$ mv miz/mizshare/mml/mml.lar miz/mizshare/mml/mml.lar.bak
$ echo "tlarus" >> miz/mizshare/mml/mml.lar
$ cat >> tlarus.miz << EOF
environ
begin
scheme SMyT { eqnative[object,object], betS[object,object,object],
cong[object,object,object,object], out[object,object,object],
betScong0[object,object,object,object,object],
betSbetS3[object,object,object,object] }:
for A, B, E being object holds betS[A,B,E] & A <> B implies out[A,B,E]
provided
lemmaextension: for A, B, P, Q being object holds A <> B & P <> Q implies ex
X being object st betS[A,B,X] & cong[B,X,P,Q] and
axiombetweennesssymmetry: for A, B, C being object holds betS[A,B,C] implies
betS[C,B,A] and
axiominnertransitivity: for A, B, C, D being object holds betS[A,B,D] &
betS[B,C,D] implies betS[A,B,C] and
defray: for A, B, C being object holds out[A,B,C] implies ex X being object
st betS[X,A,C] & betS[X,A,B] and
defray2: for A, B, C, X being object holds betS[X,A,C] & betS[X,A,B] implies
out[A,B,C] and
lemma37b: for A, B, C, D being object holds betS[A,B,C] & betS[B,C,D] implies
betS[A,B,D]
proof
let a, b, c be object;
assume H0: betS[a,b,c];
assume H1: a <> b;
H2: b <> a by H1;
consider c34 being object such that H3: betS[b,a,c34] & cong[a,c34,b,a] by
H2,H2,lemmaextension;
H4: c34 = c34;
H5: betS[b,a,c34] by H3;
H6: betS[c34,a,b] by H5,axiombetweennesssymmetry;
H7: betS[c34,a,c] by H6,H0,lemma37b;
H8: out[a,b,c] by H7,H6,defray2;
H9: out[a,b,c] by H4,H8;
thus thesis by H9;
end;
EOF
$ cargo run --release
Finished release [optimized + debuginfo] target(s) in 0.09s
Running `target/release/miz-rs`
0: tlarus in 0.004s
success: 9
$
Wow, this is not the kind of proof I was expecting to verify, but it's good to hear that it's working as intended. I'll close this issue, but please open another one if you find something that doesn't work.
Good news,
Larus can export a file in the Mizar format: (see https://github.com/janicicpredrag/Larus) mizar-rs can correctly check this mizar file.
Test (Larus export: ./proofs/PROOF030_lemma_ray4_3pQF_BV.miz" from https://github.com/janicicpredrag/Larus/blob/master/benchmarks/tptp-problems/euclid-native-eq/030_lemma_ray4_3.p) rename tlarus.miz: