formula: track Δ₁, Σ₂, Π₂, and Δ₂ membership
* spot/tl/formula.hh, spot/tl/formula.cc: Update the properties and track them. * tests/core/kind.test: Augment the test case. * doc/tl/tl.tex, doc/spot.bib, NEWS: Document these new classes.
This commit is contained in:
Alexandre Duret-Lutz
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0c52c49079
commit
7901a37747
6 changed files with 473 additions and 175 deletions
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@ -25,118 +25,120 @@
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set -e
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cat >input<<EOF
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a,B&!xfLPSFsgopra
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a<->b,BxfLPSFsgopra
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!a,B&!xfLPSFsgopra
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!(a|b),B&xfLPSFsgopra
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F(a),&!xLPegopra
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G(a),&!xLPusopra
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a U b,&!xfLPgopra
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a U Fb,&!xLPegopra
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Ga U b,&!xLPopra
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1 U a,&!xfLPegopra
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a W b,&!xfLPsopra
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a W 0,&!xfLPusopra
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a M b,&!xfLPgopra
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a M 1,&!xfLPegopra
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a R b,&!xfLPsopra
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0 R b,&!xfLPusopra
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a R (b R (c R d)),&!xfLPsopra
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a U (b U (c U d)),&!xfLPgopra
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a W (b W (c W d)),&!xfLPsopra
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a M (b M (c M d)),&!xfLPgopra
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Fa -> Fb,xLPopra
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Ga -> Fb,xLPegopra
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Fa -> Gb,xLPusopra
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(Ga|Fc) -> Fb,xLPopra
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(Ga|Fa) -> Gb,xLPopra
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{a;c*;b}|->!Xb,&fPsopra
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{a;c*;b}|->X!b,&!fPsopra
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{a;c*;b}|->!Fb,&Psopra
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{a;c*;b}|->G!b,&!Psopra
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{a;c*;b}|->!Gb,&Pra
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{a;c*;b}|->F!b,&!Pra
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{a;c*;b}|->GFa,&!Pra
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a,B&!xfLPSFsgopraOPRD
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a<->b,BxfLPSFsgopraOPRD
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!a,B&!xfLPSFsgopraOPRD
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!(a|b),B&xfLPSFsgopraOPRD
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F(a),&!xLPegopraOPRD
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G(a),&!xLPusopraOPRD
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a U b,&!xfLPgopraOPRD
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a U Fb,&!xLPegopraOPRD
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Ga U b,&!xLPopraPD
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1 U a,&!xfLPegopraOPRD
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a W b,&!xfLPsopraOPRD
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a W 0,&!xfLPusopraOPRD
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a M b,&!xfLPgopraOPRD
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a M 1,&!xfLPegopraOPRD
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a R b,&!xfLPsopraOPRD
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0 R b,&!xfLPusopraOPRD
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a R (b R (c R d)),&!xfLPsopraOPRD
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a U (b U (c U d)),&!xfLPgopraOPRD
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a W (b W (c W d)),&!xfLPsopraOPRD
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a M (b M (c M d)),&!xfLPgopraOPRD
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Fa -> Fb,xLPopraOPRD
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Ga -> Fb,xLPegopraOPRD
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Fa -> Gb,xLPusopraOPRD
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(Ga|Fc) -> Fb,xLPopraOPRD
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(Ga|Fa) -> Gb,xLPopraOPRD
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{a;c*;b}|->!Xb,&fPsopraOPRD
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{a;c*;b}|->X!b,&!fPsopraOPRD
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{a;c*;b}|->!Fb,&PsopraOPRD
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{a;c*;b}|->G!b,&!PsopraOPRD
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{a;c*;b}|->!Gb,&PraRD
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{a;c*;b}|->F!b,&!PraRD
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{a;c*;b}|->GFa,&!PraRD
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{a;c*;b}|->FGa,&!Pa
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{a[+];c[+];b*}|->!Fb,&Psopra
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{a*;c[+];b*}|->!Fb,&xPsopra
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{a[+];c*;b[+]}|->G!b,&!Psopra
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{a*;c[+];b[+]}|->!Gb,&Pra
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{a[+];c*;b[+]}|->F!b,&!Pra
