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-rw-r--r--test/golden/geometry/encoding tasks.golden109
-rw-r--r--test/golden/geometry/generating tasks.golden14419
-rw-r--r--test/golden/geometry/glossing.golden2187
-rw-r--r--test/golden/geometry/parsing.golden1198
-rw-r--r--test/golden/geometry/scanning.golden15
-rw-r--r--test/golden/geometry/tokenizing.golden975
-rw-r--r--test/golden/geometry/verification.golden1
7 files changed, 18904 insertions, 0 deletions
diff --git a/test/golden/geometry/encoding tasks.golden b/test/golden/geometry/encoding tasks.golden
new file mode 100644
index 0000000..f4bbc14
--- /dev/null
+++ b/test/golden/geometry/encoding tasks.golden
@@ -0,0 +1,109 @@
+fof(cong_refl,conjecture,'Cong'(fa,fb,fa,fb)).
+fof(upperdim,axiom,![Xx,Xy,Xz,Xu,Xv]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv))=>(('Cong'(Xx,Xu,Xx,Xv)&'Cong'(Xy,Xu,Xy,Xv)&'Cong'(Xz,Xu,Xz,Xv)&Xu!=Xv)=>collinear(Xx,Xy,Xz)))).
+fof(innerpasch,axiom,![Xx,Xy,Xz,Xu,Xv,Xw]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv)&point(Xw))=>(('Betw'(Xx,Xu,Xz)&'Betw'(Xy,Xv,Xz))=>?[Xw]:(point(Xw)&'Betw'(Xu,Xw,Xy)&'Betw'(Xv,Xw,Xx))))).
+fof(betw_id,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>('Betw'(Xa,Xb,Xa)=>Xa=Xb))).
+fof(five_segment,axiom,![Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&point(Xaprime)&point(Xbprime)&point(Xcprime)&point(Xdprime))=>(('OFS'(Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime)&Xa!=Xb)=>'Cong'(Xc,Xd,Xcprime,Xdprime)))).
+fof(ofs,axiom,![Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp]:((point(Xx)&point(Xy)&point(Xz)&point(Xr)&point(Xu)&point(Xv)&point(Xw)&point(Xp))=>('OFS'(Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp)<=>('Betw'(Xx,Xy,Xz)&'Betw'(Xu,Xv,Xw)&'Cong'(Xx,Xy,Xu,Xv)&'Cong'(Xy,Xz,Xv,Xw)&'Cong'(Xx,Xr,Xu,Xp)&'Cong'(Xy,Xr,Xv,Xp))))).
+fof(segment_construction,axiom,![Xa,Xb,Xd,Xe]:?[Xc]:(point(Xc)&'Betw'(Xa,Xb,Xc)&'Cong'(Xb,Xc,Xd,Xe))).
+fof(cong_id,axiom,![Xa,Xb,Xc]:((point(Xa)&point(Xb)&point(Xc))=>('Cong'(Xa,Xb,Xc,Xc)=>Xa=Xb))).
+fof(cong_pseudotransitive,axiom,![Xa,Xb,Xc,Xd,Xe,Xf]:((point(Xa)&point(Xb)&point(Xc)&point(Xd))=>(('Cong'(Xc,Xd,Xa,Xb)&'Cong'(Xc,Xd,Xe,Xf))=>'Cong'(Xa,Xb,Xe,Xf)))).
+fof(cong_refl_swap,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>'Cong'(Xa,Xb,Xb,Xa))).
+fof(collinear,axiom,![Xa,Xb,Xc]:(collinear(Xa,Xb,Xc)<=>('Betw'(Xa,Xb,Xc)|'Betw'(Xb,Xc,Xa)|'Betw'(Xc,Xa,Xb)))).
+fof(cong_refl1,axiom,point(fb)).
+fof(cong_refl2,axiom,point(fa)).
+------------------
+fof(cong_sym,conjecture,'Cong'(fc,fd,fa,fb)).
+fof(cong_refl,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>'Cong'(Xa,Xb,Xa,Xb))).
+fof(upperdim,axiom,![Xx,Xy,Xz,Xu,Xv]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv))=>(('Cong'(Xx,Xu,Xx,Xv)&'Cong'(Xy,Xu,Xy,Xv)&'Cong'(Xz,Xu,Xz,Xv)&Xu!=Xv)=>collinear(Xx,Xy,Xz)))).
+fof(innerpasch,axiom,![Xx,Xy,Xz,Xu,Xv,Xw]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv)&point(Xw))=>(('Betw'(Xx,Xu,Xz)&'Betw'(Xy,Xv,Xz))=>?[Xw]:(point(Xw)&'Betw'(Xu,Xw,Xy)&'Betw'(Xv,Xw,Xx))))).
+fof(betw_id,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>('Betw'(Xa,Xb,Xa)=>Xa=Xb))).
+fof(five_segment,axiom,![Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&point(Xaprime)&point(Xbprime)&point(Xcprime)&point(Xdprime))=>(('OFS'(Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime)&Xa!=Xb)=>'Cong'(Xc,Xd,Xcprime,Xdprime)))).
+fof(ofs,axiom,![Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp]:((point(Xx)&point(Xy)&point(Xz)&point(Xr)&point(Xu)&point(Xv)&point(Xw)&point(Xp))=>('OFS'(Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp)<=>('Betw'(Xx,Xy,Xz)&'Betw'(Xu,Xv,Xw)&'Cong'(Xx,Xy,Xu,Xv)&'Cong'(Xy,Xz,Xv,Xw)&'Cong'(Xx,Xr,Xu,Xp)&'Cong'(Xy,Xr,Xv,Xp))))).
+fof(segment_construction,axiom,![Xa,Xb,Xd,Xe]:?[Xc]:(point(Xc)&'Betw'(Xa,Xb,Xc)&'Cong'(Xb,Xc,Xd,Xe))).
+fof(cong_id,axiom,![Xa,Xb,Xc]:((point(Xa)&point(Xb)&point(Xc))=>('Cong'(Xa,Xb,Xc,Xc)=>Xa=Xb))).
+fof(cong_pseudotransitive,axiom,![Xa,Xb,Xc,Xd,Xe,Xf]:((point(Xa)&point(Xb)&point(Xc)&point(Xd))=>(('Cong'(Xc,Xd,Xa,Xb)&'Cong'(Xc,Xd,Xe,Xf))=>'Cong'(Xa,Xb,Xe,Xf)))).
+fof(cong_refl_swap,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>'Cong'(Xa,Xb,Xb,Xa))).
+fof(collinear,axiom,![Xa,Xb,Xc]:(collinear(Xa,Xb,Xc)<=>('Betw'(Xa,Xb,Xc)|'Betw'(Xb,Xc,Xa)|'Betw'(Xc,Xa,Xb)))).
+fof(cong_sym1,axiom,'Cong'(fa,fb,fc,fd)).
+fof(cong_sym2,axiom,point(fd)).
+fof(cong_sym3,axiom,point(fc)).
+fof(cong_sym4,axiom,point(fb)).
+fof(cong_sym5,axiom,point(fa)).
+------------------
+fof(cong_transitive,conjecture,('Cong'(fa,fb,fc,fd)&'Cong'(fc,fd,fe,ff))=>'Cong'(fa,fb,fe,ff)).
+fof(cong_sym,axiom,![Xa,Xb,Xc,Xd]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&'Cong'(Xa,Xb,Xc,Xd))=>'Cong'(Xc,Xd,Xa,Xb))).
+fof(cong_refl,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>'Cong'(Xa,Xb,Xa,Xb))).
+fof(upperdim,axiom,![Xx,Xy,Xz,Xu,Xv]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv))=>(('Cong'(Xx,Xu,Xx,Xv)&'Cong'(Xy,Xu,Xy,Xv)&'Cong'(Xz,Xu,Xz,Xv)&Xu!=Xv)=>collinear(Xx,Xy,Xz)))).
+fof(innerpasch,axiom,![Xx,Xy,Xz,Xu,Xv,Xw]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv)&point(Xw))=>(('Betw'(Xx,Xu,Xz)&'Betw'(Xy,Xv,Xz))=>?[Xw]:(point(Xw)&'Betw'(Xu,Xw,Xy)&'Betw'(Xv,Xw,Xx))))).
+fof(betw_id,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>('Betw'(Xa,Xb,Xa)=>Xa=Xb))).
+fof(five_segment,axiom,![Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&point(Xaprime)&point(Xbprime)&point(Xcprime)&point(Xdprime))=>(('OFS'(Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime)&Xa!=Xb)=>'Cong'(Xc,Xd,Xcprime,Xdprime)))).
+fof(ofs,axiom,![Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp]:((point(Xx)&point(Xy)&point(Xz)&point(Xr)&point(Xu)&point(Xv)&point(Xw)&point(Xp))=>('OFS'(Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp)<=>('Betw'(Xx,Xy,Xz)&'Betw'(Xu,Xv,Xw)&'Cong'(Xx,Xy,Xu,Xv)&'Cong'(Xy,Xz,Xv,Xw)&'Cong'(Xx,Xr,Xu,Xp)&'Cong'(Xy,Xr,Xv,Xp))))).
+fof(segment_construction,axiom,![Xa,Xb,Xd,Xe]:?[Xc]:(point(Xc)&'Betw'(Xa,Xb,Xc)&'Cong'(Xb,Xc,Xd,Xe))).
+fof(cong_id,axiom,![Xa,Xb,Xc]:((point(Xa)&point(Xb)&point(Xc))=>('Cong'(Xa,Xb,Xc,Xc)=>Xa=Xb))).
+fof(cong_pseudotransitive,axiom,![Xa,Xb,Xc,Xd,Xe,Xf]:((point(Xa)&point(Xb)&point(Xc)&point(Xd))=>(('Cong'(Xc,Xd,Xa,Xb)&'Cong'(Xc,Xd,Xe,Xf))=>'Cong'(Xa,Xb,Xe,Xf)))).
+fof(cong_refl_swap,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>'Cong'(Xa,Xb,Xb,Xa))).
+fof(collinear,axiom,![Xa,Xb,Xc]:(collinear(Xa,Xb,Xc)<=>('Betw'(Xa,Xb,Xc)|'Betw'(Xb,Xc,Xa)|'Betw'(Xc,Xa,Xb)))).
+fof(cong_transitive1,axiom,point(ff)).
+fof(cong_transitive2,axiom,point(fe)).
+fof(cong_transitive3,axiom,point(fd)).
+fof(cong_transitive4,axiom,point(fc)).
+fof(cong_transitive5,axiom,point(fb)).
+fof(cong_transitive6,axiom,point(fa)).
+------------------
+fof(cong_shuffle_left,conjecture,'Cong'(fa,fb,fc,fd)=>'Cong'(fb,fa,fc,fd)).
+fof(cong_transitive,axiom,![Xa,Xb,Xc,Xd,Xe,Xf]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&point(Xe)&point(Xf))=>(('Cong'(Xa,Xb,Xc,Xd)&'Cong'(Xc,Xd,Xe,Xf))=>'Cong'(Xa,Xb,Xe,Xf)))).
+fof(cong_sym,axiom,![Xa,Xb,Xc,Xd]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&'Cong'(Xa,Xb,Xc,Xd))=>'Cong'(Xc,Xd,Xa,Xb))).
+fof(cong_refl,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>'Cong'(Xa,Xb,Xa,Xb))).
