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View Code? Open in Web Editor NEW🎼 Translate answer set programs to first-order theorem prover language
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License: MIT License
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Unexpected failure to parse Vampire output
Sometimes, anthem fails to parse Vampire’s output.
Finished release [optimized] target(s) in 0.02s
Running `target/release/anthem vprog examples/example-exact-cover.lp examples/example-exact-cover.spec`
Started verification of specification from translated program
Presupposed assumption: n >= 0
Presupposed assumption: forall X1 (exists X2 s(X2, X1) -> exists N (X1 = N and N >= 1 and N <= n))
Presupposed completed definition of covered/1: forall X (covered(X) <-> exists N (in_cover(N) and s(X, N)))
Presupposed completed definition of in_cover/1: forall X (in_cover(X) <-> in_cover(X) and exists N (1 <= N and N <= n and X = N))
Presupposed integrity constraint: forall N1, N2, X not (N1 != N2 and in_cover(N1) and in_cover(N2) and s(X, N1) and s(X, N2))
Presupposed integrity constraint: forall X, N not (s(X, N) and not covered(X))
Verified spec: forall X (in_cover(X) -> exists N (X = N and N >= 1 and N <= n)) in 0.003 seconds
ERROR anthem::commands::verify_program > could not verify program: could not parse Vampire output
==== stdout ===========================================================
% (193365)lrs+1011_2:1_add=large:afr=on:afp=4000:afq=1.1:amm=off:anc=none:cond=on:fsr=off:gs=on:irw=on:nm=64:nwc=1:sas=z3:stl=30:sos=on:sp=reverse_arity:thf=on:urr=on:updr=off_2 on
% (193366)lrs+1_2:3_afr=on:afp=1000:afq=1.1:amm=sco:anc=none:fsr=off:fde=none:gs=on:gsaa=full_model:gsem=on:lma=on:nm=64:nwc=1.3:sas=z3:stl=30:sac=on:tha=off:uwa=one_side_interpreted:updr=off_2 on
% (193367)lrs+1010_4:1_aac=none:add=off:afp=40000:afq=1.0:amm=sco:anc=none:bd=off:cond=on:gs=on:gsem=on:irw=on:nm=0:nwc=2.5:sas=z3:stl=30:sos=theory:sp=reverse_arity:updr=off_2 on
% (193368)dis+10_5_add=off:afp=4000:afq=1.1:anc=none:cond=fast:ep=RSTC:fsr=off:gs=on:gsem=on:lwlo=on:nm=64:nwc=1:sp=reverse_arity:thi=all_3 on
% (193369)dis+4_3:2_afr=on:afp=1000:afq=1.1:amm=sco:bs=unit_only:cond=fast:fsr=off:fde=none:gsp=input_only:gs=on:gsem=off:inw=on:lcm=reverse:nwc=1:sas=z3:sos=all:sp=reverse_arity:tha=off:updr=off_4 on
% (193370)dis+10_5_add=large:amm=sco:anc=none:fsr=off:gs=on:irw=on:lma=on:nm=64:nwc=1:sas=z3:sos=all:tha=off:thf=on_2 on
% (193371)dis+11_4_afp=100000:afq=1.1:anc=none:cond=on:gs=on:gsaa=full_model:nm=64:nwc=1:sac=on:sp=reverse_arity:thi=all_2 on
% (193372)dis+11_3_add=off:afp=10000:afq=2.0:amm=sco:anc=none:ep=RST:gs=on:gsaa=from_current:gsem=on:inw=on:nm=64:nwc=1:sd=10:ss=axioms:st=5.0:sos=all:tha=off:updr=off:uhcvi=on_59 on
% (193369)Refutation found. Thanks to Tanya!