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{a[+];c[+];b*}|->GFa,&!Pra
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{a[+];c[+];b*}|->!Fb,&PsopraOPRD
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{a*;c[+];b*}|->!Fb,&xPsopraOPRD
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{a[+];c*;b[+]}|->G!b,&!PsopraOPRD
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{a*;c[+];b[+]}|->!Gb,&PraRD
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{a[+];c*;b[+]}|->F!b,&!PraRD
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{a[+];c[+];b*}|->GFa,&!PraRD
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{a*;c[+];b[+]}|->FGa,&!Pa
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{a;c;b|(d;e)}|->!Xb,&fPFsgopra
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{a;c;b|(d;e)}|->X!b,&!fPFsgopra
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{a;c;b|(d;e)}|->!Fb,&Psopra
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{a;c;b|(d;e)}|->G!b,&!Psopra
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{a;c;b|(d;e)}|->!Gb,&Pgopra
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{a;c;b|(d;e)}|->F!b,&!Pgopra
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{a;c;b|(d;e)}|->GFa,&!Pra
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{a;c;b|(d;e)}|->FGa,&!Ppa
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{a[+] && c[+]}|->!Xb,&fPsopra
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{a[+] && c[+]}|->X!b,&!fPsopra
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{a[+] && c[+]}|->!Fb,&xPsopra
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{a[+] && c[+]}|->G!b,&!xPsopra
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{a[+] && c[+]}|->!Gb,&xPra
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{a[+] && c[+]}|->F!b,&!xPra
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{a[+] && c[+]}|->GFa,&!xPra
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{a;c;b|(d;e)}|->!Xb,&fPFsgopraOPRD
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{a;c;b|(d;e)}|->X!b,&!fPFsgopraOPRD
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{a;c;b|(d;e)}|->!Fb,&PsopraOPRD
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{a;c;b|(d;e)}|->G!b,&!PsopraOPRD
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{a;c;b|(d;e)}|->!Gb,&PgopraOPRD
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{a;c;b|(d;e)}|->F!b,&!PgopraOPRD
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{a;c;b|(d;e)}|->GFa,&!PraRD
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{a;c;b|(d;e)}|->FGa,&!PpaPD
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{a[+] && c[+]}|->!Xb,&fPsopraOPRD
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{a[+] && c[+]}|->X!b,&!fPsopraOPRD
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{a[+] && c[+]}|->!Fb,&xPsopraOPRD
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{a[+] && c[+]}|->G!b,&!xPsopraOPRD
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{a[+] && c[+]}|->!Gb,&xPraRD
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{a[+] && c[+]}|->F!b,&!xPraRD
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{a[+] && c[+]}|->GFa,&!xPraRD
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{a[+] && c[+]}|->FGa,&!xPa
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{a;c*;b}<>->!Gb,&Pgopra
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{a;c*;b}<>->F!b,&!Pgopra
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{a;c*;b}<>->FGb,&!Ppa
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{a;c*;b}<>->!GFb,&Ppa
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{a;c*;b}<>->!Gb,&PgopraOPRD
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{a;c*;b}<>->F!b,&!PgopraOPRD
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{a;c*;b}<>->FGb,&!PpaPD
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{a;c*;b}<>->!GFb,&PpaPD
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{a;c*;b}<>->GFb,&!Pa
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{a;c*;b}<>->!FGb,&Pa
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{a*;c[+];b[+]}<>->!FGb,&Pa
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{a;c|d;b}<>->!Gb,&Pgopra
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{a;c|d;b}<>->G!b,&!Psopra
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{a;c|d;b}<>->FGb,&!Ppa
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{a;c|d;b}<>->!GFb,&Ppa
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{a;c|d;b}<>->GFb,&!Pra
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{a;c|d;_b}<>->!FGb,&Pr
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{a;c|d;b}<>->!Gb,&PgopraOPRD
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{a;c|d;b}<>->G!b,&!PsopraOPRD
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{a;c|d;b}<>->FGb,&!PpaPD
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{a;c|d;b}<>->!GFb,&PpaPD
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{a;c|d;b}<>->GFb,&!PraRD
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{a;c|d;_b}<>->!FGb,&PrRD
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# Equivalent to a&b&c&d
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{a:b:c:d}!,B&!xfLPSFsgopra
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a&b&c&d,B&!xfLPSFsgopra
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(Xa <-> XXXc) U (b & Fe),LPgopra
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(!X(a|X(!b))&(FX(g xor h)))U(!G(a|b)),LPegopra
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(!X(a|X(!b))&(GX(g xor h)))R(!F(a|b)),LPusopra
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(!X(a|X(!b))&(GX(g xor h)))U(!G(a|b)),LPeopra
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(!X(a|X(!b))&(FX(g xor h)))R(!F(a|b)),LPuopra
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(!X(a|X(!b))&(GX(g xor h)))U(!F(a|b)),LPpa
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(!X(a|X(!b))&(FX(g xor h)))R(!G(a|b)),LPra
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(!X(a|GXF(!b))&(FGX(g xor h)))U(!F(a|b)),LPpa
