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RRABC
ANBEABD+EEABDB+EEACDC+NEBC  defn:rightangle
BEABD 
EEABDB
EEABBD  lemma:congruenceflip
EEACDC
NEBC
MIABD   defn:midpoint
BEACD  assumption
 EEACCD lemma:congruenceflip
 MIACD  defn:midpoint
 EQBC   lemma:midpointunique
NOBEACD  reductio
NEAB    lemma:betweennotequal
EQCA    assumption
 EEACDC
 EECCDC  cn:equalitysub
 EEDCCC  lemma:congruencesymmetric
 NEDC    assumption
  NECC   axiom:nocollapse
  EQCC   cn:equalityreflexive
 EQDC    reductio
 EQAC    lemma:equalitysymmetric
 EQDA    cn:equalitytransitive
 EQAD    lemma:equalitysymmetric
 NEAD    lemma:betweennotequal
NECA     reductio
EQCD     assumption
 EEACDC
 EEACDD  cn:equalitysub
 NEAC    assumption
  NEDD   axiom:nocollapse
  EQDD   cn:equalityreflexive
 EQAC    reductio
 EQCA    lemma:equalitysymmetric
NECD     reductio
BECAD    assumption
 EECACD   lemma:congruenceflip
 NOEECACD   lemma:partnotequalwhole
NOBECAD  reductio
BEADC    assumption
 BECDA   axiom:betweennesssymmetry
 EECDCA  lemma:doublereverse
 NOEECDCA  lemma:partnotequalwhole
NOBEADC  reductio
COABC     assumption
 COABD    defn:collinear
 COBAC    lemma:collinearorder
 COBAD    lemma:collinearorder
 NEBA     lemma:inequalitysymmetric
 COACD    lemma:collinear4
 OREQAC|EQAD|EQCD|BECAD|BEACD|BEADC  defn:collinear
 cases NCABC:EQAC|EQAD|EQCD|BECAD|BEACD|BEADC
  case 1:EQAC
   COABC  assumption
   NEAC   lemma:inequalitysymmetric
   NCABC  reductio
  qedcase
  case 2:EQAD
   COABC  assumption
   NEAD  lemma:betweennotequal
   NCABC  reductio
  qedcase
  case 3:EQCD
    COABC  assumption
    NECD
    NCABC reductio
  qedcase
  case 4:BECAD
    COABC  assumption
    NOBECAD
    NCABC reductio
  qedcase
  case 5:BEACD
    COABC  assumption
    NOBEACD
    NCABC reductio
  qedcase
  case 6:BEADC
    COABC  assumption
    NOBEADC
    NCABC reductio
  qedcase
 NCABC cases
NCABC     reductio