+fof(upperdim,axiom,![Xx,Xy,Xz,Xu,Xv]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv))=>(('Cong'(Xx,Xu,Xx,Xv)&'Cong'(Xy,Xu,Xy,Xv)&'Cong'(Xz,Xu,Xz,Xv)&Xu!=Xv)=>collinear(Xx,Xy,Xz)))).
+fof(innerpasch,axiom,![Xx,Xy,Xz,Xu,Xv,Xw]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv)&point(Xw))=>(('Betw'(Xx,Xu,Xz)&'Betw'(Xy,Xv,Xz))=>?[Xw]:(point(Xw)&'Betw'(Xu,Xw,Xy)&'Betw'(Xv,Xw,Xx))))).
+fof(betw_id,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>('Betw'(Xa,Xb,Xa)=>Xa=Xb))).
+fof(five_segment,axiom,![Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&point(Xaprime)&point(Xbprime)&point(Xcprime)&point(Xdprime))=>(('OFS'(Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime)&Xa!=Xb)=>'Cong'(Xc,Xd,Xcprime,Xdprime)))).
+fof(ofs,axiom,![Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp]:((point(Xx)&point(Xy)&point(Xz)&point(Xr)&point(Xu)&point(Xv)&point(Xw)&point(Xp))=>('OFS'(Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp)<=>('Betw'(Xx,Xy,Xz)&'Betw'(Xu,Xv,Xw)&'Cong'(Xx,Xy,Xu,Xv)&'Cong'(Xy,Xz,Xv,Xw)&'Cong'(Xx,Xr,Xu,Xp)&'Cong'(Xy,Xr,Xv,Xp))))).
+fof(segment_construction,axiom,![Xa,Xb,Xd,Xe]:?[Xc]:(point(Xc)&'Betw'(Xa,Xb,Xc)&'Cong'(Xb,Xc,Xd,Xe))).
+fof(cong_id,axiom,![Xa,Xb,Xc]:((point(Xa)&point(Xb)&point(Xc))=>('Cong'(Xa,Xb,Xc,Xc)=>Xa=Xb))).
+fof(cong_pseudotransitive,axiom,![Xa,Xb,Xc,Xd,Xe,Xf]:((point(Xa)&point(Xb)&point(Xc)&point(Xd))=>(('Cong'(Xc,Xd,Xa,Xb)&'Cong'(Xc,Xd,Xe,Xf))=>'Cong'(Xa,Xb,Xe,Xf)))).
+fof(cong_refl_swap,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>'Cong'(Xa,Xb,Xb,Xa))).
+fof(collinear,axiom,![Xa,Xb,Xc]:(collinear(Xa,Xb,Xc)<=>('Betw'(Xa,Xb,Xc)|'Betw'(Xb,Xc,Xa)|'Betw'(Xc,Xa,Xb)))).
+fof(cong_shuffle_left1,axiom,point(fd)).
+fof(cong_shuffle_left2,axiom,point(fc)).
+fof(cong_shuffle_left3,axiom,point(fb)).
+fof(cong_shuffle_left4,axiom,point(fa)).
+------------------
+fof(cong_shuffle_right,conjecture,'Cong'(fa,fb,fc,fd)=>'Cong'(fb,fa,fd,fc)).
+fof(cong_shuffle_left,axiom,![Xa,Xb,Xc,Xd]:((point(Xa)&point(Xb)&point(Xc)&point(Xd))=>('Cong'(Xa,Xb,Xc,Xd)=>'Cong'(Xb,Xa,Xc,Xd)))).
+fof(cong_transitive,axiom,![Xa,Xb,Xc,Xd,Xe,Xf]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&point(Xe)&point(Xf))=>(('Cong'(Xa,Xb,Xc,Xd)&'Cong'(Xc,Xd,Xe,Xf))=>'Cong'(Xa,Xb,Xe,Xf)))).
+fof(cong_sym,axiom,![Xa,Xb,Xc,Xd]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&'Cong'(Xa,Xb,Xc,Xd))=>'Cong'(Xc,Xd,Xa,Xb))).
+fof(cong_refl,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>'Cong'(Xa,Xb,Xa,Xb))).
+fof(upperdim,axiom,![Xx,Xy,Xz,Xu,Xv]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv))=>(('Cong'(Xx,Xu,Xx,Xv)&'Cong'(Xy,Xu,Xy,Xv)&'Cong'(Xz,Xu,Xz,Xv)&Xu!=Xv)=>collinear(Xx,Xy,Xz)))).
+fof(innerpasch,axiom,![Xx,Xy,Xz,Xu,Xv,Xw]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv)&point(Xw))=>(('Betw'(Xx,Xu,Xz)&'Betw'(Xy,Xv,Xz))=>?[Xw]:(point(Xw)&'Betw'(Xu,Xw,Xy)&'Betw'(Xv,Xw,Xx))))).
+fof(betw_id,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>('Betw'(Xa,Xb,Xa)=>Xa=Xb))).
+fof(five_segment,axiom,![Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&point(Xaprime)&point(Xbprime)&point(Xcprime)&point(Xdprime))=>(('OFS'(Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime)&Xa!=Xb)=>'Cong'(Xc,Xd,Xcprime,Xdprime)))).
+fof(ofs,axiom,![Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp]:((point(Xx)&point(Xy)&point(Xz)&point(Xr)&point(Xu)&point(Xv)&point(Xw)&point(Xp))=>('OFS'(Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp)<=>('Betw'(Xx,Xy,Xz)&'Betw'(Xu,Xv,Xw)&'Cong'(Xx,Xy,Xu,Xv)&'Cong'(Xy,Xz,Xv,Xw)&'Cong'(Xx,Xr,Xu,Xp)&'Cong'(Xy,Xr,Xv,Xp))))).
+fof(segment_construction,axiom,![Xa,Xb,Xd,Xe]:?[Xc]:(point(Xc)&'Betw'(Xa,Xb,Xc)&'Cong'(Xb,Xc,Xd,Xe))).
+fof(cong_id,axiom,![Xa,Xb,Xc]:((point(Xa)&point(Xb)&point(Xc))=>('Cong'(Xa,Xb,Xc,Xc)=>Xa=Xb))).
+fof(cong_pseudotransitive,axiom,![Xa,Xb,Xc,Xd,Xe,Xf]:((point(Xa)&point(Xb)&point(Xc)&point(Xd))=>(('Cong'(Xc,Xd,Xa,Xb)&'Cong'(Xc,Xd,Xe,Xf))=>'Cong'(Xa,Xb,Xe,Xf)))).
+fof(cong_refl_swap,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>'Cong'(Xa,Xb,Xb,Xa))).
+fof(collinear,axiom,![Xa,Xb,Xc]:(collinear(Xa,Xb,Xc)<=>('Betw'(Xa,Xb,Xc)|'Betw'(Xb,Xc,Xa)|'Betw'(Xc,Xa,Xb)))).
+fof(cong_shuffle_right1,axiom,point(fd)).
+fof(cong_shuffle_right2,axiom,point(fc)).
+fof(cong_shuffle_right3,axiom,point(fb)).
+fof(cong_shuffle_right4,axiom,point(fa)).
+------------------
+fof(cong_zero,conjecture,'Cong'(fa,fa,fb,fb)).
+fof(cong_shuffle_right,axiom,![Xa,Xb,Xc,Xd]:((point(Xa)&point(Xb)&point(Xc)&point(Xd))=>('Cong'(Xa,Xb,Xc,Xd)=>'Cong'(Xb,Xa,Xd,Xc)))).
+fof(cong_shuffle_left,axiom,![Xa,Xb,Xc,Xd]:((point(Xa)&point(Xb)&point(Xc)&point(Xd))=>('Cong'(Xa,Xb,Xc,Xd)=>'Cong'(Xb,Xa,Xc,Xd)))).
+fof(cong_transitive,axiom,![Xa,Xb,Xc,Xd,Xe,Xf]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&point(Xe)&point(Xf))=>(('Cong'(Xa,Xb,Xc,Xd)&'Cong'(Xc,Xd,Xe,Xf))=>'Cong'(Xa,Xb,Xe,Xf)))).
+fof(cong_sym,axiom,![Xa,Xb,Xc,Xd]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&'Cong'(Xa,Xb,Xc,Xd))=>'Cong'(Xc,Xd,Xa,Xb))).
+fof(cong_refl,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>'Cong'(Xa,Xb,Xa,Xb))).
+fof(upperdim,axiom,![Xx,Xy,Xz,Xu,Xv]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv))=>(('Cong'(Xx,Xu,Xx,Xv)&'Cong'(Xy,Xu,Xy,Xv)&'Cong'(Xz,Xu,Xz,Xv)&Xu!=Xv)=>collinear(Xx,Xy,Xz)))).
+fof(innerpasch,axiom,![Xx,Xy,Xz,Xu,Xv,Xw]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv)&point(Xw))=>(('Betw'(Xx,Xu,Xz)&'Betw'(Xy,Xv,Xz))=>?[Xw]:(point(Xw)&'Betw'(Xu,Xw,Xy)&'Betw'(Xv,Xw,Xx))))).
+fof(betw_id,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>('Betw'(Xa,Xb,Xa)=>Xa=Xb))).
+fof(five_segment,axiom,![Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&point(Xaprime)&point(Xbprime)&point(Xcprime)&point(Xdprime))=>(('OFS'(Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime)&Xa!=Xb)=>'Cong'(Xc,Xd,Xcprime,Xdprime)))).
+fof(ofs,axiom,![Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp]:((point(Xx)&point(Xy)&point(Xz)&point(Xr)&point(Xu)&point(Xv)&point(Xw)&point(Xp))=>('OFS'(Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp)<=>('Betw'(Xx,Xy,Xz)&'Betw'(Xu,Xv,Xw)&'Cong'(Xx,Xy,Xu,Xv)&'Cong'(Xy,Xz,Xv,Xw)&'Cong'(Xx,Xr,Xu,Xp)&'Cong'(Xy,Xr,Xv,Xp))))).
+fof(segment_construction,axiom,![Xa,Xb,Xd,Xe]:?[Xc]:(point(Xc)&'Betw'(Xa,Xb,Xc)&'Cong'(Xb,Xc,Xd,Xe))).
+fof(cong_id,axiom,![Xa,Xb,Xc]:((point(Xa)&point(Xb)&point(Xc))=>('Cong'(Xa,Xb,Xc,Xc)=>Xa=Xb))).
+fof(cong_pseudotransitive,axiom,![Xa,Xb,Xc,Xd,Xe,Xf]:((point(Xa)&point(Xb)&point(Xc)&point(Xd))=>(('Cong'(Xc,Xd,Xa,Xb)&'Cong'(Xc,Xd,Xe,Xf))=>'Cong'(Xa,Xb,Xe,Xf)))).
+fof(cong_refl_swap,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>'Cong'(Xa,Xb,Xb,Xa))).
+fof(collinear,axiom,![Xa,Xb,Xc]:(collinear(Xa,Xb,Xc)<=>('Betw'(Xa,Xb,Xc)|'Betw'(Xb,Xc,Xa)|'Betw'(Xc,Xa,Xb)))).
+fof(cong_zero1,axiom,point(fb)).
