Sindbad~EG File Manager

Length of proof is 72.  Level of proof is 16.
 
---------------- PROOF ----------------
 
2 [] -E(x,y,z,v)| -E(x,y,z2,v2)|E(z,v,z2,v2).
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).
13 [] E(xa,xb,xa,xb).
15 [] -E(xa,xb,xc,xd)| -E(xc,xd,xe,xf)|E(xa,xb,xe,xf).
17 [] -E(xa,xb,xc,xd)|E(xa,xb,xd,xc).
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).
27 [] -T(xa,xb,xc)| -T(xb,xa,xc)|xa=xb.
29 [] -T(xa,xb,xc)| -T(xa,xc,xd)|T(xb,xc,xd).
42 [] -T(xa,xb,xc)| -T(xa1,xb1,xc1)| -E(xa,xc,xa1,xc1)| -E(xb,xc,xb1,xc1)|E(xa,xb,xa1,xb1).
50 [] -Col(xa,xb,xc)|Col(xa,xc,xb).
51 [] Col(xa,xa,xb).
52 [] Col(xa,xb,xa).
58 [] -T(xa,xc,xb)| -E(xa,xc,xa,xc1)| -E(xb,xc,xb,xc1)|xc=xc1.
86 [] sameside(xa,xp,xb)| -Col(xa,xp,xb)|T(xa,xp,xb).
103 [] xa=xb|xp=xq| -Col(xp,xq,xa)| -Col(xp,xq,xb)| -Col(xp,xq,xr)|Col(xa,xb,xr).
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).
114 [] s(xa,xp)!=xr|s(xa,xq)!=xr|xp=xq.
117 [] s(xa,xp)=xp|xp!=xa.
118 [] E(xp,xq,s(xa,xp),s(xa,xq)).
119 [] -T(xp,xq,xr)|T(s(xa,xp),s(xa,xq),s(xa,xr)).
154 [] -perp(xa,xb,xp,xq)| -Col(xa,xb,xc)| -Col(xp,xq,xc)|perpAt(xa,xb,xc,xp,xq).
156 [] xa=xb| -Col(xa,xb,xd)| -perp(xa,xb,xc,xd)|perpAt(xa,xb,xd,xc,xd).
174 [] M(xa,midpoint(xa,xb),xb).
184 [] -Col(xa,xb,xp)| -Col(xa,xb,xq)|xp=xq|xa=xb|perp(xc,xd,xp,xq)| -perp(xc,xd,xa,xb).
203 [] xa=xb| -M(u,v,w)| -Col(xa,xb,u)| -Col(xa,xb,w)|Col(xa,xb,v).
213 [] xa=xb|Col(xa,xb,midpoint(xp,reflect(xa,xb,xp))).
214 [] xa=xb|xp=reflect(xa,xb,xp)|perp(xa,xb,xp,reflect(xa,xb,xp)).
221 [] xa=xb|reflect(xa,xb,xp)!=xp|Col(xa,xb,xp).
223 [] xa=xb| -Col(xa,xb,xp)|E(xp,xq,reflect(xa,xb,xp),reflect(xa,xb,xq)).
244 [] Col(xa,xb,xc)| -T(xa,xb,xc).
256 [] -sameside(xa,xp,xb)|xb!=xp.
260 [] -M(xa,xm,xb)|T(xa,xm,xb).
261 [] -M(xa,xm,xb)|E(xm,xa,xm,xb).
262 [] -T(xa,xm,xb)| -E(xm,xa,xm,xb)|M(xa,xm,xb).
270 [] -R(xa,xb,xc)|E(xa,xc,xa,s(xb,xc)).
276 [] -perpAt(y,z,x,y1,z1)| -Col(y,z,u)| -Col(y1,z1,v)|R(u,x,v).
300 [] a!=b.
301 [] -E(p,q,reflect(a,b,p),reflect(a,b,q)).
302 [] p1=reflect(a,b,p).
303 [] q1=reflect(a,b,q).
304 [] cx=midpoint(p,p1).
305 [] cy=midpoint(q,q1).
306 [] cz=midpoint(cx,cy).
307 [] r=s(cz,p).
308 [] r1=s(cz,p1).
309 [] reflect(a,b,p)=p1.
310 [] reflect(a,b,q)=q1.
311 [] midpoint(p,p1)=cx.
312 [] midpoint(q,q1)=cy.
313 [] midpoint(cx,cy)=cz.
314 [] s(cz,p)=r.
402 [binary,300.1,203.1] -M(x,y,z)| -Col(a,b,x)| -Col(a,b,z)|Col(a,b,y).
405 [binary,300.1,156.1] -Col(a,b,x)| -perp(a,b,y,x)|perpAt(a,b,x,y,x).
445 [binary,301.1,223.3,unit_del,300] -Col(a,b,p).
450 [ur,42,24,24,18,301,demod,309,310] -E(p,q,p1,q1).
461 [para_from,302.1.2,214.2.2,demod,309,unit_del,300] p=p1|perp(a,b,p,p1).
462 [para_from,302.1.2,221.2.1,unit_del,300,445] p1!=p.
464 [para_from,302.1.2,213.2.3.2,demod,311,unit_del,300] Col(a,b,cx).
474 [para_into,303.1.2,214.2.2,demod,310,unit_del,300] q1=q|perp(a,b,q,q1).
478 [para_from,303.1.2,213.2.3.2,demod,312,unit_del,300] Col(a,b,cy).
