228.1,161.1,demod,234] Col(a,b,cx).
387 [binary,228.1,50.2] -Col(a,c,b).
389 [binary,228.1,48.2] -Col(c,b,a).
391 [binary,228.1,46.2] -Col(c,a,b).
394 [ur,103,226,51,51,51,228] x=x.
411 [para_from,230.1.2,213.2.4] -R(x,cx,c)|E(x,c,x,c1).
413 [para_from,230.1.2,124.1.2] s(x,c)!=c1|x=cx.
422 [para_from,230.1.2,110.1.3] M(c,cx,c1).
431 [para_from,231.1.2,214.2.4] R(x,a,c)| -E(x,c,x,a1).
432 [para_from,231.1.2,134.2.3] -R(x,a,c)|R(x,a,a1).
433 [para_from,231.1.2,124.1.2] s(x,c)!=a1|x=a.
436 [para_from,231.1.2,115.1.2] s(a,x)!=a1|x=c.
441 [para_from,231.1.2,112.2.2] -M(c,a,x)|x=a1.
442 [para_from,231.1.2,110.1.3] M(c,a,a1).
456 [ur,114,113,350,demod,225] b!=a.
478 [hyper,103,360,52,52,unit_del,226,456] Col(a,b,b).
489 [binary,383.1,156.3,unit_del,226,384] perpAt(a,b,cx,c,cx).
493 [binary,384.1,102.2,unit_del,226] Col(b,a,cx).
495 [binary,384.1,50.1] Col(a,cx,b).
497 [binary,384.1,47.1] Col(cx,a,b).
535 [ur,98,226,38,37,391] c!=a.
546 [binary,394.1,109.2] M(x,x,x).
562 [para_into,413.1.1,117.1.1] c!=c1|x=cx|c!=x.
564 [binary,422.1,204.1] E(cx,c,cx,c1).
565 [binary,422.1,203.1] T(c,cx,c1).
579 [para_into,433.1.1,230.1.2] c1!=a1|cx=a.
589 [binary,442.1,204.1] E(a,c,a,a1).
590 [binary,442.1,203.1] T(c,a,a1).
618 [ur,98,456,38,37,389] c!=b.
646 [binary,489.1,218.1] c!=cx.
652 [hyper,219,489,478,52] R(b,cx,c).
654 [hyper,219,489,52,52] R(a,cx,c).
695 [binary,535.1,116.2,demod,236] a1!=c.
762 [binary,562.3,436.2,demod,236,unit_del,646,394] c!=c1.
783 [binary,565.1,187.2] Col(c,cx,c1).
800 [binary,565.1,25.1] T(c1,cx,c).
861 [binary,589.1,431.2] R(a,a,c).
881 [binary,590.1,227.3,unit_del,52] -perp(a,b,a1,a).
884 [binary,590.1,189.2] Col(a,a1,c).
885 [binary,590.1,188.2] Col(a1,c,a).
886 [binary,590.1,187.2] Col(c,a,a1).
903 [binary,590.1,25.1] T(a1,a,c).
939 [ur,98,618,38,37,387] a!=c.
1020 [binary,652.1,132.1] R(c,cx,b).
1023 [binary,654.1,411.1] E(a,c,a,c1).
1203 [binary,884.1,50.1] Col(a,c,a1).
1242 [hyper,166,886,52,885,unit_del,535,695] Col(c,a,a).
1300 [ur,164,861,546,939,demod,236] a!=a1.
1363 [hyper,2,1023,589] E(a,c1,a,a1).
1370 [hyper,166,52,884,1203,unit_del,1300,939] Col(a,a1,a1).
1410 [ur,166,226,1300,52,884,228] -Col(a,b,a1).
1468 [binary,1363.1,131.1,demod,237] M(c1,p,a1).
1504 [ur,159,226,52,478,456,881,1410] -R(a1,a,b).
1522 [binary,1468.1,204.1] E(p,c1,p,a1).
1523 [binary,1468.1,203.1] T(c1,p,a1).
1529 [binary,1468.1,107.1] M(a1,p,c1).
1544 [binary,1504.1,132.2] -R(b,a,a1).
1567 [ur,133,535,1203,1504] -R(c,a,b).
1589 [binary,1523.1,189.2] Col(p,a1,c1).
1606 [binary,1523.1,25.1] T(a1,p,c1).
1636 [binary,1544.1,432.2] -R(b,a,c).
1674 [para_into,1567.1.2,579.2.2,unit_del,1020] c1!=a1.
1712 [hyper,40,903,800,1606,demod,238] T(a,t,cx).
1713 [hyper,39,903,800,1606,demod,238] T(p,t,c).
1741 [binary,1674.1,441.2] -M(c,a,c1).
1759 [ur,111,1468,1674] -M(c1,p,c1).
1761 [ur,111,1529,1674] -M(a1,p,a1).
1806 [binary,1712.1,188.2] Col(cx,a,t).
1853 [binary,1713.1,25.1] T(c,t,p).
1874 [binary,1741.1,126.4,unit_del,1023,762] -Col(c,a,c1).
1879 [binary,1759.1,109.1] p!=c1.
1883 [binary,1761.1,109.1] p!=a1.
1951 [ur,166,535,1300,1242,886,1874] -Col(a,a1,c1).
1953 [ur,104,646,535,1242,52,52,939,783,1874] -Col(c,cx,a).
2115 [ur,166,1300,1883,1370,1589,1951] -Col(a,a1,p).
2145 [binary,1953.1,47.2] -Col(cx,a,c).
2173 [binary,2115.1,50.2] -Col(a,p,a1).
2177 [binary,2115.1,46.2] -Col(p,a,a1).
2203 [ur,98,939,1300,590,2145] cx!=a.
2235 [ur,98,1883,1879,1606,2173] a!=p.
2261 [ur,98,1300,939,903,2177] p!=a.
2298 [ur,166,226,2203,384,52,1806] Col(a,b,t).
2302 [ur,133,2203,495,1636] -R(cx,a,c).
2311 [ur,103,2203,456,493,360,360] Col(cx,a,a).
2378 [ur,102,2235,52] Col(p,a,a).
2509 [ur,227,2298,1853] -perp(a,b,p,a).
2529 [binary,2302.1,431.1] -E(cx,c,cx,a1).
2630 [ur,15,564,2529] -E(cx,c1,cx,a1).
2642 [ur,56,2261,1522,1363,2630] -Col(p,a,cx).
2668 [ur,104,226,2261,52,52,2378,2261,384,2642] -Col(a,b,p).
2700 [ur,159,226,52,478,456,2509,2668] -R(p,a,b).
2729 [ur,158,2203,2311,497,456,2700] -perp(cx,a,p,a).
2737 [binary,2729.1,142.2] -perp(p,a,cx,a).
2771 [ur,159,2261,2378,52,2261,2737,2642] -R(cx,a,p).
2776 [ur,163,654,2771,demod,236,235] -M(a1,p,c1).
2777 [binary,2776.1,1529.1] $F.