% SZS status Theorem for
% SZS output start Proof for
tff(type_def_5, type, object: $tType).
tff(func_def_0, type, f__integer__: $int > object).
tff(func_def_1, type, f__symbolic__: $i > object).
tff(func_def_2, type, c__infimum__: object).
tff(func_def_3, type, c__supremum__: object).
tff(func_def_4, type, n: $int).
tff(func_def_7, type, sK0: object).
tff(func_def_8, type, sK1: object).
tff(func_def_9, type, sK2: object > $int).
tff(func_def_10, type, sK3: object > $int).
tff(func_def_11, type, sK4: object > $int).
tff(func_def_12, type, sK5: object > $i).
tff(func_def_13, type, sK6: object > $int).
tff(func_def_14, type, sK7: object > $int).
tff(pred_def_1, type, p__is_integer__: object > $o).
tff(pred_def_2, type, p__is_symbolic__: object > $o).
tff(pred_def_3, type, p__less_equal__: (object * object) > $o).
tff(pred_def_4, type, p__less__: (object * object) > $o).
tff(pred_def_5, type, p__greater_equal__: (object * object) > $o).
tff(pred_def_6, type, p__greater__: (object * object) > $o).
tff(pred_def_8, type, covered: object > $o).
tff(pred_def_9, type, in_cover: object > $o).
tff(pred_def_10, type, s: (object * object) > $o).
tff(f1,axiom,(
! [X0 : object] : (p__is_integer__(X0) <=> ? [X1 : $int] : f__integer__(X1) = X0)),
file(unknown,axiom)).
tff(f6,axiom,(
! [X4 : $int,X5 : $int] : (p__less_equal__(f__integer__(X4),f__integer__(X5)) <=> $lesseq(X4,X5))),
file(unknown,axiom)).
tff(f10,axiom,(
! [X2 : object,X3 : object] : (p__less__(X2,X3) <=> (X2 != X3 & p__less_equal__(X2,X3)))),
file(unknown,axiom)).
tff(f13,axiom,(
! [X1 : $int] : p__less__(c__infimum__,f__integer__(X1))),
file(unknown,axiom)).
tff(f17,axiom,(
! [X2 : object] : (? [X3 : object] : s(X3,X2) => ? [X1 : $int] : ($lesseq(X1,n) & $greatereq(X1,1) & f__integer__(X1) = X2))),
file(unknown,statement_2)).
tff(f18,axiom,(
! [X0 : object] : (covered(X0) <=> ? [X1 : $int] : (s(X0,f__integer__(X1)) & in_cover(f__integer__(X1))))),
file(unknown,completed_definition_covered_1)).
tff(f21,axiom,(
! [X0 : object,X1 : $int] : ~(~covered(X0) & s(X0,f__integer__(X1)))),
file(unknown,integrity_constraint)).
tff(f23,conjecture,(
! [X2 : object] : (? [X3 : object] : s(X2,X3) => ? [X8 : object] : (in_cover(X8) & s(X2,X8)))),
file(unknown,statement_2)).
tff(f24,negated_conjecture,(
~! [X2 : object] : (? [X3 : object] : s(X2,X3) => ? [X8 : object] : (in_cover(X8) & s(X2,X8)))),
inference(negated_conjecture,[],[f23])).
tff(f27,plain,(
! [X2 : object] : (? [X3 : object] : s(X3,X2) => ? [X1 : $int] : (~$less(n,X1) & ~$less(X1,1) & f__integer__(X1) = X2))),
inference(evaluation,[],[f17])).
tff(f29,plain,(
! [X4 : $int,X5 : $int] : (p__less_equal__(f__integer__(X4),f__integer__(X5)) <=> ~$less(X5,X4))),
inference(evaluation,[],[f6])).
tff(f30,plain,(
~! [X0 : object] : (? [X1 : object] : s(X0,X1) => ? [X2 : object] : (in_cover(X2) & s(X0,X2)))),
inference(rectify,[],[f24])).
tff(f31,plain,(
! [X0 : $int] : p__less__(c__infimum__,f__integer__(X0))),
inference(rectify,[],[f13])).
tff(f33,plain,(
! [X0 : object] : (? [X1 : object] : s(X1,X0) => ? [X2 : $int] : (~$less(n,X2) & ~$less(X2,1) & f__integer__(X2) = X0))),
inference(rectify,[],[f27])).
tff(f40,plain,(
! [X0 : object,X1 : object] : (p__less__(X0,X1) <=> (X0 != X1 & p__less_equal__(X0,X1)))),
inference(rectify,[],[f10])).
tff(f43,plain,(
! [X0 : $int,X1 : $int] : (p__less_equal__(f__integer__(X0),f__integer__(X1)) <=> ~$less(X1,X0))),
inference(rectify,[],[f29])).
tff(f46,plain,(
? [X0 : object] : (! [X2 : object] : (~in_cover(X2) | ~s(X0,X2)) & ? [X1 : object] : s(X0,X1))),
inference(ennf_transformation,[],[f30])).
