Sindbad~EG File Manager

Length of proof is 3.  Level of proof is 2.
 
---------------- PROOF ----------------
 
113 [] s(xa,s(xa,xp))=xp.
123 [] -M(xp,xa,xq)| -M(xp,xb,xq)|xa=xb.
174 [] M(xa,midpoint(xa,xb),xb).
175 [] -perp(xp,xa,xa,xb)| -perp(xq,xb,xa,xb)| -Col(xa,xb,xt)| -T(xp,xt,xq)| -T(xb,xr,xq)| -E(xa,xp,xb,xr)|xcx!=ip(xp,xt,xq,xb,xr)|M(xa,xcx,xb).
176 [] -perp(xp,xa,xa,xb)| -perp(xq,xb,xa,xb)| -Col(xa,xb,xt)| -T(xp,xt,xq)| -T(xb,xr,xq)| -E(xa,xp,xb,xr)|xcx!=ip(xp,xt,xq,xb,xr)|M(xp,xcx,xr).
235 [] s(xa,s(xa,xp))=xp.
236 [] perp(p,a,a,b).
237 [] perp(q,b,a,b).
238 [] Col(a,b,t).
239 [] T(p,t,q).
240 [] T(b,r,q).
241 [] E(a,p,b,r).
242 [] -M(p,midpoint(a,b),r).
246 [] ip(p,t,q,b,r)=cx.
862 [hyper,175,236,237,238,239,240,241,113,demod,246,235] M(a,cx,b).
919 [ur,176,236,237,238,239,240,241,242,demod,246] midpoint(a,b)!=cx.
3774 [hyper,123,174,862] midpoint(a,b)=cx.
3775 [binary,3774.1,919.1] $F.