487 [para_from,304.1.2,174.1.2] M(p,cx,p1).
496 [para_from,305.1.2,174.1.2] M(q,cy,q1).
505 [para_from,306.1.2,174.1.2] M(cx,cz,cy).
518 [para_from,307.1.2,118.1.4] E(x,p,s(cz,x),r).
521 [para_from,307.1.2,114.2.1] s(cz,x)!=y|r!=y|x=p.
527 [para_from,307.1.2,110.1.3] M(p,cz,r).
540 [para_from,308.1.2,119.2.3] -T(x,y,p1)|T(s(cz,x),s(cz,y),r1).
541 [para_from,308.1.2,118.1.4] E(x,p1,s(cz,x),r1).
549 [para_from,308.1.2,110.1.3] M(p1,cz,r1).
583 [ur,103,300,51,51,51,445] x=x.
631 [ur,27,24,462] -T(p,p1,p).
635 [para_into,462.1.1,461.1.2,unit_del,583] perp(a,b,p,p1).
687 [hyper,402,174,464,478,demod,313] Col(a,b,cz).
726 [binary,487.1,261.1] E(cx,p,cx,p1).
727 [binary,487.1,260.1] T(p,cx,p1).
730 [binary,487.1,112.1] p1=s(cx,p).
739 [binary,496.1,260.1] T(q,cy,q1).
742 [binary,496.1,112.1] q1=s(cy,q).
757 [hyper,111,110,505] s(cz,cx)=cy.
776 [para_into,521.1.1,117.1.1] x!=y|r!=y|x=p|x!=cz.
778 [binary,527.1,261.1] E(cz,p,cz,r).
779 [binary,527.1,260.1] T(p,cz,r).
803 [binary,549.1,261.1] E(cz,p1,cz,r1).
804 [binary,549.1,260.1] T(p1,cz,r1).
832 [binary,631.1,86.3,unit_del,52] sameside(p,p1,p).
946 [binary,727.1,540.1,demod,314] T(r,s(cz,cx),r1).
951 [binary,727.1,244.2] Col(p,cx,p1).
989 [para_into,730.1.2,117.1.1,unit_del,462] p!=cx.
999 [para_from,730.1.2,270.2.4] -R(x,cx,p)|E(x,p,x,p1).
1025 [binary,739.1,244.2] Col(q,cy,q1).
1065 [para_from,742.1.2,270.2.4] -R(x,cy,q)|E(x,q,x,q1).
1069 [para_from,742.1.2,118.1.3] E(q,x,q1,s(cy,x)).
1088 [para_from,757.1.1,541.1.3] E(cx,p1,cy,r1).
1089 [para_from,757.1.1,518.1.3] E(cx,p,cy,r).
1118 [binary,778.1,17.1] E(cz,p,r,cz).
1153 [binary,779.1,25.1] T(r,cz,p).
1206 [binary,804.1,25.1] T(r1,cz,p1).
1225 [binary,832.1,256.1] p!=p1.
1240 [para_into,946.1.2,757.1.1] T(r,cy,r1).
1252 [binary,951.1,50.1] Col(p,p1,cx).
1319 [binary,1025.1,50.1] Col(q,q1,cy).
1442 [hyper,2,1089,726] E(cy,r,cx,p1).
1613 [hyper,184,52,1252,635,unit_del,989,1225] perp(a,b,p,cx).
1642 [hyper,15,1442,1088] E(cy,r,cy,r1).
1647 [binary,1613.1,405.2,unit_del,464] perpAt(a,b,cx,p,cx).
1676 [binary,1642.1,262.2,unit_del,1240] M(r,cy,r1).
1702 [hyper,276,1647,687,52] R(cz,cx,p).
1713 [binary,1676.1,112.1] r1=s(cy,r).
1724 [binary,1702.1,999.1] E(cz,p,cz,p1).
1766 [para_from,1713.1.2,1069.1.4] E(q,r,q1,r1).
1801 [hyper,15,1724,803] E(cz,p,cz,r1).
1810 [ur,58,1724,1724,1225] -T(cz,p,cz).
1813 [binary,1766.1,22.1] E(r,q,r1,q1).
1853 [hyper,2,1118,1801] E(r,cz,cz,r1).
1906 [ur,29,1153,1810] -T(r,p,cz).
1926 [binary,1853.1,17.1] E(r,cz,r1,cz).
1960 [para_into,1906.1.2,776.3.2] -T(r,x,cz)|x!=y|r!=y|x!=cz.
1961 [factor,1960.2.3,unit_del,26,factor_simp] r!=cz.
2094 [ur,6,1926,1724,1813,1153,1206,1961,450] -E(cz,q,cz,q1).
2095 [binary,2094.1,1065.2] -R(cz,cy,q).
2108 [para_into,2094.1.2,474.1.2,unit_del,13] perp(a,b,q,q1).
2113 [ur,276,687,52,2095] -perpAt(a,b,cy,q,x).
2136 [hyper,154,2108,478,1319] perpAt(a,b,cy,q,q1).
2137 [binary,2136.1,2113.1] $F.