tff(f48,plain,(
! [X0 : object] : (? [X2 : $int] : (~$less(n,X2) & ~$less(X2,1) & f__integer__(X2) = X0) | ! [X1 : object] : ~s(X1,X0))),
inference(ennf_transformation,[],[f33])).
tff(f51,plain,(
! [X0 : object,X1 : $int] : (covered(X0) | ~s(X0,f__integer__(X1)))),
inference(ennf_transformation,[],[f21])).
tff(f55,plain,(
? [X0 : object] : (! [X1 : object] : (~in_cover(X1) | ~s(X0,X1)) & ? [X2 : object] : s(X0,X2))),
inference(rectify,[],[f46])).
tff(f56,plain,(
? [X0 : object] : (! [X1 : object] : (~in_cover(X1) | ~s(X0,X1)) & ? [X2 : object] : s(X0,X2)) => (! [X1 : object] : (~in_cover(X1) | ~s(sK0,X1)) & ? [X2 : object] : s(sK0,X2))),
introduced(choice_axiom,[])).
tff(f57,plain,(
( ! [X0:object] : (? [X2 : object] : s(X0,X2) => s(X0,sK1)) )),
introduced(choice_axiom,[])).
tff(f58,plain,(
! [X1 : object] : (~in_cover(X1) | ~s(sK0,X1)) & s(sK0,sK1)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f55,f57,f56])).
tff(f61,plain,(
! [X0 : object] : (? [X1 : $int] : (~$less(n,X1) & ~$less(X1,1) & f__integer__(X1) = X0) | ! [X2 : object] : ~s(X2,X0))),
inference(rectify,[],[f48])).
tff(f62,plain,(
! [X0 : object] : (? [X1 : $int] : (~$less(n,X1) & ~$less(X1,1) & f__integer__(X1) = X0) => (~$less(n,sK3(X0)) & ~$less(sK3(X0),1) & f__integer__(sK3(X0)) = X0))),
introduced(choice_axiom,[])).
tff(f63,plain,(
! [X0 : object] : ((~$less(n,sK3(X0)) & ~$less(sK3(X0),1) & f__integer__(sK3(X0)) = X0) | ! [X2 : object] : ~s(X2,X0))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f61,f62])).
tff(f73,plain,(
! [X0 : object] : ((p__is_integer__(X0) | ! [X1 : $int] : f__integer__(X1) != X0) & (? [X1 : $int] : f__integer__(X1) = X0 | ~p__is_integer__(X0)))),
inference(nnf_transformation,[],[f1])).
tff(f74,plain,(
! [X0 : object] : ((p__is_integer__(X0) | ! [X1 : $int] : f__integer__(X1) != X0) & (? [X2 : $int] : f__integer__(X2) = X0 | ~p__is_integer__(X0)))),
inference(rectify,[],[f73])).
tff(f75,plain,(
! [X0 : object] : (? [X2 : $int] : f__integer__(X2) = X0 => f__integer__(sK6(X0)) = X0)),
introduced(choice_axiom,[])).
tff(f76,plain,(
! [X0 : object] : ((p__is_integer__(X0) | ! [X1 : $int] : f__integer__(X1) != X0) & (f__integer__(sK6(X0)) = X0 | ~p__is_integer__(X0)))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f74,f75])).
tff(f77,plain,(
! [X0 : object] : ((covered(X0) | ! [X1 : $int] : (~s(X0,f__integer__(X1)) | ~in_cover(f__integer__(X1)))) & (? [X1 : $int] : (s(X0,f__integer__(X1)) & in_cover(f__integer__(X1))) | ~covered(X0)))),
inference(nnf_transformation,[],[f18])).
tff(f78,plain,(
! [X0 : object] : ((covered(X0) | ! [X1 : $int] : (~s(X0,f__integer__(X1)) | ~in_cover(f__integer__(X1)))) & (? [X2 : $int] : (s(X0,f__integer__(X2)) & in_cover(f__integer__(X2))) | ~covered(X0)))),
inference(rectify,[],[f77])).
tff(f79,plain,(
! [X0 : object] : (? [X2 : $int] : (s(X0,f__integer__(X2)) & in_cover(f__integer__(X2))) => (s(X0,f__integer__(sK7(X0))) & in_cover(f__integer__(sK7(X0)))))),
introduced(choice_axiom,[])).
