Of=SrSSKrSSKrSSKrSSKJrJr SSKJrJ r J r J r J r J r JrJrJr SSSSS S S S S S. r"SS5r"SS\\5r"SS5rSrSr"SS\\5r"SS\5r"SS\5r"SS\5rSrS rS!rS"/4S#/4S$/4S%/4S&/4S#/4S$/4S&/4S'/4S(/4S)S*S+/4S,/4S-/4S./4S/S0/4S1S0/4/r/S2Qr S6S3jr!S4r"\#S5:Xa\""5 gg)7zD A theorem prover that makes use of the external 'Prover9' package. N)BaseProverCommandProver) AllExpression AndExpressionEqualityExpressionExistsExpression Expression IffExpression ImpExpressionNegatedExpression OrExpressionTz(FATAL)Fz (MAX_MEGS)z (MAX_SECONDS)z (MAX_GIVEN)z (MAX_KEPT)z(ACTION)z (SIGSEGV)) rec"\rSrSrSrSSjrSrg)Prover9CommandParent/z A common base class used by both ``Prover9Command`` and ``MaceCommand``, which is responsible for maintaining a goal and a set of assumptions, and generating prover9-style input files from them. c UR5S:Xa#UR5Hn[U5 M gUR5S:Xa,[UR55Hn[U5 M g[ SU-5e)z, Print the list of the current assumptions. nltkprover9z*Unrecognized value for 'output_format': %sN)lower assumptionsprintconvert_to_prover9 NameError)self output_formatas 8/usr/lib/python3/dist-packages/nltk/inference/prover9.pyprint_assumptions&Prover9CommandParent.print_assumptions6sv    F *%%'a(  "i /'(8(8(:;a<<}L N)r)__name__ __module__ __qualname____firstlineno____doc__r%__static_attributes__r(r'r$rr/s  r'rc,\rSrSrSrSSjrSSjrSrg) Prover9CommandFz A ``ProverCommand`` specific to the ``Prover9`` prover. It contains the a print_assumptions() method that is used to print the list of assumptions in multiple formats. NcU(d/nUb[U[5(deO [U5n[R"XX5 g)al :param goal: Input expression to prove :type goal: sem.Expression :param assumptions: Input expressions to use as assumptions in the proof. :type assumptions: list(sem.Expression) :param timeout: number of seconds before timeout; set to 0 for no timeout. :type timeout: int :param prover: a prover. If not set, one will be created. :type prover: Prover9 N) isinstanceProver9r__init__)r!goalrtimeoutprovers r$r5Prover9Command.__init__Ms?K  fg.. ..W%F""4Cr'cU(a.URRUS/5SR5$UR5$)z) :see BaseProverCommand.decorate_proof() striplabelsr)_prover_call_prooftransrstrip)r! proof_stringsimplifys r$decorate_proofProver9Command.decorate_proofdsB <<00 Ofh  &&( (r'r()NN<N)T)r)r*r+r,r-r5rAr.r(r'r$r0r0Fs D. )r'r0cJ\rSrSrSrSrS SjrSrSrS Sjr /S4S jr S r g) Prover9Parentpz A common class extended by both ``Prover9`` and ``Mace ``. It contains the functionality required to convert NLTK-style expressions into Prover9-style expressions. NFc UcSUlSUlgSn[RR UUS/SX3S-/US9UlURR [ RRS5Ulg)NrPROVER9'https://www.cs.unm.edu/~mccune/prover9/.exe) path_to_binenv_varsurl binary_namesverboser) _binary_location _prover9_binr internals