diff options
| author | adelon <22380201+adelon@users.noreply.github.com> | 2024-02-10 02:22:14 +0100 |
|---|---|---|
| committer | adelon <22380201+adelon@users.noreply.github.com> | 2024-02-10 02:22:14 +0100 |
| commit | 442d732696ad431b84f6e5c72b6ee785be4fd968 (patch) | |
| tree | b476f395e7e91d67bacb6758bc84914b8711593f /test/golden/geometry/encoding tasks.golden | |
Initial commit
Diffstat (limited to 'test/golden/geometry/encoding tasks.golden')
| -rw-r--r-- | test/golden/geometry/encoding tasks.golden | 109 |
1 files changed, 109 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)).
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