+fof(cong_zero2,axiom,point(fa)). \ No newline at end of file
diff --git a/test/golden/geometry/generating tasks.golden b/test/golden/geometry/generating tasks.golden
new file mode 100644
index 0000000..a2869ea
--- /dev/null
+++ b/test/golden/geometry/generating tasks.golden
@@ -0,0 +1,14419 @@
+[ Task
+ { taskDirectness = Direct
+ , taskHypotheses =
+ [
+ ( Marker "upperdim"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
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+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
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+ )
+ [ TermVar
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+ )
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+ )
+ [ TermVar
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+ )
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+ [ Just
+ ( Word "point" )
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+ ( Word "points" )
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+ )
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+ )
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+ )
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+ )
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+ )
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+ ( Connected Conjunction
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+ )
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+ ( B
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+ )
+ , TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ , TermVar
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+ )
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+ ( B
+ ( NamedVar "v" )
+ )
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+ )
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+ )
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+ ( TermSymbol
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+ ( PredicateAdj
+ [ Just
+ ( Word "collinear" )
+ , Just
+ ( Word "with" )
+ , Nothing
+ , Just
+ ( Word "and" )
+ , Nothing
+ ]
+ )
+ )
+ [ TermVar
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+ )
+ , TermVar
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+ ( NamedVar "y" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "innerpasch"
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+ ( Connected Conjunction
+ ( Connected Conjunction
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+ ( B
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+ ( NamedVar "x" )
+ )
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+ )
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+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "betw_id"
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+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
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+ )
+ )
+ )
+ )
+ ,
+ ( Marker "five_segment"
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+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
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+ ( NamedVar "dprime" )
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+ ( Marker "ofs"
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+ ( NamedVar "c" )
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+ ]
+ )
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ )
+ )
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+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "e" )
+ )
+ )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_id"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateRelation
+ ( Symbol "=" )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_pseudotransitive"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "e" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "f" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "e" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "f" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_refl_swap"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "collinear"
+ , Quantified Universally
+ ( Scope
+ ( Connected Equivalence
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateAdj
+ [ Just
+ ( Word "collinear" )
+ , Just
+ ( Word "with" )
+ , Nothing
+ , Just
+ ( Word "and" )
+ , Nothing
+ ]
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ ( Quantified Universally
+ ( Scope
+ ( Connected Disjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ )
+ )
+ ]
+ )
+ ( Connected Disjunction
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+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_refl1"
+ , TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( NamedVar "b" )
+ ]
+ )
+ ,
+ ( Marker "cong_refl2"
+ , TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( NamedVar "a" )
+ ]
+ )
+ ]
+ , taskConjectureLabel = Marker "cong_refl"
+ , taskConjecture = TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( NamedVar "a" )
+ , TermVar
+ ( NamedVar "b" )
+ , TermVar
+ ( NamedVar "a" )
+ , TermVar
+ ( NamedVar "b" )
+ ]
+ }
+, Task
+ { taskDirectness = Direct
+ , taskHypotheses =
+ [
+ ( Marker "cong_refl"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "upperdim"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateRelation
+ ( Command "neq" )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateAdj
+ [ Just
+ ( Word "collinear" )
+ , Just
+ ( Word "with" )
+ , Nothing
+ , Just
+ ( Word "and" )
+ , Nothing
+ ]
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "innerpasch"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "w" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ ]
+ )
+ )
+ ( Quantified Existentially
+ ( Scope
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "w" )
+ )
+ ]
+ )
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "w" )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "w" )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "betw_id"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateRelation
+ ( Symbol "=" )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "five_segment"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
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+ [ Just
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+ [ Just
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+ { sg =
+ [ Just
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+ [ Just
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+ [ Just
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+ )
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+ )
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+ ( B
+ ( NamedVar "dprime" )
+ )
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+ )
+ )
+ )
+ )
+ )
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+ ( Marker "ofs"
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+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
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+ )
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+ ( NamedVar "p" )
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+ { sg =
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+ ( NamedVar "a" )
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+ )
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+ )
+ )
+ )
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+ { sg =
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+ )
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+ ( Marker "cong_pseudotransitive"
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+ ( NamedVar "f" )
+ )
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+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
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+ ( NamedVar "b" )
+ )
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+ ( B
+ ( NamedVar "a" )
+ )
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+ )
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+ ( Connected Equivalence
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateAdj
+ [ Just
+ ( Word "collinear" )
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+ ( Word "with" )
+ , Nothing
+ , Just
+ ( Word "and" )
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+ ( NamedVar "a" )
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+ ( NamedVar "b" )
+ )
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+ ( B
+ ( NamedVar "c" )
+ )
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+ ( PredicateSymbol "Betw" )
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+ ( TermVar
+ ( B
+ ( NamedVar "a" )
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+ )
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+ ( NamedVar "b" )
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+ )
+ )
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+ ( B
+ ( NamedVar "c" )
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+ )
+ ]
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+ ( PredicateSymbol "Betw" )
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+ ( B
+ ( NamedVar "b" )
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+ )
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+ ( B
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+ )
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+ ( NamedVar "a" )
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+ )
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+ ( B
+ ( NamedVar "a" )
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+ )
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+ ( NamedVar "b" )
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+ )
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+ )
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+ )
+ )
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+ ( NamedVar "a" )
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+ ( NamedVar "b" )
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+ ( NamedVar "c" )
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+ ( NamedVar "d" )
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+ ( Marker "cong_sym2"
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+ { sg =
+ [ Just
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+ ( Word "points" )
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+ [ TermVar
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+ { sg =
+ [ Just
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+ [ TermVar
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+ { sg =
+ [ Just
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+ [ TermVar
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+ { sg =
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+ )
+ [ TermVar
+ ( NamedVar "a" )
+ ]
+ )
+ ]
+ , taskConjectureLabel = Marker "cong_sym"
+ , taskConjecture = TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( NamedVar "c" )
+ , TermVar
+ ( NamedVar "d" )
+ , TermVar
+ ( NamedVar "a" )
+ , TermVar
+ ( NamedVar "b" )
+ ]
+ }
+, Task
+ { taskDirectness = Direct
+ , taskHypotheses =
+ [
+ ( Marker "cong_sym"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_refl"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "upperdim"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateRelation
+ ( Command "neq" )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateAdj
+ [ Just
+ ( Word "collinear" )
+ , Just
+ ( Word "with" )
+ , Nothing
+ , Just
+ ( Word "and" )
+ , Nothing
+ ]
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "innerpasch"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "w" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ ]
+ )
+ )
+ ( Quantified Existentially
+ ( Scope
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "w" )
+ )
+ ]
+ )
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "w" )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "w" )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "betw_id"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateRelation
+ ( Symbol "=" )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "five_segment"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "aprime" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "bprime" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "cprime" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "dprime" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "OFS" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "aprime" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "bprime" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "cprime" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "dprime" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateRelation
+ ( Command "neq" )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "cprime" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "dprime" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "ofs"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "r" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "w" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "p" )
+ )
+ ]
+ )
+ )
+ ( Connected Equivalence
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "OFS" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "r" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "w" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "p" )
+ )
+ ]
+ )
+ ( Quantified Universally
+ ( Scope
+ ( Connected Conjunction
+ ( Connected Conjunction
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+ ( PredicateSymbol "Betw" )
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+ ( TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ )
+ )
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+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ )
+ )
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+ ( TermSymbol
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+ ( PredicateSymbol "Betw" )
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+ ( F
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+ )
+ )
+ )
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+ ( F
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+ ( B
+ ( NamedVar "v" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "w" )
+ )
+ )
+ )
+ ]
+ )
+ )
+ ( Connected Conjunction
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+ ( Connected Conjunction
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+ ( F
+ ( TermVar
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+ ( NamedVar "x" )
+ )
+ )
+ )
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+ ( TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ )
+ )
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+ ( TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ )
+ )
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+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ )
+ )
+ ]
+ )
+ ( TermSymbol
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+ ( PredicateSymbol "Cong" )
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+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ )
+ )
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+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ )
+ )
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+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "w" )
+ )
+ )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
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+ ( PredicateSymbol "Cong" )
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+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ )
+ )
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+ ( F
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+ ( NamedVar "r" )
+ )
+ )
+ )
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+ ( B
+ ( NamedVar "u" )
+ )
+ )
+ )
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+ ( F
+ ( TermVar
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+ )
+ )
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+ )
+ )
+ ( TermSymbol
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+ ( PredicateSymbol "Cong" )
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+ ( F
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+ ( B
+ ( NamedVar "y" )
+ )
+ )
+ )
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+ ( NamedVar "r" )
+ )
+ )
+ )
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+ ( F
+ ( TermVar
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+ ( NamedVar "v" )
+ )
+ )
+ )
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+ ( F
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+ ( B
+ ( NamedVar "p" )
+ )
+ )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "segment_construction"
+ , Quantified Universally
+ ( Scope
+ ( Quantified Existentially
+ ( Scope
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
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+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ , pl =
+ [ Just
+ ( Word "points" )
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+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ ( Connected Conjunction
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+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ )
+ )
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+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ )
+ )
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+ ( B
+ ( NamedVar "c" )
+ )
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+ ( F
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+ ( B
+ ( NamedVar "d" )
+ )
+ )
+ )
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+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "e" )
+ )
+ )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_id"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
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+ [ Just
+ ( Word "points" )
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+ )
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+ )
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+ )
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+ ( PredicateNoun
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+ { sg =
+ [ Just
+ ( Word "point" )
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+ , pl =
+ [ Just
+ ( Word "points" )
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+ )
+ )
+ )
+ [ TermVar
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+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
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+ { sg =
+ [ Just
+ ( Word "point" )
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+ [ Just
+ ( Word "points" )
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+ )
+ )
+ )
+ [ TermVar
+ ( B
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+ )
+ ]
+ )
+ )
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+ )
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+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
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+ ( NamedVar "c" )
+ )
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+ ( NamedVar "c" )
+ )
+ ]
+ )
+ ( TermSymbol
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+ )
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+ )
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+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_pseudotransitive"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
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+ { sg =
+ [ Just
+ ( Word "point" )
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+ , pl =
+ [ Just
+ ( Word "points" )
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+ )
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+ )
+ [ TermVar
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+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
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+ { sg =
+ [ Just
+ ( Word "point" )
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+ [ Just
+ ( Word "points" )
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+ [ TermVar
+ ( B
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+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ [ Just
+ ( Word "points" )
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+ )
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+ )
+ ( TermSymbol
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+ { sg =
+ [ Just
+ ( Word "point" )
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+ [ Just
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+ )
+ [ TermVar
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+ )
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+ ( Connected Implication
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+ ( NamedVar "a" )
+ )
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+ ( NamedVar "b" )
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+ ( NamedVar "c" )
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+ ( NamedVar "e" )
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+ ( NamedVar "f" )
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+ )
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+ ( B
+ ( NamedVar "f" )
+ )
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+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_refl_swap"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ [ Just
+ ( Word "points" )
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+ )
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+ [ TermVar
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+ ( NamedVar "a" )
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+ ( TermSymbol
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+ ( PredicateNoun
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+ { sg =
+ [ Just
+ ( Word "point" )
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+ [ Just
+ ( Word "points" )
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+ )
+ [ TermVar
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+ ( NamedVar "b" )
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+ )
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+ ( NamedVar "a" )
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+ ( NamedVar "b" )
+ )
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+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "collinear"
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+ ( Scope
+ ( Connected Equivalence
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateAdj
+ [ Just
+ ( Word "collinear" )
+ , Just
+ ( Word "with" )
+ , Nothing
+ , Just
+ ( Word "and" )
+ , Nothing
+ ]
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+ )
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+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
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+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ ( Quantified Universally
+ ( Scope
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+ ( PredicateSymbol "Betw" )
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+ ( B
+ ( NamedVar "a" )
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+ )
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+ ( NamedVar "b" )
+ )
+ )
+ )
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+ ( B
+ ( NamedVar "c" )
+ )
+ )
+ )
+ ]
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+ ( Connected Disjunction
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+ ( PredicateSymbol "Betw" )
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+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "b" )
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+ )
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+ )
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+ ( NamedVar "a" )
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+ )
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+ ( TermSymbol
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+ )
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+ ( NamedVar "a" )
+ )
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+ )
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+ ( NamedVar "b" )
+ )
+ )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ )
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+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ , pl =
+ [ Just
+ ( Word "points" )
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+ )
+ )
+ )
+ [ TermVar
+ ( NamedVar "f" )
+ ]
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+ ( Marker "cong_transitive2"
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+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
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+ }
+ )
+ )
+ )
+ [ TermVar
+ ( NamedVar "e" )
+ ]
+ )
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+ ( Marker "cong_transitive3"
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+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ [ Just
+ ( Word "points" )
+ ]
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+ )
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+ )
+ [ TermVar
+ ( NamedVar "d" )
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+ ( Marker "cong_transitive4"
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+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ [ Just
+ ( Word "points" )
+ ]
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+ )
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+ )
+ [ TermVar
+ ( NamedVar "c" )
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+ ( Marker "cong_transitive5"
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+ ( PredicateNoun
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+ { sg =
+ [ Just
+ ( Word "point" )
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+ [ Just
+ ( Word "points" )
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+ )
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+ )
+ [ TermVar
+ ( NamedVar "b" )
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+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ [ Just
+ ( Word "points" )
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+ )
+ )
+ )
+ [ TermVar
+ ( NamedVar "a" )
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+ , taskConjectureLabel = Marker "cong_transitive"
+ , taskConjecture = Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
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+ [ TermVar
+ ( NamedVar "a" )
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+ ( NamedVar "b" )
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+ ( NamedVar "e" )
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+ ( NamedVar "f" )
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+ )
+ }
+, Task
+ { taskDirectness = Direct
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+ [
+ ( Marker "cong_transitive"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
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+ ( PredicateNoun
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+ { sg =
+ [ Just
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+ [ TermVar
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+ ( TermSymbol
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+ { sg =
+ [ Just
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+ ( TermSymbol
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+ [ Just
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+ ( TermSymbol
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+ [ TermVar
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+ ( TermSymbol
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+ ( PredicateNoun
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+ ( Word "point" )
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+ [ TermVar
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+ ( TermSymbol
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+ [ Just
+ ( Word "point" )
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+ [ TermVar
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+ ( Connected Implication
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+ ( PredicateSymbol "Cong" )
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+ ( NamedVar "a" )
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+ ( NamedVar "c" )
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+ ( NamedVar "d" )
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+ ( TermSymbol
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+ ( NamedVar "e" )
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+ ( NamedVar "f" )
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+ ( TermSymbol
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+ ( NamedVar "e" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "f" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_sym"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ [ Just
+ ( Word "points" )
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+ )
+ [ TermVar
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+ ( NamedVar "a" )
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+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
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+ { sg =
+ [ Just
+ ( Word "point" )
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+ ( Word "points" )
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+ [ TermVar
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+ ( NamedVar "b" )
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+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
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+ { sg =
+ [ Just
+ ( Word "point" )
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+ [ Just
+ ( Word "points" )
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+ [ TermVar
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+ ( NamedVar "c" )
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+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ [ Just
+ ( Word "points" )
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+ [ TermVar
+ ( B
+ ( NamedVar "d" )
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+ ( TermSymbol
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+ ( PredicateSymbol "Cong" )
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+ ( B
+ ( NamedVar "a" )