find_binaryrsplitospathsep)r!binary_locationrOnames r$config_prover9Prover9Parent.config_prover9ysy  "$(D ! $D D $ : :+#="6M2 !;!D %)$5$5$<$[SUR5 U(a [S US5 U(a [S US5 URS 5UR4$![a Nf=f) a Call the binary with the given input. :param input_str: A string whose contents are used as stdin. :param binary: The location of the binary to call :param args: A list of command-line arguments. :return: A tuple (stdout, returncode) :see: ``config_prover9`` zCalling:zArgs:zInput:  utf8)stdoutstderrstdin)inputz Return code:zstdout: zstderr: zutf-8) rencodeAttributeError subprocessPopenPIPESTDOUT communicate returncodedecode) r! input_strbinaryargsrOcmdprlrms r$_callProver9Parent._calls  *f % '4 *i .ho !((0I      0A0A ==y=9  .!,, /k640k640 g& 55   sC99 DD)rPrQ)F) r)r*r+r,r-rPrZr`rcrgr~r.r(r'r$rErEps0 M *    -/!6r'rEc[U[5(a6/nUH,nUR[UR 555 M. U$[UR 55$! [ SU-5 e=f! [ SU-5 e=f)z3 Convert a ``logic.Expression`` to Prover9 format. z4input %s cannot be converted to Prover9 input syntax)r3listappend_convert_to_prover9r@r)roresultr^s r$rrs%A  1!**,?@   &u~~'78 8  LuTU   H5P Q s(A& A:&A7:B cj[U[5(a1S[UR5-S-[ UR 5-$[U[ 5(a1S[UR5-S-[ UR 5-$[U[5(aS[ UR 5-S-$[U[5(a4S[ UR5-S-[ UR5-S-$[U[5(a4S[ UR5-S-[ UR5-S-$[U[5(a4S[ UR5-S -[ UR5-S-$[U[5(a4S[ UR5-S -[ UR5-S-$[U[5(a4S[ UR5-S -[ UR5-S-$[U5$) z; Convert ``logic.Expression`` to Prover9 formatted string. zexists  zall z-()(z & z | z -> z <-> z = )r3rstrvariablertermrr rfirstsecondr r r r) expressions r$rrsW*.// *%%& ' "*//2 3 J . . *%%& ' "*//2 3 J 1 2 2)*//::S@@ J . . !*"2"23 4 "*"3"34 5    J - - !*"2"23 4 "*"3"34 5    J . . !*"2"23 4 "*"3"34 5    J . . !*"2"23 4 "*"3"34 5    J 2 3 3 !*"2"23 4 "*"3"34 5   :r'cR\rSrSrSrSrS SjrS SjrSr/S4Sjr /S4Sjr S r g) r4i3NcXlg)N)_timeout)r!r7s r$r5Prover9.__init__7s   &r'FcdU(d/nURURX5US9upEUS:HU4$)z Use Prover9 to prove a theorem. :return: A pair whose first element is a boolean indicating if the proof was successful (i.e. returns value of 0) and whose second element is the output of the prover. )rOr) _call_prover9r`)r!r6rrOrlrws r$_proveProver9._prove=sEK!//   t 170 a((r'c8SnU[RXU5-$)z# :see: Prover9Parent.prover9_input zclear(auto_denials). )rEr`)r!r6rr^s r$r`Prover9.prover9_inputLs! %=..t;GGGr'czURcURSU5UlSnURS:aUSUR-- nXA- nURX@RX#5upVUS;aISnXu;a$UR U5nXXSR 5n OSn US;a [ Xi5e[Xi5eXV4$) z Call the ``prover9`` binary with the given input. :param input_str: A string whose contents are used as stdin. :param args: A list of command-line arguments. :return: A tuple (stdout, returncode) :see: ``config_prover9`` Nrr]rzassign(max_seconds, %d). )rrz%%ERROR:)rrrr)rQrgrr~indexstripProver9LimitExceededExceptionProver9FatalException) r!ryr{rOupdated_input_strrlrwerrormsgprefixmsgstarterrormsgs r$rProver9._call_prover9Ss    $ $ 1 1)W ED  ==1  !?$--!O O &!ZZ 00$  V #'N'!<<7!),224\)3JII+JAA!!r'cURcURSU5UlURXRX#5$)z Call the ``prooftrans`` binary with the given input. :param input_str: A string whose contents are used as stdin. :param args: A list of command-line arguments. :return: A tuple (stdout, returncode) :see: ``config_prover9`` prooftrans)_prooftrans_binrgr~)r!ryr{rOs r$r=Prover9._call_prooftransvs<    '#'#4#4\7#KD zz)%9%94IIr')rrQr)rC)NNF) r)r*r+r,rQrr5rr`rr=r.r(r'r$r4r43s6LO& )H-/!"F025 Jr'r4c\rSrSrSrSrg)Prover9Exceptionic^[UnU(aUSU-- n[RX5 g)Nz %s)p9_return_codes Exceptionr5)r!rwmessagemsgs r$r5Prover9Exception.__init__s,j)  6G# #C4%r'r(N)r)r*r+r,r5r.r(r'r$rrs&r'rc\rSrSrSrg)rir(Nr)r*r+r,r.r(r'r$rrr'rc\rSrSrSrg)rir(Nrr(r'r$rrrr'rc[R"S5n[R"S5n[X/S9nSUl/UlUR 5 [ UR 55 [ UR55 g)Nz(walk(j) & sing(j))zwalk(j)r)r fromstringr0_executable_pathprover9_searchproverproof)r#gr}s r$ test_configrsd34Ai(Aqc*AAAGGI !'') !'')r'cjUH-n[R"U5n[[U55 M/ g)z Test that parsing works OK. N)r rrr)exprtes r$test_convert_to_prover9rs,  ! !! $  #$r'cUHup[R"U5nUVs/sHn[R"U5PM nn[X5S9R5nUHn[ SU-5 M [ SUSUS35 M gs snf)z* Try some proofs and exhibit the results. rz %sz|- z: rjN)r rr0rr) argumentsr6rrr#alistr}s r$ test_provers'  ! !$ '3>?;a&&q);? 1 0 6 6 8A 'A+  A3b2 '?s B z(man(x) <-> (not (not man(x))))z(not (man(x) & (not man(x))))z(man(x) | (not man(x)))z(man(x) & (not man(x)))z(man(x) -> man(x))z(man(x) <-> man(x))z(not (man(x) <-> (not man(x))))zmortal(Socrates)zall x.(man(x) -> mortal(x))z man(Socrates)zA((all x.(man(x) -> walks(x)) & man(Socrates)) -> some y.walks(y))z(all x.man(x) -> all x.man(x))zsome x.all y.sees(x,y)z#some e3.(walk(e3) & subj(e3, mary))zWsome e1.(see(e1) & subj(e1, john) & some e2.(pred(e1, e2) & walk(e2) & subj(e2, mary)))zVsome x e1.(see(e1) & subj(e1, x) & some e2.(pred(e1, e2) & walk(e2) & subj(e2, mary)))) zsome x y.sees(x,y)zsome x.(man(x) & walks(x))z\x.(man(x) & walks(x))z\x y.sees(x,y)z walks(john)z\x.big(x, \y.mouse(y))z/(walks(x) & (runs(x) & (threes(x) & fours(x))))z(walks(x) -> runs(x))zsome x.(PRO(x) & sees(John, x))z some x.(man(x) & (not walks(x)))zall x.(man(x) -> walks(x))c [SU-5 g)N-)r)nums r$spacerrs #)r'c[S5 [5 [5 [5 [S5 [5 [[5 [5 [S5 [5 [ [ 5 g)NzTesting configurationz$Testing conversion to Prover9 formatzTesting proofs)rrrr expressionsrrr(r'r$demorsK !" HM G 01 HK( G  Hyr'__main__)-)$r-rUrrrnltk.inference.apirrnltk.sem.logicrrrrr r r r r rrr0rErrr4rrrrrrrrrrrr)r(r'r$rs  8        .'))+<')Tk6k6\*=@OJmVOJd&y& ,  $4  %  '+$b)##2$b)#2B&+7IJH"M%r*r"- e  a e +  :    zFr'