tff(f80,plain,(
! [X0 : object] : ((covered(X0) | ! [X1 : $int] : (~s(X0,f__integer__(X1)) | ~in_cover(f__integer__(X1)))) & ((s(X0,f__integer__(sK7(X0))) & in_cover(f__integer__(sK7(X0)))) | ~covered(X0)))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f78,f79])).
tff(f84,plain,(
! [X0 : object,X1 : object] : ((p__less__(X0,X1) | (X0 = X1 | ~p__less_equal__(X0,X1))) & ((X0 != X1 & p__less_equal__(X0,X1)) | ~p__less__(X0,X1)))),
inference(nnf_transformation,[],[f40])).
tff(f85,plain,(
! [X0 : object,X1 : object] : ((p__less__(X0,X1) | X0 = X1 | ~p__less_equal__(X0,X1)) & ((X0 != X1 & p__less_equal__(X0,X1)) | ~p__less__(X0,X1)))),
inference(flattening,[],[f84])).
tff(f88,plain,(
! [X0 : $int,X1 : $int] : ((p__less_equal__(f__integer__(X0),f__integer__(X1)) | $less(X1,X0)) & (~$less(X1,X0) | ~p__less_equal__(f__integer__(X0),f__integer__(X1))))),
inference(nnf_transformation,[],[f43])).
tff(f89,plain,(
s(sK0,sK1)),
inference(cnf_transformation,[],[f58])).
tff(f90,plain,(
( ! [X1:object] : (~s(sK0,X1) | ~in_cover(X1)) )),
inference(cnf_transformation,[],[f58])).
tff(f92,plain,(
( ! [X0:$int] : (p__less__(c__infimum__,f__integer__(X0))) )),
inference(cnf_transformation,[],[f31])).
tff(f98,plain,(
( ! [X2:object,X0:object] : (f__integer__(sK3(X0)) = X0 | ~s(X2,X0)) )),
inference(cnf_transformation,[],[f63])).
tff(f99,plain,(
( ! [X2:object,X0:object] : (~$less(sK3(X0),1) | ~s(X2,X0)) )),
inference(cnf_transformation,[],[f63])).
tff(f100,plain,(
( ! [X2:object,X0:object] : (~$less(n,sK3(X0)) | ~s(X2,X0)) )),
inference(cnf_transformation,[],[f63])).
tff(f108,plain,(
( ! [X0:object] : (f__integer__(sK6(X0)) = X0 | ~p__is_integer__(X0)) )),
inference(cnf_transformation,[],[f76])).
tff(f109,plain,(
( ! [X0:object,X1:$int] : (p__is_integer__(X0) | f__integer__(X1) != X0) )),
inference(cnf_transformation,[],[f76])).
tff(f110,plain,(
( ! [X0:object] : (in_cover(f__integer__(sK7(X0))) | ~covered(X0)) )),
inference(cnf_transformation,[],[f80])).
tff(f111,plain,(
( ! [X0:object] : (s(X0,f__integer__(sK7(X0))) | ~covered(X0)) )),
inference(cnf_transformation,[],[f80])).
tff(f121,plain,(
( ! [X0:object,X1:object] : (p__less_equal__(X0,X1) | ~p__less__(X0,X1)) )),
inference(cnf_transformation,[],[f85])).
tff(f129,plain,(
( ! [X0:$int,X1:$int] : (p__less_equal__(f__integer__(X0),f__integer__(X1)) | $less(X1,X0)) )),
inference(cnf_transformation,[],[f88])).
tff(f130,plain,(
( ! [X0:object,X1:$int] : (covered(X0) | ~s(X0,f__integer__(X1))) )),
inference(cnf_transformation,[],[f51])).
tff(f135,plain,(
( ! [X1:$int] : (p__is_integer__(f__integer__(X1))) )),
inference(equality_resolution,[],[f109])).
tff(f141,plain,(
spl8_1 <=> ~s(sK0,sK1)),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])])).
tff(f144,plain,(
spl8_0 <=> s(sK0,sK1)),
introduced(avatar_definition,[new_symbols(naming,[spl8_0])])).
tff(f145,plain,(
s(sK0,sK1) | ~spl8_0),
inference(avatar_component_clause,[],[f144])).
tff(f146,plain,(
spl8_0),
inference(avatar_split_clause,[],[f89,f144])).
tff(f147,plain,(
f__integer__(sK3(sK1)) = sK1 | ~spl8_0),
inference(resolution,[],[f145,f98])).
tff(f148,plain,(
~$less(sK3(sK1),1) | ~spl8_0),
inference(resolution,[],[f145,f99])).
tff(f149,plain,(
~$less(n,sK3(sK1)) | ~spl8_0),
inference(resolution,[],[f145,f100])).
tff(f154,plain,(
spl8_2 <=> f__integer__(sK3(sK1)) = sK1),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])])).
tff(f155,plain,(
f__integer__(sK3(sK1)) = sK1 | ~spl8_2),
inference(avatar_component_clause,[],[f154])).
tff(f156,plain,(
spl8_2 | ~spl8_0),
inference(avatar_split_clause,[],[f147,f144,f154])).
tff(f161,plain,(
spl8_5 <=> ~$less(sK3(sK1),1)),
introduced(avatar_definition,[new_symbols(naming,[spl8_5])])).
tff(f162,plain,(
~$less(sK3(sK1),1) | ~spl8_5),
inference(avatar_component_clause,[],[f161])).
tff(f163,plain,(
~spl8_5 | ~spl8_0),
inference(avatar_split_clause,[],[f148,f144,f161])).
tff(f168,plain,(
spl8_7 <=> ~$less(n,sK3(sK1))),
introduced(avatar_definition,[new_symbols(naming,[spl8_7])])).
tff(f169,plain,(
~$less(n,sK3(sK1)) | ~spl8_7),
inference(avatar_component_clause,[],[f168])).
tff(f170,plain,(
~spl8_7 | ~spl8_0),
inference(avatar_split_clause,[],[f149,f144,f168])).
tff(f171,plain,(
p__less_equal__(f__integer__(1),f__integer__(sK3(sK1))) | ~spl8_5),
inference(resolution,[],[f162,f129])).
tff(f176,plain,(
spl8_8 <=> p__less_equal__(f__integer__(1),f__integer__(sK3(sK1)))),
introduced(avatar_definition,[new_symbols(naming,[spl8_8])])).
tff(f178,plain,(
spl8_8 | spl8_5),
inference(avatar_split_clause,[],[f171,f161,f176])).
tff(f179,plain,(
~in_cover(sK1) | ~spl8_0),
inference(resolution,[],[f90,f145])).
tff(f180,plain,(
~in_cover(f__integer__(sK7(sK0))) | ~covered(sK0)),
inference(resolution,[],[f90,f111])).
tff(f185,plain,(
spl8_11 <=> ~in_cover(sK1)),
introduced(avatar_definition,[new_symbols(naming,[spl8_11])])).
tff(f187,plain,(
~spl8_11 | ~spl8_0),
inference(avatar_split_clause,[],[f179,f144,f185])).
tff(f192,plain,(
spl8_13 <=> ~covered(sK0)),
introduced(avatar_definition,[new_symbols(naming,[spl8_13])])).
tff(f193,plain,(
~covered(sK0) | ~spl8_13),
inference(avatar_component_clause,[],[f192])).
tff(f198,plain,(
spl8_15 <=> ~in_cover(f__integer__(sK7(sK0)))),
introduced(avatar_definition,[new_symbols(naming,[spl8_15])])).
tff(f199,plain,(
~in_cover(f__integer__(sK7(sK0))) | ~spl8_15),
inference(avatar_component_clause,[],[f198])).
tff(f200,plain,(
~spl8_13 | ~spl8_15),
inference(avatar_split_clause,[],[f180,f198,f192])).
tff(f201,plain,(
p__less_equal__(f__integer__(sK3(sK1)),f__integer__(n)) | ~spl8_7),
inference(resolution,[],[f169,f129])).
tff(f206,plain,(
spl8_16 <=> p__less_equal__(f__integer__(sK3(sK1)),f__integer__(n))),
introduced(avatar_definition,[new_symbols(naming,[spl8_16])])).
tff(f208,plain,(
spl8_16 | spl8_7),
inference(avatar_split_clause,[],[f201,f168,f206])).