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+ ( NamedVar "b" )
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+ ( B
+ ( NamedVar "c" )
+ )
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+ ( B
+ ( NamedVar "d" )
+ )
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+ ( TermSymbol
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+ ( PredicateSymbol "Cong" )
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+ ( NamedVar "c" )
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+ ( NamedVar "d" )
+ )
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+ ( B
+ ( NamedVar "a" )
+ )
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+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_refl"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "upperdim"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
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+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ , pl =
+ [ Just
+ ( Word "points" )
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+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ , pl =
+ [ Just
+ ( Word "points" )
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+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
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+ ( B
+ ( NamedVar "x" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ ( Connected Conjunction
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+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateRelation
+ ( Command "neq" )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "v" )
+ )
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+ )
+ )
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateAdj
+ [ Just
+ ( Word "collinear" )
+ , Just
+ ( Word "with" )
+ , Nothing
+ , Just
+ ( Word "and" )
+ , Nothing
+ ]
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "innerpasch"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
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+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ , pl =
+ [ Just
+ ( Word "points" )
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+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "y" )
+ )
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+ )
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+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ [ Just
+ ( Word "points" )
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+ ( NamedVar "z" )
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+ ( TermSymbol
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+ ( PredicateNoun
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+ { sg =
+ [ Just
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+ ( Word "points" )
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+ ( TermSymbol
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+ { sg =
+ [ Just
+ ( Word "point" )
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+ ( Word "points" )
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+ ( TermSymbol
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+ { sg =
+ [ Just
+ ( Word "point" )
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+ [ Just
+ ( Word "points" )
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+ )
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+ ( B
+ ( NamedVar "w" )
+ )
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+ ( PredicateSymbol "Betw" )
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+ ( B
+ ( NamedVar "x" )
+ )
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+ ( B
+ ( NamedVar "u" )
+ )
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+ ( NamedVar "z" )
+ )
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+ )
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+ ( NamedVar "y" )
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+ ( B
+ ( NamedVar "v" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "z" )
+ )
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+ { sg =
+ [ Just
+ ( Word "point" )
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+ , pl =
+ [ Just
+ ( Word "points" )
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+ )
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+ )
+ [ TermVar
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+ ( NamedVar "w" )
+ )
+ ]
+ )
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+ ( PredicateSymbol "Betw" )
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+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ )
+ )
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+ ( NamedVar "w" )
+ )
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+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ )
+ )
+ ]
+ )
+ ( TermSymbol
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+ ( PredicateSymbol "Betw" )
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+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ )
+ )
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+ )
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+ ( TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "betw_id"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ , pl =
+ [ Just
+ ( Word "points" )
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+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ , pl =
+ [ Just
+ ( Word "points" )
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+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
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+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
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+ ( NamedVar "a" )
+ )
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+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "five_segment"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
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+ ( TermSymbol
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+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ ( NamedVar "a" )
+ )
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+ ( TermSymbol
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+ ( PredicateNoun
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+ { sg =
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+ ( Word "point" )
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+ )
+ ( TermSymbol
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+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ ( Word "points" )
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+ ( TermSymbol
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+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ ( Word "points" )
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+ )
+ [ TermVar
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+ ( NamedVar "d" )
+ )
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+ )
+ ( TermSymbol
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+ { sg =
+ [ Just
+ ( Word "point" )
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+ ( Word "points" )
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+ ( TermSymbol
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+ { sg =
+ [ Just
+ ( Word "point" )
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+ ( Word "points" )
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+ ( TermSymbol
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+ )
+ [ TermVar
+ ( B
+ ( NamedVar "dprime" )
+ )
+ ]
+ )
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+ ( Connected Implication
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+ ( TermSymbol
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+ ( PredicateSymbol "OFS" )
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+ ( B
+ ( NamedVar "a" )
+ )
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+ ( NamedVar "b" )
+ )
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+ )
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+ ( NamedVar "b" )
+ )
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+ )
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+ ( B
+ ( NamedVar "dprime" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "ofs"
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+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
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+ [ Just
+ ( Word "point" )
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+ { sg =
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+ ( NamedVar "x" )
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+ ( B
+ ( NamedVar "w" )
+ )
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+ ( B
+ ( NamedVar "p" )
+ )
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+ ( PredicateSymbol "Betw" )
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+ [ TermVar
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+ )
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+ )
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+ ( NamedVar "w" )
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+ )
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+ )
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+ ( TermSymbol
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+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "r" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "p" )
+ )
+ )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "segment_construction"
+ , Quantified Universally
+ ( Scope
+ ( Quantified Existentially
+ ( Scope
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "e" )
+ )
+ )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_id"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateRelation
+ ( Symbol "=" )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_pseudotransitive"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "e" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "f" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "e" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "f" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_refl_swap"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "collinear"
+ , Quantified Universally
+ ( Scope
+ ( Connected Equivalence
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateAdj
+ [ Just
+ ( Word "collinear" )
+ , Just
+ ( Word "with" )
+ , Nothing
+ , Just
+ ( Word "and" )
+ , Nothing
+ ]
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ ( Quantified Universally
+ ( Scope
+ ( Connected Disjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ )
+ )
+ ]
+ )
+ ( Connected Disjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_shuffle_left1"
+ , TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( NamedVar "d" )
+ ]
+ )
+ ,
+ ( Marker "cong_shuffle_left2"
+ , TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( NamedVar "c" )
+ ]
+ )
+ ,
+ ( Marker "cong_shuffle_left3"
+ , TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( NamedVar "b" )
+ ]
+ )
+ ,
+ ( Marker "cong_shuffle_left4"
+ , TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( NamedVar "a" )
+ ]
+ )
+ ]
+ , taskConjectureLabel = Marker "cong_shuffle_left"
+ , taskConjecture = Connected Implication
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( NamedVar "a" )
+ , TermVar
+ ( NamedVar "b" )
+ , TermVar
+ ( NamedVar "c" )
+ , TermVar
+ ( NamedVar "d" )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( NamedVar "b" )
+ , TermVar
+ ( NamedVar "a" )
+ , TermVar
+ ( NamedVar "c" )
+ , TermVar
+ ( NamedVar "d" )
+ ]
+ )
+ }
+, Task
+ { taskDirectness = Direct
+ , taskHypotheses =
+ [
+ ( Marker "cong_shuffle_left"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_transitive"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "e" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "f" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "e" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "f" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "e" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "f" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_sym"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_refl"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "upperdim"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateRelation
+ ( Command "neq" )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateAdj
+ [ Just
+ ( Word "collinear" )
+ , Just
+ ( Word "with" )
+ , Nothing
+ , Just
+ ( Word "and" )
+ , Nothing
+ ]
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "innerpasch"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "w" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ ]
+ )
+ )
+ ( Quantified Existentially
+ ( Scope
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "w" )
+ )
+ ]
+ )
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "w" )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "w" )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "betw_id"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateRelation
+ ( Symbol "=" )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "five_segment"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "aprime" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "bprime" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "cprime" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "dprime" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "OFS" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "aprime" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "bprime" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "cprime" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "dprime" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateRelation
+ ( Command "neq" )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "cprime" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "dprime" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "ofs"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "r" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "w" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "p" )
+ )
+ ]
+ )
+ )
+ ( Connected Equivalence
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "OFS" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "r" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "w" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "p" )
+ )
+ ]
+ )
+ ( Quantified Universally
+ ( Scope
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "w" )
+ )
+ )
+ )
+ ]
+ )
+ )
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "z" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "w" )
+ )
+ )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "x" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "r" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "u" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "p" )
+ )
+ )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "y" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "r" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "v" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "p" )
+ )
+ )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "segment_construction"
+ , Quantified Universally
