Sindbad~EG File Manager

Length of proof is 60.  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).
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).
18 [] E(xa,xa,xb,xb).
22 [] -E(xa,xb,xc,xd)|E(xb,xa,xd,xc).
26 [] T(xa1,xa1,xb1).
37 [] T(xa,xb,ext(xa,xb,alpha,gamma)).
38 [] xb!=ext(xa,xb,alpha,gamma).
49 [] -Col(xa,xb,xc)|Col(xb,xa,xc).
50 [] -Col(xa,xb,xc)|Col(xa,xc,xb).
52 [] Col(xa,xb,xa).
87 [] xa=xp|sameside(xa,xp,xa).
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).
107 [] -M(xa,xm,xb)|M(xb,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.
117 [] s(xa,xp)=xp|xp!=xa.
123 [] -M(xp,xa,xq)| -M(xp,xb,xq)|xa=xb.
126 [] -Col(xa,xm,xb)| -E(xm,xa,xm,xb)|xa=xb|M(xa,xm,xb).
130 [] -T(xa1,xc,xa2)| -T(xb1,xc,xb2)| -E(xc,xa1,xc,xb1)| -E(xc,xa2,xc,xb2)| -M(xa1,xm1,xb1)| -M(xa2,xm2,xb2)|T(xm1,xc,xm2).
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)).
139 [] -R(xa,xb,xc)| -Col(xa,xb,xc)|xa=xb|xc=xb.
140 [] -R(xa,xb,xc)| -E3(xa,xb,xc,xa1,xb1,xc1)|R(xa1,xb1,xc1).
142 [] -perp(xa,xb,xp,xq)|perp(xp,xq,xa,xb).
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).
165 [] -perp(xa,xb,xp,xq)|perp(xb,xa,xp,xq).
174 [] M(xa,midpoint(xa,xb),xb).
215 [] xa=xb| -Col(xa,xb,midpoint(xp,xp1))| -perp(xa,xb,xp,xp1)|xp1=reflect(xa,xb,xp).
216 [] xa=xb| -Col(xa,xb,midpoint(xp,xp1))|xp!=xp1|xp1=reflect(xa,xb,xp).
224 [] xa=xb|E(xp,xq,reflect(xa,xb,xp),reflect(xa,xb,xq)).
225 [] -R(xa,xb,xc)| -R(xa1,xb,xc)| -E(xa,xb,xa1,xb)|E(xa,xc,xa1,xc).
226 [] -R(xa,xb,xc)| -R(xa1,xb,xc1)| -E(xa,xb,xa1,xb)| -E(xb,xc,xb,xc1)|E(xa,xc,xa1,xc1)|xb!=midpoint(xc,xc1)|xc=xc1.
245 [] -E(xa1,xa2,xb1,xb2)| -E(xa1,xa3,xb1,xb3)| -E(xa2,xa3,xb2,xb3)|E3(xa1,xa2,xa3,xb1,xb2,xb3).
247 [] Col(xa,xb,xc)| -T(xa,xb,xc).
249 [] Col(xa,xb,xc)| -T(xc,xa,xb).
259 [] -sameside(xa,xp,xb)|xb!=xp.
263 [] -M(xa,xm,xb)|T(xa,xm,xb).
274 [] R(xa,xb,xc)| -E(xa,xc,xa,s(xb,xc)).
302 [] s(xa,s(xa,xp))=xp.
303 [] R(a,b,c).
304 [] R(a1,b,c1).
305 [] E(a,b,a1,b).
306 [] E(b,c,b,c1).
307 [] -E(a,c,a1,c1).
308 [] cy=midpoint(c,c1).
309 [] a2=reflect(b,cy,a1).
310 [] c=c1|c!=c1.
311 [] midpoint(c,c1)=cy.
385 [binary,303.1,225.2] -R(x,b,c)| -E(x,b,a,b)|E(x,c,a,c).
386 [binary,303.1,225.1] -R(x,b,c)| -E(a,b,x,b)|E(a,c,x,c).
396 [binary,304.1,132.1] R(c1,b,a1).
398 [binary,305.1,22.1] E(b,a,b,a1).
401 [binary,305.1,14.1] E(a1,b,a,b).
418 [binary,306.1,14.1] E(b,c1,b,c).
422 [hyper,226,303,304,305,306,87,demod,311,unit_del,307] c=c1|sameside(b,cy,b).