tff(f209,plain,(
~covered(sK0) | ~spl8_15),
inference(resolution,[],[f199,f110])).
tff(f210,plain,(
~spl8_13 | spl8_15),
inference(avatar_split_clause,[],[f209,f198,f192])).
tff(f211,plain,(
( ! [X0:$int] : (~s(sK0,f__integer__(X0))) ) | ~spl8_13),
inference(resolution,[],[f193,f130])).
tff(f213,plain,(
p__less__(c__infimum__,sK1) | ~spl8_2),
inference(superposition,[],[f92,f155])).
tff(f228,plain,(
p__is_integer__(sK1) | ~spl8_2),
inference(superposition,[],[f135,f155])).
tff(f233,plain,(
spl8_18 <=> p__less__(c__infimum__,sK1)),
introduced(avatar_definition,[new_symbols(naming,[spl8_18])])).
tff(f234,plain,(
p__less__(c__infimum__,sK1) | ~spl8_18),
inference(avatar_component_clause,[],[f233])).
tff(f235,plain,(
spl8_18 | ~spl8_2),
inference(avatar_split_clause,[],[f213,f154,f233])).
tff(f243,plain,(
spl8_20 <=> p__is_integer__(sK1)),
introduced(avatar_definition,[new_symbols(naming,[spl8_20])])).
tff(f244,plain,(
p__is_integer__(sK1) | ~spl8_20),
inference(avatar_component_clause,[],[f243])).
tff(f245,plain,(
spl8_20 | ~spl8_2),
inference(avatar_split_clause,[],[f228,f154,f243])).
tff(f246,plain,(
f__integer__(sK6(sK1)) = sK1 | ~spl8_20),
inference(resolution,[],[f244,f108])).
tff(f251,plain,(
spl8_22 <=> f__integer__(sK6(sK1)) = sK1),
introduced(avatar_definition,[new_symbols(naming,[spl8_22])])).
tff(f253,plain,(
spl8_22 | ~spl8_20),
inference(avatar_split_clause,[],[f246,f243,f251])).
tff(f254,plain,(
p__less_equal__(c__infimum__,sK1) | ~spl8_18),
inference(resolution,[],[f234,f121])).
tff(f260,plain,(
spl8_24 <=> p__less_equal__(c__infimum__,sK1)),
introduced(avatar_definition,[new_symbols(naming,[spl8_24])])).
tff(f262,plain,(
spl8_24 | ~spl8_18),
inference(avatar_split_clause,[],[f254,f233,f260])).
tff(f266,plain,(
~s(sK0,sK1) | (~spl8_2 | ~spl8_13)),
inference(superposition,[],[f211,f155])).
tff(f270,plain,(
~spl8_1 | ~spl8_2 | spl8_13),
inference(avatar_split_clause,[],[f266,f192,f154,f141])).
tff(f271,plain,(
$false),
inference(avatar_sat_refutation,[],[f146,f156,f163,f170,f178,f187,f200,f208,f210,f235,f245,f253,f262,f270])).
% SZS output end Proof for
% (193364)Success in time 0.029 s
==== stderr ===========================================================
Sort inference for variables
If we want to use Anthem to verify a program, that program's rules must contain variables that are variants of I,J,K etc if they are of an integer sort, and X,Y,Z, etc if they are of a program sort. A more user-friendly version would allow the input program to keep their expressive variable names and do the re-naming under the hood. I'm not sure how easy it would be to automatically infer sorts for program variables, or if the user would have to specify them explicitly. It may be something to discuss at the next Anthem meeting.
Greater equal
Symbol >= in ASP programs seems to be understood as >.
Rewriting programs to use <= instead of >= works.
Wish list for anthem 1.0.0-beta.4
- Bug: For the rule "p(X) :- X >= 1." the competed definition produced by anthem is "forall X (p(X) <-> X > 1)".
- Improve error messages.
- Implement natural translation for regular rules.
- Replace an error message by a warning when the program is non-tight.
- Allow matching two programs, not only a program and a specification.
- Generate induction axioms instead of entering them manually.
- Mark lemmas of the general nature (not related to specific problems) so that there will be no need to prove them over and over again.
Negative variables in specs
Anthem cannot parse a specification file containing the following:
lemma: forall N ((-N)(-N)=NN).
But it can parse
lemma: forall N ((0-N)(0-N)=NN).
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