+ ( Scope
+ ( Quantified Existentially
+ ( Scope
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "e" )
+ )
+ )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_id"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
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+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateRelation
+ ( Symbol "=" )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_pseudotransitive"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "e" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "f" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "e" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "f" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_refl_swap"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "collinear"
+ , Quantified Universally
+ ( Scope
+ ( Connected Equivalence
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateAdj
+ [ Just
+ ( Word "collinear" )
+ , Just
+ ( Word "with" )
+ , Nothing
+ , Just
+ ( Word "and" )
+ , Nothing
+ ]
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ ( Quantified Universally
+ ( Scope
+ ( Connected Disjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ )
+ )
+ ]
+ )
+ ( Connected Disjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Betw" )
+ )
+ [ TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ )
+ )
+ , TermVar
+ ( F
+ ( TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_shuffle_right1"
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+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
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+ )
+ )
+ )
+ [ TermVar
+ ( NamedVar "d" )
+ ]
+ )
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+ ( Marker "cong_shuffle_right2"
+ , TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
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+ )
+ )
+ )
+ [ TermVar
+ ( NamedVar "c" )
+ ]
+ )
+ ,
+ ( Marker "cong_shuffle_right3"
+ , TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( NamedVar "b" )
+ ]
+ )
+ ,
+ ( Marker "cong_shuffle_right4"
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+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( NamedVar "a" )
+ ]
+ )
+ ]
+ , taskConjectureLabel = Marker "cong_shuffle_right"
+ , taskConjecture = Connected Implication
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( NamedVar "a" )
+ , TermVar
+ ( NamedVar "b" )
+ , TermVar
+ ( NamedVar "c" )
+ , TermVar
+ ( NamedVar "d" )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( NamedVar "b" )
+ , TermVar
+ ( NamedVar "a" )
+ , TermVar
+ ( NamedVar "d" )
+ , TermVar
+ ( NamedVar "c" )
+ ]
+ )
+ }
+, Task
+ { taskDirectness = Direct
+ , taskHypotheses =
+ [
+ ( Marker "cong_shuffle_right"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ , pl =
+ [ Just
+ ( Word "points" )
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+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
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+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ [ Just
+ ( Word "points" )
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+ [ TermVar
+ ( B
+ ( NamedVar "b" )
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+ )
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+ ( TermSymbol
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+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ ( Word "points" )
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+ [ TermVar
+ ( B
+ ( NamedVar "c" )
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+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ [ Just
+ ( Word "points" )
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+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
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+ ( B
+ ( NamedVar "c" )
+ )
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+ ( B
+ ( NamedVar "d" )
+ )
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+ ( TermSymbol
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+ ( PredicateSymbol "Cong" )
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+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "a" )
+ )
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+ ( B
+ ( NamedVar "d" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_shuffle_left"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
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+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
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+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
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+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_transitive"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
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+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
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+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "e" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "f" )
+ )
+ ]
+ )
+ )
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "e" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "f" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "e" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "f" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_sym"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ ]
+ )
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( B
+ ( NamedVar "c" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "d" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "a" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "b" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ ,
+ ( Marker "cong_refl"
+ , Quantified Universally
+ ( Scope
+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ , pl =
+ [ Just
+ ( Word "points" )
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+ }
+ )
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+ )
+ [ TermVar
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+ ( NamedVar "b" )
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+ ( NamedVar "a" )
+ )
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+ ( B
+ ( NamedVar "b" )
+ )
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+ )
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+ ( Marker "upperdim"
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+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
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+ { sg =
+ [ Just
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+ [ Just
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+ ( TermSymbol
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+ ( PredicateNoun
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+ { sg =
+ [ Just
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+ ( TermSymbol
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+ ( PredicateNoun
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+ { sg =
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+ { sg =
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+ [ Just
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+ )
+ )
+ )
+ [ TermVar
+ ( B
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+ )
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+ )
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+ ( B
+ ( NamedVar "x" )
+ )
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+ ( B
+ ( NamedVar "u" )
+ )
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+ ( B
+ ( NamedVar "x" )
+ )
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+ ( B
+ ( NamedVar "v" )
+ )
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+ ( B
+ ( NamedVar "y" )
+ )
+ , TermVar
+ ( B
+ ( NamedVar "u" )
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+ , TermVar
+ ( B
+ ( NamedVar "y" )
+ )
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+ ( B
+ ( NamedVar "v" )
+ )
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+ )
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+ ( B
+ ( NamedVar "z" )
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+ )
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+ )
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+ )
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+ ( NamedVar "v" )
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+ ( Word "collinear" )
+ , Just
+ ( Word "with" )
+ , Nothing
+ , Just
+ ( Word "and" )
+ , Nothing
+ ]
+ )
+ )
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+ ( NamedVar "x" )
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+ ( B
+ ( NamedVar "y" )
+ )
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+ ( B
+ ( NamedVar "z" )
+ )
+ ]
+ )
+ )
+ )
+ )
+ )
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+ ( Marker "innerpasch"
+ , Quantified Universally
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+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( TermSymbol
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+ { sg =
+ [ Just
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+ [ Just
+ ( Word "points" )
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+ ( NamedVar "x" )
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+ ( PredicateNoun
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+ { sg =
+ [ Just
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+ ( NamedVar "u" )
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+ )
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+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ )
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+ ( Marker "betw_id"
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+ ( Connected Implication
+ ( Connected Conjunction
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
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+ ( NamedVar "b" )
+ )
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+ )
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+ ( Marker "five_segment"
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+ ( Connected Conjunction
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+ ( B
+ ( NamedVar "dprime" )
+ )
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+ )
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+ ( Marker "ofs"
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+ ( NamedVar "p" )
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+ ( PredicateSymbol "Betw" )
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+ }
+] \ No newline at end of file
diff --git a/test/golden/geometry/glossing.golden b/test/golden/geometry/glossing.golden
new file mode 100644
index 0000000..f1e1bd2
--- /dev/null
+++ b/test/golden/geometry/glossing.golden
@@ -0,0 +1,2187 @@
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+ , Asm
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( NamedVar "c" )
+ ]
+ )
+ , Asm
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( NamedVar "d" )
+ ]
+ )
+ ]
+ ( Connected Implication
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( NamedVar "a" )
+ , TermVar
+ ( NamedVar "b" )
+ , TermVar
+ ( NamedVar "c" )
+ , TermVar
+ ( NamedVar "d" )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( NamedVar "b" )
+ , TermVar
+ ( NamedVar "a" )
+ , TermVar
+ ( NamedVar "c" )
+ , TermVar
+ ( NamedVar "d" )
+ ]
+ )
+ )
+ )
+, BlockLemma
+ ( SourcePos
+ { sourceName = "test/examples/geometry.tex"
+ , sourceLine = Pos 109
+ , sourceColumn = Pos 1
+ }
+ )
+ ( Marker "cong_shuffle_right" )
+ ( Lemma
+ [ Asm
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( NamedVar "a" )
+ ]
+ )
+ , Asm
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( NamedVar "b" )
+ ]
+ )
+ , Asm
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( NamedVar "c" )
+ ]
+ )
+ , Asm
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( NamedVar "d" )
+ ]
+ )
+ ]
+ ( Connected Implication
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( NamedVar "a" )
+ , TermVar
+ ( NamedVar "b" )
+ , TermVar
+ ( NamedVar "c" )
+ , TermVar
+ ( NamedVar "d" )
+ ]
+ )
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( NamedVar "b" )
+ , TermVar
+ ( NamedVar "a" )
+ , TermVar
+ ( NamedVar "d" )
+ , TermVar
+ ( NamedVar "c" )
+ ]
+ )
+ )
+ )
+, BlockLemma
+ ( SourcePos
+ { sourceName = "test/examples/geometry.tex"
+ , sourceLine = Pos 116
+ , sourceColumn = Pos 1
+ }
+ )
+ ( Marker "cong_zero" )
+ ( Lemma
+ [ Asm
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( NamedVar "a" )
+ ]
+ )
+ , Asm
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateNoun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ )
+ )
+ )
+ [ TermVar
+ ( NamedVar "b" )
+ ]
+ )
+ ]
+ ( TermSymbol
+ ( SymbolPredicate
+ ( PredicateSymbol "Cong" )
+ )
+ [ TermVar
+ ( NamedVar "a" )
+ , TermVar
+ ( NamedVar "a" )
+ , TermVar
+ ( NamedVar "b" )
+ , TermVar
+ ( NamedVar "b" )
+ ]
+ )
+ )
+] \ No newline at end of file
diff --git a/test/golden/geometry/parsing.golden b/test/golden/geometry/parsing.golden
new file mode 100644
index 0000000..b57f76c
--- /dev/null
+++ b/test/golden/geometry/parsing.golden
@@ -0,0 +1,1198 @@
+[ BlockDefn
+ ( SourcePos
+ { sourceName = "test/examples/geometry.tex"
+ , sourceLine = Pos 1
+ , sourceColumn = Pos 1
+ }
+ )
+ ( Marker "collinear" )
+ ( Defn []
+ ( DefnAdj Nothing
+ ( NamedVar "a" )
+ ( Adj
+ [ Just
+ ( Word "collinear" )
+ , Just
+ ( Word "with" )
+ , Nothing
+ , Just
+ ( Word "and" )
+ , Nothing
+ ]
+ [ NamedVar "b"
+ , NamedVar "c"
+ ]
+ )
+ )
+ ( StmtConnected Disjunction
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Betw" 3 )
+ ( ExprVar
+ ( NamedVar "a" ) :|
+ [ ExprVar
+ ( NamedVar "b" )
+ , ExprVar
+ ( NamedVar "c" )
+ ]
+ )
+ )
+ )
+ ( StmtConnected Disjunction
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Betw" 3 )
+ ( ExprVar
+ ( NamedVar "b" ) :|
+ [ ExprVar
+ ( NamedVar "c" )
+ , ExprVar
+ ( NamedVar "a" )
+ ]
+ )
+ )
+ )
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Betw" 3 )
+ ( ExprVar
+ ( NamedVar "c" ) :|
+ [ ExprVar
+ ( NamedVar "a" )
+ , ExprVar
+ ( NamedVar "b" )
+ ]
+ )
+ )
+ )
+ )
+ )
+ )
+, BlockAxiom
+ ( SourcePos
+ { sourceName = "test/examples/geometry.tex"
+ , sourceLine = Pos 5
+ , sourceColumn = Pos 1
+ }
+ )
+ ( Marker "cong_refl_swap" )
+ ( Axiom
+ [ AsmLetNoun
+ ( NamedVar "a" :|
+ [ NamedVar "b" ]
+ ) NounPhrase ( [] )
+ ( Noun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ ) []
+ ) ( Nothing ) ( [] ) ( Nothing )
+ ]
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "a" ) :|
+ [ ExprVar
+ ( NamedVar "b" )
+ , ExprVar
+ ( NamedVar "b" )
+ , ExprVar
+ ( NamedVar "a" )
+ ]
+ )
+ )
+ )
+ )
+, BlockAxiom
+ ( SourcePos
+ { sourceName = "test/examples/geometry.tex"
+ , sourceLine = Pos 10
+ , sourceColumn = Pos 1
+ }
+ )
+ ( Marker "cong_pseudotransitive" )
+ ( Axiom
+ [ AsmLetNoun
+ ( NamedVar "a" :|
+ [ NamedVar "b"
+ , NamedVar "c"
+ , NamedVar "d"
+ ]
+ ) NounPhrase ( [] )
+ ( Noun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ ) []
+ ) ( Nothing ) ( [] ) ( Nothing )
+ ]
+ ( StmtConnected Implication
+ ( StmtConnected Conjunction
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "c" ) :|
+ [ ExprVar
+ ( NamedVar "d" )
+ , ExprVar
+ ( NamedVar "a" )