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{a:b:c:d}!,B&!xfLPSFsgopraOPRD
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a&b&c&d,B&!xfLPSFsgopraOPRD
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(Xa <-> XXXc) U (b & Fe),LPgopraOPRD
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(!X(a|X(!b))&(FX(g xor h)))U(!G(a|b)),LPegopraOPRD
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(!X(a|X(!b))&(GX(g xor h)))R(!F(a|b)),LPusopraOPRD
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(!X(a|X(!b))&(GX(g xor h)))U(!G(a|b)),LPeopraPD
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(!X(a|X(!b))&(FX(g xor h)))R(!F(a|b)),LPuopraRD
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(!X(a|X(!b))&(GX(g xor h)))U(!F(a|b)),LPpaPD
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(!X(a|X(!b))&(FX(g xor h)))R(!G(a|b)),LPraRD
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(!X(a|GXF(!b))&(FGX(g xor h)))U(!F(a|b)),LPpaPD
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(!X(a|GXF(!b))&(FGX(g xor h)))R(!F(a|b)),LPupa
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(!X(a|FXG(!b))&(GFX(g xor h)))R(!G(a|b)),LPra
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(!X(a|FXG(!b))&(GFX(g xor h)))R(!G(a|b)),LPraRD
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(!X(a|FXG(!b))&(GFX(g xor h)))U(!G(a|b)),LPera
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(!X(a|GXF(!b))&(FGX(g xor h)))U(!G(a|Fb)),LPepa
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(!X(a|GXF(!b))&(FGX(g xor h)))U(!G(a|Fb)),LPepaPD
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(!X(a|GXF(!b))&(FGX(g xor h)))U(!F(a|Gb)),LPa
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(!X(a|FXG(!b))&(GFX(g xor h)))R(!F(a|Gb)),LPura
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(!X(a|FXG(!b))&(GFX(g xor h)))R(!F(a|Gb)),LPuraRD
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(!X(a|FXG(!b))&(GFX(g xor h)))R(!G(a|Fb)),LPa
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GFa M GFb,&!xLPeua
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FGa M FGb,&!xLPeupa
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FGa M FGb,&!xLPeupaPD
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Fa M GFb,&!xLPera
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GFa W GFb,&!xLPeura
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GFa W GFb,&!xLPeuraRD
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FGa W FGb,&!xLPeua
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Ga W FGb,&!xLPupa
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Ga W b,&!xLPsopra
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Fa M b,&!xLPgopra
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{a;b*;c},&!fPsopra
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{a;b*;c}!,&!fPgopra
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Ga W b,&!xLPsopraOPRD
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Fa M b,&!xLPgopraOPRD
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{a;b*;c},&!fPsopraOPRD
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{a;b*;c}!,&!fPgopraOPRD
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# The negative normal form is {a;b*;c}[]->1
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!{a;b*;c}!,&fPsopra
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{a;b*;p112}[]->0,&!fPsopra
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!{a;b*;c.2},&!fPgopr
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!{a[+];b*;c[+]},&!fPgopra
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!{a[+];b*;c*},&!xfPgopra
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{a[+];b*;c[+]},&!fPsopra
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{a[+] && b || c[+]},&!fPsopra
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{a[+] && b[+] || c[+]},&!xfPsopra
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{p[+]:p[+]},&!xfPsoprla
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(!p W Gp) | ({(!p[*];(p[+]:(p[*];!p[+])))[:*4][:+]}<>-> (!p W Gp)),&!xPpla
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{b[+][:*0..3]},&!fPsopra
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{a->c[*]},xfPsopra
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{(a[+];b*);c*}<>->d,&!xfPgopra
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{first_match(a[+];b*);c*}<>->d,&!fPgopra
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!{a;b*;c}!,&fPsopraOPRD
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{a;b*;p112}[]->0,&!fPsopraOPRD
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!{a;b*;c.2},&!fPgoprOPRD
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!{a[+];b*;c[+]},&!fPgopraOPRD
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!{a[+];b*;c*},&!xfPgopraOPRD
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{a[+];b*;c[+]},&!fPsopraOPRD
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{a[+] && b || c[+]},&!fPsopraOPRD
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{a[+] && b[+] || c[+]},&!xfPsopraOPRD
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{p[+]:p[+]},&!xfPsoprlaOPRD
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(!p W Gp) | ({(!p[*];(p[+]:(p[*];!p[+])))[:*4][:+]}<>-> (!p W Gp)),&!xPplaPD
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{b[+][:*0..3]},&!fPsopraOPRD
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{a->c[*]},xfPsopraOPRD
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{(a[+];b*);c*}<>->d,&!xfPgopraOPRD
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{first_match(a[+];b*);c*}<>->d,&!fPgopraOPRD
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G(Ga U b),&!xLPura
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GFb & G(Ga R b),&!xLPuraRD
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EOF
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run 0 ../kind input
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