Possibly wrong rule in the solver ruleset #17
Description
The sample solution generated for the orthocentre problem by alhpageometry looks like this:
* From theorem premises:
A B C D : Points
BD ⟂ AC [00]
CD ⟂ AB [01]
* Auxiliary Constructions:
E : Points
C,A,E are collinear [02]
B,D,E are collinear [03]
* Proof steps:
001. E,C,A are collinear [02] & B,E,D are collinear [03] & BD ⟂ AC [00] ⇒ ∠CED = ∠BEA [04]
002. E,C,A are collinear [02] & B,E,D are collinear [03] & BD ⟂ AC [00] ⇒ ∠DEA = ∠CEB [05]
003. BD ⟂ AC [00] & CD ⟂ AB [01] ⇒ ∠BAC = ∠CDB [06]
004. B,D,E are collinear [03] & E,A,C are collinear [02] & ∠CDB = ∠BAC [06] ⇒ ∠CDE = ∠BAE [07]
005. ∠CED = ∠BEA [04] & ∠CDE = ∠BAE [07] (Similar Triangles)⇒ CE:BE = DE:EA [08]
006. CE:BE = DE:EA [08] & ∠DEA = ∠CEB [05] (Similar Triangles)⇒ ∠DAE = ∠CBE [09]
007. CE:BE = DE:EA [08] & ∠DEA = ∠CEB [05] (Similar Triangles)⇒ ∠EDA = ∠ECB [10]
008. ∠DAE = ∠CBE [09] & C,A,E are collinear [02] & B,D,E are collinear [03] & ∠EDA = ∠ECB [10] ⇒ AD ⟂ BC
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I0118 18:44:43.041623 139894856428416 alphageometry.py:575] Solved.
As far as I understand, step 003 is wrong: the statement is correct for the angles between two straight lines, not for angles BAC and CDB. Does that mean the network has generated the wrong text? Or it just used a rule from the set, and the rule is wrong?