+ , ExprVar
+ ( NamedVar "b" )
+ ]
+ )
+ )
+ )
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "c" ) :|
+ [ ExprVar
+ ( NamedVar "d" )
+ , ExprVar
+ ( NamedVar "e" )
+ , ExprVar
+ ( NamedVar "f" )
+ ]
+ )
+ )
+ )
+ )
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "a" ) :|
+ [ ExprVar
+ ( NamedVar "b" )
+ , ExprVar
+ ( NamedVar "e" )
+ , ExprVar
+ ( NamedVar "f" )
+ ]
+ )
+ )
+ )
+ )
+ )
+, BlockAxiom
+ ( SourcePos
+ { sourceName = "test/examples/geometry.tex"
+ , sourceLine = Pos 15
+ , sourceColumn = Pos 1
+ }
+ )
+ ( Marker "cong_id" )
+ ( Axiom
+ [ AsmLetNoun
+ ( NamedVar "a" :|
+ [ NamedVar "b"
+ , NamedVar "c"
+ ]
+ ) NounPhrase ( [] )
+ ( Noun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ ) []
+ ) ( Nothing ) ( [] ) ( Nothing )
+ ]
+ ( StmtConnected Implication
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "a" ) :|
+ [ ExprVar
+ ( NamedVar "b" )
+ , ExprVar
+ ( NamedVar "c" )
+ , ExprVar
+ ( NamedVar "c" )
+ ]
+ )
+ )
+ )
+ ( StmtFormula
+ ( FormulaChain
+ ( ChainBase
+ ( ExprVar
+ ( NamedVar "a" ) :| []
+ ) Positive
+ ( RelationSymbol
+ ( Symbol "=" )
+ )
+ ( ExprVar
+ ( NamedVar "b" ) :| []
+ )
+ )
+ )
+ )
+ )
+ )
+, BlockAxiom
+ ( SourcePos
+ { sourceName = "test/examples/geometry.tex"
+ , sourceLine = Pos 21
+ , sourceColumn = Pos 1
+ }
+ )
+ ( Marker "segment_construction" )
+ ( Axiom []
+ ( StmtExists NounPhrase ( [] )
+ ( Noun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ ) []
+ )
+ (
+ [ NamedVar "c" ]
+ ) ( [] )
+ ( Just
+ ( StmtConnected Conjunction
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Betw" 3 )
+ ( ExprVar
+ ( NamedVar "a" ) :|
+ [ ExprVar
+ ( NamedVar "b" )
+ , ExprVar
+ ( NamedVar "c" )
+ ]
+ )
+ )
+ )
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "b" ) :|
+ [ ExprVar
+ ( NamedVar "c" )
+ , ExprVar
+ ( NamedVar "d" )
+ , ExprVar
+ ( NamedVar "e" )
+ ]
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+, BlockDefn
+ ( SourcePos
+ { sourceName = "test/examples/geometry.tex"
+ , sourceLine = Pos 26
+ , sourceColumn = Pos 1
+ }
+ )
+ ( Marker "ofs" )
+ ( Defn
+ [ AsmLetNoun
+ ( NamedVar "x" :|
+ [ NamedVar "y"
+ , NamedVar "z"
+ , NamedVar "r"
+ , NamedVar "u"
+ , NamedVar "v"
+ , NamedVar "w"
+ , NamedVar "p"
+ ]
+ ) NounPhrase ( [] )
+ ( Noun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ ) []
+ ) ( Nothing ) ( [] ) ( Nothing )
+ ]
+ ( DefnSymbolicPredicate
+ ( PrefixPredicate "OFS" 8 )
+ ( NamedVar "x" :|
+ [ NamedVar "y"
+ , NamedVar "z"
+ , NamedVar "r"
+ , NamedVar "u"
+ , NamedVar "v"
+ , NamedVar "w"
+ , NamedVar "p"
+ ]
+ )
+ )
+ ( StmtConnected Conjunction
+ ( StmtFormula
+ ( Connected Conjunction
+ ( FormulaPredicate
+ ( PrefixPredicate "Betw" 3 )
+ ( ExprVar
+ ( NamedVar "x" ) :|
+ [ ExprVar
+ ( NamedVar "y" )
+ , ExprVar
+ ( NamedVar "z" )
+ ]
+ )
+ )
+ ( FormulaPredicate
+ ( PrefixPredicate "Betw" 3 )
+ ( ExprVar
+ ( NamedVar "u" ) :|
+ [ ExprVar
+ ( NamedVar "v" )
+ , ExprVar
+ ( NamedVar "w" )
+ ]
+ )
+ )
+ )
+ )
+ ( StmtFormula
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( Connected Conjunction
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "x" ) :|
+ [ ExprVar
+ ( NamedVar "y" )
+ , ExprVar
+ ( NamedVar "u" )
+ , ExprVar
+ ( NamedVar "v" )
+ ]
+ )
+ )
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "y" ) :|
+ [ ExprVar
+ ( NamedVar "z" )
+ , ExprVar
+ ( NamedVar "v" )
+ , ExprVar
+ ( NamedVar "w" )
+ ]
+ )
+ )
+ )
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "x" ) :|
+ [ ExprVar
+ ( NamedVar "r" )
+ , ExprVar
+ ( NamedVar "u" )
+ , ExprVar
+ ( NamedVar "p" )
+ ]
+ )
+ )
+ )
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "y" ) :|
+ [ ExprVar
+ ( NamedVar "r" )
+ , ExprVar
+ ( NamedVar "v" )
+ , ExprVar
+ ( NamedVar "p" )
+ ]
+ )
+ )
+ )
+ )
+ )
+ )
+, BlockAxiom
+ ( SourcePos
+ { sourceName = "test/examples/geometry.tex"
+ , sourceLine = Pos 39
+ , sourceColumn = Pos 1
+ }
+ )
+ ( Marker "five_segment" )
+ ( Axiom
+ [ AsmLetNoun
+ ( NamedVar "a" :|
+ [ NamedVar "b"
+ , NamedVar "c"
+ , NamedVar "d"
+ , NamedVar "aprime"
+ , NamedVar "bprime"
+ , NamedVar "cprime"
+ , NamedVar "dprime"
+ ]
+ ) NounPhrase ( [] )
+ ( Noun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ ) []
+ ) ( Nothing ) ( [] ) ( Nothing )
+ ]
+ ( StmtConnected Implication
+ ( StmtConnected Conjunction
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "OFS" 8 )
+ ( ExprVar
+ ( NamedVar "a" ) :|
+ [ ExprVar
+ ( NamedVar "b" )
+ , ExprVar
+ ( NamedVar "c" )
+ , ExprVar
+ ( NamedVar "d" )
+ , ExprVar
+ ( NamedVar "aprime" )
+ , ExprVar
+ ( NamedVar "bprime" )
+ , ExprVar
+ ( NamedVar "cprime" )
+ , ExprVar
+ ( NamedVar "dprime" )
+ ]
+ )
+ )
+ )
+ ( StmtFormula
+ ( FormulaChain
+ ( ChainBase
+ ( ExprVar
+ ( NamedVar "a" ) :| []
+ ) Positive
+ ( RelationSymbol
+ ( Command "neq" )
+ )
+ ( ExprVar
+ ( NamedVar "b" ) :| []
+ )
+ )
+ )
+ )
+ )
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "c" ) :|
+ [ ExprVar
+ ( NamedVar "d" )
+ , ExprVar
+ ( NamedVar "cprime" )
+ , ExprVar
+ ( NamedVar "dprime" )
+ ]
+ )
+ )
+ )
+ )
+ )
+, BlockAxiom
+ ( SourcePos
+ { sourceName = "test/examples/geometry.tex"
+ , sourceLine = Pos 46
+ , sourceColumn = Pos 1
+ }
+ )
+ ( Marker "betw_id" )
+ ( Axiom
+ [ AsmLetNoun
+ ( NamedVar "a" :|
+ [ NamedVar "b" ]
+ ) NounPhrase ( [] )
+ ( Noun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ ) []
+ ) ( Nothing ) ( [] ) ( Nothing )
+ ]
+ ( StmtConnected Implication
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Betw" 3 )
+ ( ExprVar
+ ( NamedVar "a" ) :|
+ [ ExprVar
+ ( NamedVar "b" )
+ , ExprVar
+ ( NamedVar "a" )
+ ]
+ )
+ )
+ )
+ ( StmtFormula
+ ( FormulaChain
+ ( ChainBase
+ ( ExprVar
+ ( NamedVar "a" ) :| []
+ ) Positive
+ ( RelationSymbol
+ ( Symbol "=" )
+ )
+ ( ExprVar
+ ( NamedVar "b" ) :| []
+ )
+ )
+ )
+ )
+ )
+ )
+, BlockAxiom
+ ( SourcePos
+ { sourceName = "test/examples/geometry.tex"
+ , sourceLine = Pos 52
+ , sourceColumn = Pos 1
+ }
+ )
+ ( Marker "innerpasch" )
+ ( Axiom
+ [ AsmLetNoun
+ ( NamedVar "x" :|
+ [ NamedVar "y"
+ , NamedVar "z"
+ , NamedVar "u"
+ , NamedVar "v"
+ , NamedVar "w"
+ ]
+ ) NounPhrase ( [] )
+ ( Noun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ ) []
+ ) ( Nothing ) ( [] ) ( Nothing )
+ ]
+ ( StmtConnected Implication
+ ( StmtConnected Conjunction
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Betw" 3 )
+ ( ExprVar
+ ( NamedVar "x" ) :|
+ [ ExprVar
+ ( NamedVar "u" )
+ , ExprVar
+ ( NamedVar "z" )
+ ]
+ )
+ )
+ )
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Betw" 3 )
+ ( ExprVar
+ ( NamedVar "y" ) :|
+ [ ExprVar
+ ( NamedVar "v" )
+ , ExprVar
+ ( NamedVar "z" )
+ ]
+ )
+ )
+ )
+ )
+ ( StmtExists NounPhrase ( [] )
+ ( Noun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ ) []
+ )
+ (
+ [ NamedVar "w" ]
+ ) ( [] )
+ ( Just
+ ( StmtConnected Conjunction
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Betw" 3 )
+ ( ExprVar
+ ( NamedVar "u" ) :|
+ [ ExprVar
+ ( NamedVar "w" )
+ , ExprVar
+ ( NamedVar "y" )
+ ]
+ )
+ )
+ )
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Betw" 3 )
+ ( ExprVar
+ ( NamedVar "v" ) :|
+ [ ExprVar
+ ( NamedVar "w" )
+ , ExprVar
+ ( NamedVar "x" )
+ ]
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+, BlockAxiom
+ ( SourcePos
+ { sourceName = "test/examples/geometry.tex"
+ , sourceLine = Pos 66
+ , sourceColumn = Pos 1
+ }
+ )
+ ( Marker "upperdim" )
+ ( Axiom
+ [ AsmLetNoun
+ ( NamedVar "x" :|
+ [ NamedVar "y"
+ , NamedVar "z"
+ , NamedVar "u"
+ , NamedVar "v"
+ ]
+ ) NounPhrase ( [] )
+ ( Noun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ ) []
+ ) ( Nothing ) ( [] ) ( Nothing )
+ ]
+ ( StmtConnected Implication
+ ( StmtConnected Conjunction
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "x" ) :|
+ [ ExprVar
+ ( NamedVar "u" )
+ , ExprVar
+ ( NamedVar "x" )
+ , ExprVar
+ ( NamedVar "v" )
+ ]
+ )
+ )
+ )
+ ( StmtConnected Conjunction
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "y" ) :|
+ [ ExprVar
+ ( NamedVar "u" )
+ , ExprVar
+ ( NamedVar "y" )
+ , ExprVar
+ ( NamedVar "v" )
+ ]
+ )
+ )
+ )
+ ( StmtConnected Conjunction
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "z" ) :|
+ [ ExprVar
+ ( NamedVar "u" )
+ , ExprVar
+ ( NamedVar "z" )
+ , ExprVar
+ ( NamedVar "v" )
+ ]
+ )
+ )
+ )
+ ( StmtFormula
+ ( FormulaChain
+ ( ChainBase
+ ( ExprVar
+ ( NamedVar "u" ) :| []
+ ) Positive
+ ( RelationSymbol
+ ( Command "neq" )
+ )
+ ( ExprVar
+ ( NamedVar "v" ) :| []
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ ( StmtVerbPhrase
+ ( TermExpr
+ ( ExprVar
+ ( NamedVar "x" )
+ ) :| []
+ )
+ ( VPAdj
+ ( Adj
+ [ Just
+ ( Word "collinear" )
+ , Just
+ ( Word "with" )
+ , Nothing
+ , Just
+ ( Word "and" )
+ , Nothing
+ ]
+ [ TermExpr
+ ( ExprVar
+ ( NamedVar "y" )
+ )
+ , TermExpr
+ ( ExprVar
+ ( NamedVar "z" )
+ )
+ ] :| []
+ )
+ )
+ )
+ )
+ )
+, BlockLemma
+ ( SourcePos
+ { sourceName = "test/examples/geometry.tex"
+ , sourceLine = Pos 82
+ , sourceColumn = Pos 1
+ }
+ )
+ ( Marker "cong_refl" )
+ ( Lemma
+ [ AsmLetNoun
+ ( NamedVar "a" :|
+ [ NamedVar "b" ]
+ ) NounPhrase ( [] )
+ ( Noun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ ) []
+ ) ( Nothing ) ( [] ) ( Nothing )
+ ]
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "a" ) :|
+ [ ExprVar
+ ( NamedVar "b" )
+ , ExprVar
+ ( NamedVar "a" )
+ , ExprVar
+ ( NamedVar "b" )
+ ]
+ )
+ )
+ )
+ )
+, BlockLemma
+ ( SourcePos
+ { sourceName = "test/examples/geometry.tex"
+ , sourceLine = Pos 88
+ , sourceColumn = Pos 1
+ }
+ )
+ ( Marker "cong_sym" )
+ ( Lemma
+ [ AsmLetNoun
+ ( NamedVar "a" :|
+ [ NamedVar "b"
+ , NamedVar "c"
+ , NamedVar "d"
+ ]
+ ) NounPhrase ( [] )
+ ( Noun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ ) []
+ ) ( Nothing ) ( [] ) ( Nothing )
+ , AsmSuppose
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "a" ) :|
+ [ ExprVar
+ ( NamedVar "b" )
+ , ExprVar
+ ( NamedVar "c" )
+ , ExprVar
+ ( NamedVar "d" )
+ ]
+ )
+ )
+ )
+ ]
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "c" ) :|
+ [ ExprVar
+ ( NamedVar "d" )
+ , ExprVar
+ ( NamedVar "a" )
+ , ExprVar
+ ( NamedVar "b" )
+ ]
+ )
+ )
+ )
+ )
+, BlockLemma
+ ( SourcePos
+ { sourceName = "test/examples/geometry.tex"
+ , sourceLine = Pos 95
+ , sourceColumn = Pos 1
+ }
+ )
+ ( Marker "cong_transitive" )
+ ( Lemma
+ [ AsmLetNoun
+ ( NamedVar "a" :|
+ [ NamedVar "b"
+ , NamedVar "c"
+ , NamedVar "d"
+ , NamedVar "e"
+ , NamedVar "f"
+ ]
+ ) NounPhrase ( [] )
+ ( Noun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ ) []
+ ) ( Nothing ) ( [] ) ( Nothing )
+ ]
+ ( StmtConnected Implication
+ ( StmtConnected Conjunction
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "a" ) :|
+ [ ExprVar
+ ( NamedVar "b" )
+ , ExprVar
+ ( NamedVar "c" )
+ , ExprVar
+ ( NamedVar "d" )
+ ]
+ )
+ )
+ )
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "c" ) :|
+ [ ExprVar
+ ( NamedVar "d" )
+ , ExprVar
+ ( NamedVar "e" )
+ , ExprVar
+ ( NamedVar "f" )
+ ]
+ )
+ )
+ )
+ )
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "a" ) :|
+ [ ExprVar
+ ( NamedVar "b" )
+ , ExprVar
+ ( NamedVar "e" )
+ , ExprVar
+ ( NamedVar "f" )
+ ]
+ )
+ )
+ )
+ )
+ )
+, BlockLemma
+ ( SourcePos
+ { sourceName = "test/examples/geometry.tex"
+ , sourceLine = Pos 102
+ , sourceColumn = Pos 1
+ }
+ )
+ ( Marker "cong_shuffle_left" )
+ ( Lemma
+ [ AsmLetNoun
+ ( NamedVar "a" :|
+ [ NamedVar "b"
+ , NamedVar "c"
+ , NamedVar "d"
+ ]
+ ) NounPhrase ( [] )
+ ( Noun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ ) []
+ ) ( Nothing ) ( [] ) ( Nothing )
+ ]
+ ( StmtConnected Implication
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "a" ) :|
+ [ ExprVar
+ ( NamedVar "b" )
+ , ExprVar
+ ( NamedVar "c" )
+ , ExprVar
+ ( NamedVar "d" )
+ ]
+ )
+ )
+ )
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "b" ) :|
+ [ ExprVar
+ ( NamedVar "a" )
+ , ExprVar
+ ( NamedVar "c" )
+ , ExprVar
+ ( NamedVar "d" )
+ ]
+ )
+ )
+ )
+ )
+ )
+, BlockLemma
+ ( SourcePos
+ { sourceName = "test/examples/geometry.tex"
+ , sourceLine = Pos 109
+ , sourceColumn = Pos 1
+ }
+ )
+ ( Marker "cong_shuffle_right" )
+ ( Lemma
+ [ AsmLetNoun
+ ( NamedVar "a" :|
+ [ NamedVar "b"
+ , NamedVar "c"
+ , NamedVar "d"
+ ]
+ ) NounPhrase ( [] )
+ ( Noun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ ) []
+ ) ( Nothing ) ( [] ) ( Nothing )
+ ]
+ ( StmtConnected Implication
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "a" ) :|
+ [ ExprVar
+ ( NamedVar "b" )
+ , ExprVar
+ ( NamedVar "c" )
+ , ExprVar
+ ( NamedVar "d" )
+ ]
+ )
+ )
+ )
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "b" ) :|
+ [ ExprVar
+ ( NamedVar "a" )
+ , ExprVar
+ ( NamedVar "d" )
+ , ExprVar
+ ( NamedVar "c" )
+ ]
+ )
+ )
+ )
+ )
+ )
+, BlockLemma
+ ( SourcePos
+ { sourceName = "test/examples/geometry.tex"
+ , sourceLine = Pos 116
+ , sourceColumn = Pos 1
+ }
+ )
+ ( Marker "cong_zero" )
+ ( Lemma
+ [ AsmLetNoun
+ ( NamedVar "a" :|
+ [ NamedVar "b" ]
+ ) NounPhrase ( [] )
+ ( Noun
+ ( SgPl
+ { sg =
+ [ Just
+ ( Word "point" )
+ ]
+ , pl =
+ [ Just
+ ( Word "points" )
+ ]
+ }
+ ) []
+ ) ( Nothing ) ( [] ) ( Nothing )
+ ]
+ ( StmtFormula
+ ( FormulaPredicate
+ ( PrefixPredicate "Cong" 4 )
+ ( ExprVar
+ ( NamedVar "a" ) :|
+ [ ExprVar
+ ( NamedVar "a" )
+ , ExprVar
+ ( NamedVar "b" )
+ , ExprVar
+ ( NamedVar "b" )
+ ]
+ )
+ )
+ )
+ )
+] \ No newline at end of file
diff --git a/test/golden/geometry/scanning.golden b/test/golden/geometry/scanning.golden
new file mode 100644
index 0000000..c041c1a
--- /dev/null
+++ b/test/golden/geometry/scanning.golden
@@ -0,0 +1,15 @@
+[ ScanAdj
+ [ Just
+ ( Word "collinear" )
+ , Just
+ ( Word "with" )
+ , Nothing
+ , Just
+ ( Word "and" )
+ , Nothing
+ ]
+ ( Marker "collinear" )
+, ScanPrefixPredicate
+ ( PrefixPredicate "OFS" 8 )
+ ( Marker "ofs" )
+] \ No newline at end of file
diff --git a/test/golden/geometry/tokenizing.golden b/test/golden/geometry/tokenizing.golden
new file mode 100644
index 0000000..ab899fe
--- /dev/null
+++ b/test/golden/geometry/tokenizing.golden
@@ -0,0 +1,975 @@
+[ BeginEnv "definition"
+, Label "collinear"
+, BeginEnv "math"
+, Variable "a"
+, EndEnv "math"
+, Word "is"
+, Word "collinear"
+, Word "with"
+, BeginEnv "math"
+, Variable "b"
+, EndEnv "math"
+, Word "and"
+, BeginEnv "math"
+, Variable "c"
+, EndEnv "math"
+, Word "iff"
+, BeginEnv "math"
+, Command "Betw"
+, InvisibleBraceL
+, Variable "a"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "b"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "c"
+, InvisibleBraceR
+, EndEnv "math"
+, Word "or"
+, BeginEnv "math"
+, Command "Betw"
+, InvisibleBraceL
+, Variable "b"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "c"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "a"
+, InvisibleBraceR
+, EndEnv "math"
+, Word "or"
+, BeginEnv "math"
+, Command "Betw"
+, InvisibleBraceL
+, Variable "c"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "a"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "b"
+, InvisibleBraceR
+, EndEnv "math"
+, Symbol "."
+, EndEnv "definition"
+, BeginEnv "axiom"
+, BracketL
+, Word "reflexivity"
+, Word "of"
+, Word "congruence"
+, BracketR
+, Label "cong_refl_swap"
+, Word "let"
+, BeginEnv "math"
+, Variable "a"
+, Symbol ","
+, Variable "b"
+, EndEnv "math"
+, Word "be"
+, Word "points"
+, Symbol "."