423 [hyper,130,26,26,18,306,174,174,demod,311] T(midpoint(b,b),b,cy).
437 [binary,307.1,22.2] -E(c,a,c1,a1).
440 [binary,307.1,14.2] -E(a1,c1,a,c).
450 [para_from,308.1.2,174.1.2] M(c,cy,c1).
459 [para_from,309.1.2,224.2.4] b=cy|E(x,a1,reflect(b,cy,x),a2).
468 [binary,385.1,132.2] -E(x,b,a,b)|E(x,c,a,c)| -R(c,b,x).
473 [binary,386.2,305.1] -R(a1,b,c)|E(a,c,a1,c).
511 [hyper,6,18,306,398,398,26,26,unit_del,437] b=b.
523 [binary,418.1,22.1] E(c1,b,c,b).
544 [binary,422.2,259.1] c=c1|b!=cy.
550 [binary,423.1,249.2] Col(b,cy,midpoint(b,b)).
572 [binary,450.1,263.1] T(c,cy,c1).
575 [binary,450.1,112.1] c1=s(cy,c).
578 [binary,450.1,107.1] M(c1,cy,c).
580 [hyper,111,110,450] s(cy,c)=c1.
590 [para_into,473.2.4,310.1.1,unit_del,307] -R(a1,b,c)|c!=c1.
654 [binary,572.1,247.2] Col(c,cy,c1).
711 [para_from,575.1.1,306.1.4] E(b,c,b,s(cy,c)).
721 [para_from,575.1.2,113.1.1.2] s(cy,c1)=c.
729 [hyper,123,578,174] cy=midpoint(c1,c).
755 [para_into,580.1.1,117.1.1] c=c1|c!=cy.
766 [para_into,590.1.3,310.1.1,unit_del,304,factor_simp] c!=c1.
772 [binary,654.1,50.1] Col(c,c1,cy).
857 [binary,711.1,274.2] R(b,cy,c).
886 [para_from,721.1.1,117.1.1,unit_del,766] c1!=cy.
966 [para_into,755.2.2,308.1.1,demod,311,unit_del,766] c!=cy.
967 [binary,766.1,544.1] b!=cy.
1047 [binary,857.1,134.1] R(b,cy,s(cy,c)).
1111 [ur,139,654,966,886] -R(c,cy,c1).
1144 [binary,967.1,459.1] E(x,a1,reflect(b,cy,x),a2).
1160 [ur,216,967,550,511] b=reflect(b,cy,b).
1165 [ur,123,450,967] -M(c,b,c1).
1208 [para_into,1047.1.3.2,721.1.2,demod,302] R(b,cy,c1).
1270 [para_from,1160.1.2,1144.1.3] E(b,a1,b,a2).
1276 [binary,1165.1,126.4,unit_del,306,766] -Col(c,b,c1).
1287 [ur,133,1208,967,1111] -Col(cy,b,c).
1304 [binary,1270.1,22.1] E(a1,b,a2,b).
1332 [binary,1276.1,50.2] -Col(c,c1,b).
1333 [binary,1276.1,49.2] -Col(b,c,c1).
1377 [hyper,2,1304,401] E(a2,b,a,b).
1406 [ur,159,766,772,52,966,1332,857] perp(c,c1,b,cy).
1420 [ur,98,766,38,37,1333] b!=c.
1441 [binary,1406.1,165.1] perp(c1,c,b,cy).
1506 [ur,98,1420,38,37,1287] cy!=b.
1534 [binary,1441.1,142.1] perp(b,cy,c1,c).
1555 [ur,102,1506,52] Col(b,cy,cy).
1615 [para_into,1555.1.3,729.1.1] Col(b,cy,midpoint(c1,c)).
1620 [binary,1615.1,215.2,unit_del,967,1534] c=reflect(b,cy,c1).
1681 [para_from,1620.1.2,1144.1.3] E(c1,a1,c,a2).
1685 [binary,1681.1,22.1] E(a1,c1,a2,c).
1693 [hyper,245,523,1681,1270] E3(c1,b,a1,c,b,a2).
1726 [ur,15,1685,440] -E(a2,c,a,c).
1729 [binary,1693.1,140.2,unit_del,396] R(c,b,a2).
1735 [binary,1726.1,468.2,unit_del,1377,1729] $F.