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RAABC
RABAC
NEBC   lemma:raystrict
NEAC   lemma:raystrict
ORBEACB|EQBC|BEABC  lemma:ray1
ORBEACB|BEABC
ORBEBCA|EQAC|BEBAC  lemma:ray1
ORBEBCA|BEBAC
cases BEACB:BEACB|BEABC
 case 1:BEACB
 qedcase
 case 2:BEABC
  cases BEACB:BEBCA|BEBAC
   case 1:BEBCA
    BEACB  axiom:betweennesssymmetry
   qedcase
   case 2:BEBAC
    NOBEACB  assumption
     BEABA  axiom:innertransitivity
     NOBEABA  axiom:betweennessidentity
    BEACB  reductio
   qedcase
  BEACB cases
 qedcase
BEACB cases

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