+, Word "then"
+, BeginEnv "math"
+, Command "Cong"
+, InvisibleBraceL
+, Variable "a"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "b"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "b"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "a"
+, InvisibleBraceR
+, EndEnv "math"
+, Symbol "."
+, EndEnv "axiom"
+, BeginEnv "axiom"
+, BracketL
+, Word "pseudotransitivity"
+, Word "of"
+, Word "congruence"
+, BracketR
+, Label "cong_pseudotransitive"
+, Word "let"
+, BeginEnv "math"
+, Variable "a"
+, Symbol ","
+, Variable "b"
+, Symbol ","
+, Variable "c"
+, Symbol ","
+, Variable "d"
+, EndEnv "math"
+, Word "be"
+, Word "points"
+, Symbol "."
+, Word "if"
+, BeginEnv "math"
+, Command "Cong"
+, InvisibleBraceL
+, Variable "c"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "d"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "a"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "b"
+, InvisibleBraceR
+, EndEnv "math"
+, Word "and"
+, BeginEnv "math"
+, Command "Cong"
+, InvisibleBraceL
+, Variable "c"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "d"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "e"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "f"
+, InvisibleBraceR
+, EndEnv "math"
+, Word "then"
+, BeginEnv "math"
+, Command "Cong"
+, InvisibleBraceL
+, Variable "a"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "b"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "e"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "f"
+, InvisibleBraceR
+, EndEnv "math"
+, Symbol "."
+, EndEnv "axiom"
+, BeginEnv "axiom"
+, BracketL
+, Word "identity"
+, Word "of"
+, Word "congruence"
+, BracketR
+, Label "cong_id"
+, Word "let"
+, BeginEnv "math"
+, Variable "a"
+, Symbol ","
+, Variable "b"
+, Symbol ","
+, Variable "c"
+, EndEnv "math"
+, Word "be"
+, Word "points"
+, Symbol "."
+, Word "if"
+, BeginEnv "math"
+, Command "Cong"
+, InvisibleBraceL
+, Variable "a"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "b"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "c"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "c"
+, InvisibleBraceR
+, EndEnv "math"
+, Word "then"
+, BeginEnv "math"
+, Variable "a"
+, Symbol "="
+, Variable "b"
+, EndEnv "math"
+, Symbol "."
+, EndEnv "axiom"
+, BeginEnv "axiom"
+, BracketL
+, Word "segment"
+, Word "construction"
+, BracketR
+, Label "segment_construction"
+, Word "there"
+, Word "exists"
+, Word "a"
+, Word "point"
+, BeginEnv "math"
+, Variable "c"
+, EndEnv "math"
+, Word "such"
+, Word "that"
+, BeginEnv "math"
+, Command "Betw"
+, InvisibleBraceL
+, Variable "a"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "b"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "c"
+, InvisibleBraceR
+, EndEnv "math"
+, Word "and"
+, BeginEnv "math"
+, Command "Cong"
+, InvisibleBraceL
+, Variable "b"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "c"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "d"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "e"
+, InvisibleBraceR
+, EndEnv "math"
+, Symbol "."
+, EndEnv "axiom"
+, BeginEnv "definition"
+, Label "ofs"
+, Word "let"
+, BeginEnv "math"
+, Variable "x"
+, Symbol ","
+, Variable "y"
+, Symbol ","
+, Variable "z"
+, Symbol ","
+, Variable "r"
+, Symbol ","
+, Variable "u"
+, Symbol ","
+, Variable "v"
+, Symbol ","
+, Variable "w"
+, Symbol ","
+, Variable "p"
+, EndEnv "math"
+, Word "be"
+, Word "points"
+, Symbol "."
+, BeginEnv "math"
+, Command "OFS"
+, InvisibleBraceL
+, Variable "x"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "y"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "z"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "r"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "u"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "v"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "w"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "p"
+, InvisibleBraceR
+, EndEnv "math"
+, Word "if"
+, Word "and"
+, Word "only"
+, Word "if"
+, BeginEnv "math"
+, Command "Betw"
+, InvisibleBraceL
+, Variable "x"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "y"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "z"
+, InvisibleBraceR
+, Command "land"
+, Command "Betw"
+, InvisibleBraceL
+, Variable "u"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "v"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "w"
+, InvisibleBraceR
+, EndEnv "math"
+, Word "and"
+, BeginEnv "math"
+, Command "Cong"
+, InvisibleBraceL
+, Variable "x"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "y"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "u"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "v"
+, InvisibleBraceR
+, Command "land"
+, Command "Cong"
+, InvisibleBraceL
+, Variable "y"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "z"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "v"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "w"
+, InvisibleBraceR
+, Command "land"
+, Command "Cong"
+, InvisibleBraceL
+, Variable "x"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "r"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "u"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "p"
+, InvisibleBraceR
+, Command "land"
+, Command "Cong"
+, InvisibleBraceL
+, Variable "y"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "r"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "v"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "p"
+, InvisibleBraceR
+, EndEnv "math"
+, Symbol "."
+, EndEnv "definition"
+, BeginEnv "axiom"
+, BracketL
+, Word "five"
+, Word "segment"
+, Word "axiom"
+, BracketR
+, Label "five_segment"
+, Word "let"
+, BeginEnv "math"
+, Variable "a"
+, Symbol ","
+, Variable "b"
+, Symbol ","
+, Variable "c"
+, Symbol ","
+, Variable "d"
+, Symbol ","
+, Variable "aprime"
+, Symbol ","
+, Variable "bprime"
+, Symbol ","
+, Variable "cprime"
+, Symbol ","
+, Variable "dprime"
+, EndEnv "math"
+, Word "be"
+, Word "points"
+, Symbol "."
+, Word "if"
+, BeginEnv "math"
+, Command "OFS"
+, InvisibleBraceL
+, Variable "a"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "b"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "c"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "d"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "aprime"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "bprime"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "cprime"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "dprime"
+, InvisibleBraceR
+, EndEnv "math"
+, Word "and"
+, BeginEnv "math"
+, Variable "a"
+, Command "neq"
+, Variable "b"
+, EndEnv "math"
+, Word "then"
+, BeginEnv "math"
+, Command "Cong"
+, InvisibleBraceL
+, Variable "c"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "d"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "cprime"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "dprime"
+, InvisibleBraceR
+, EndEnv "math"
+, Symbol "."
+, EndEnv "axiom"
+, BeginEnv "axiom"
+, BracketL
+, Word "identity"
+, Word "of"
+, Word "betweenness"
+, BracketR
+, Label "betw_id"
+, Word "let"
+, BeginEnv "math"
+, Variable "a"
+, Symbol ","
+, Variable "b"
+, EndEnv "math"
+, Word "be"
+, Word "points"
+, Symbol "."
+, Word "if"
+, BeginEnv "math"
+, Command "Betw"
+, InvisibleBraceL
+, Variable "a"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "b"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "a"
+, InvisibleBraceR
+, EndEnv "math"
+, Word "then"
+, BeginEnv "math"
+, Variable "a"
+, Symbol "="
+, Variable "b"
+, EndEnv "math"
+, Symbol "."
+, EndEnv "axiom"
+, BeginEnv "axiom"
+, BracketL
+, Word "inner"
+, Word "pasch"
+, BracketR
+, Label "innerpasch"
+, Word "let"
+, BeginEnv "math"
+, Variable "x"
+, Symbol ","
+, Variable "y"
+, Symbol ","
+, Variable "z"
+, Symbol ","
+, Variable "u"
+, Symbol ","
+, Variable "v"
+, Symbol ","
+, Variable "w"
+, EndEnv "math"
+, Word "be"
+, Word "points"
+, Symbol "."
+, Word "if"
+, BeginEnv "math"
+, Command "Betw"
+, InvisibleBraceL
+, Variable "x"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "u"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "z"
+, InvisibleBraceR
+, EndEnv "math"
+, Word "and"
+, BeginEnv "math"
+, Command "Betw"
+, InvisibleBraceL
+, Variable "y"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "v"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "z"
+, InvisibleBraceR
+, EndEnv "math"
+, Word "then"
+, Word "there"
+, Word "exists"
+, Word "a"
+, Word "point"
+, BeginEnv "math"
+, Variable "w"
+, EndEnv "math"
+, Word "such"
+, Word "that"
+, BeginEnv "math"
+, Command "Betw"
+, InvisibleBraceL
+, Variable "u"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "w"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "y"
+, InvisibleBraceR
+, EndEnv "math"
+, Word "and"
+, BeginEnv "math"
+, Command "Betw"
+, InvisibleBraceL
+, Variable "v"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "w"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "x"
+, InvisibleBraceR
+, EndEnv "math"
+, Symbol "."
+, EndEnv "axiom"
+, BeginEnv "axiom"
+, BracketL
+, Word "upper"
+, Word "dimension"
+, BracketR
+, Label "upperdim"
+, Word "let"
+, BeginEnv "math"
+, Variable "x"
+, Symbol ","
+, Variable "y"
+, Symbol ","
+, Variable "z"
+, Symbol ","
+, Variable "u"
+, Symbol ","
+, Variable "v"
+, EndEnv "math"
+, Word "be"
+, Word "points"
+, Symbol "."
+, Word "if"
+, BeginEnv "math"
+, Command "Cong"
+, InvisibleBraceL
+, Variable "x"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "u"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "x"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "v"
+, InvisibleBraceR
+, EndEnv "math"
+, Word "and"
+, BeginEnv "math"
+, Command "Cong"
+, InvisibleBraceL
+, Variable "y"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "u"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "y"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "v"
+, InvisibleBraceR
+, EndEnv "math"
+, Word "and"
+, BeginEnv "math"
+, Command "Cong"
+, InvisibleBraceL
+, Variable "z"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "u"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "z"
+, InvisibleBraceR
+, InvisibleBraceL
+, Variable "v"
+, InvisibleBraceR
+, EndEnv "math"
+, Word "and"
+, BeginEnv "math"
+, Variable "u"
+, Command "neq"
+, Variable "v"
+, EndEnv "math"
+, Word "then"
+, BeginEnv "math"
+, Variable "x"
+, EndEnv "math"
+, Word "is"
+, Word "collinear"
+, Word "with"
+, BeginEnv "math"
+, Variable "y"
+, EndEnv "math"
+, Word "and"
+, BeginEnv "math"
+, Variable "z"
+, EndEnv "math"
+, Symbol "."
+, EndEnv "axiom"
+, BeginEnv "lemma"
+, BracketL
+, Word "reflexivity"
+, Word "of"
+, Word "congruence"
+, BracketR
+, Label "cong_refl"
+, Word "let"
+, BeginEnv "math"
+, Variable "a"
+, Symbol ","
+, Variable "b"
+, EndEnv "math"
+, Word "be"
+, Word "points"
+, Symbol "."
+, Word "then"
+, BeginEnv "math"
+, Command "Cong"
+, InvisibleBraceL
+, Variable "a"
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+] \ No newline at end of file
diff --git a/test/golden/geometry/verification.golden b/test/golden/geometry/verification.golden
new file mode 100644
index 0000000..69b9873
--- /dev/null
+++ b/test/golden/geometry/verification.golden
@@ -0,0 +1 @@
+VerificationSuccess \ No newline at end of file
generated by cgit v1.2.3 (git 2.39.1) at 2025-12-06 09:38:00 +0000