223 lines
7.6 KiB
Plaintext
223 lines
7.6 KiB
Plaintext
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.. Copyright (C) 2001-2023 NLTK Project
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.. For license information, see LICENSE.TXT
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=========================
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Resolution Theorem Prover
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=========================
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>>> from nltk.inference.resolution import *
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>>> from nltk.sem import logic
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>>> from nltk.sem.logic import *
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>>> logic._counter._value = 0
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>>> read_expr = logic.Expression.fromstring
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>>> P = read_expr('P')
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>>> Q = read_expr('Q')
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>>> R = read_expr('R')
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>>> A = read_expr('A')
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>>> B = read_expr('B')
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>>> x = read_expr('x')
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>>> y = read_expr('y')
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>>> z = read_expr('z')
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-------------------------------
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Test most_general_unification()
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-------------------------------
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>>> print(most_general_unification(x, x))
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{}
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>>> print(most_general_unification(A, A))
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{}
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>>> print(most_general_unification(A, x))
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{x: A}
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>>> print(most_general_unification(x, A))
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{x: A}
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>>> print(most_general_unification(x, y))
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{x: y}
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>>> print(most_general_unification(P(x), P(A)))
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{x: A}
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>>> print(most_general_unification(P(x,B), P(A,y)))
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{x: A, y: B}
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>>> print(most_general_unification(P(x,B), P(B,x)))
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{x: B}
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>>> print(most_general_unification(P(x,y), P(A,x)))
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{x: A, y: x}
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>>> print(most_general_unification(P(Q(x)), P(y)))
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{y: Q(x)}
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------------
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Test unify()
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------------
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>>> print(Clause([]).unify(Clause([])))
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[]
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>>> print(Clause([P(x)]).unify(Clause([-P(A)])))
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[{}]
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>>> print(Clause([P(A), Q(x)]).unify(Clause([-P(x), R(x)])))
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[{R(A), Q(A)}]
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>>> print(Clause([P(A), Q(x), R(x,y)]).unify(Clause([-P(x), Q(y)])))
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[{Q(y), Q(A), R(A,y)}]
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>>> print(Clause([P(A), -Q(y)]).unify(Clause([-P(x), Q(B)])))
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[{}]
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>>> print(Clause([P(x), Q(x)]).unify(Clause([-P(A), -Q(B)])))
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[{-Q(B), Q(A)}, {-P(A), P(B)}]
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>>> print(Clause([P(x,x), Q(x), R(x)]).unify(Clause([-P(A,z), -Q(B)])))
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[{-Q(B), Q(A), R(A)}, {-P(A,z), R(B), P(B,B)}]
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>>> a = clausify(read_expr('P(A)'))
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>>> b = clausify(read_expr('A=B'))
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>>> print(a[0].unify(b[0]))
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[{P(B)}]
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-------------------------
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Test is_tautology()
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-------------------------
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>>> print(Clause([P(A), -P(A)]).is_tautology())
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True
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>>> print(Clause([-P(A), P(A)]).is_tautology())
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True
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>>> print(Clause([P(x), -P(A)]).is_tautology())
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False
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>>> print(Clause([Q(B), -P(A), P(A)]).is_tautology())
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True
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>>> print(Clause([-Q(A), P(R(A)), -P(R(A)), Q(x), -R(y)]).is_tautology())
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True
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>>> print(Clause([P(x), -Q(A)]).is_tautology())
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False
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-------------------------
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Test subsumes()
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-------------------------
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>>> print(Clause([P(A), Q(B)]).subsumes(Clause([P(A), Q(B)])))
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True
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>>> print(Clause([-P(A)]).subsumes(Clause([P(A)])))
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False
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>>> print(Clause([P(A), Q(B)]).subsumes(Clause([Q(B), P(A)])))
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True
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>>> print(Clause([P(A), Q(B)]).subsumes(Clause([Q(B), R(A), P(A)])))
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True
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>>> print(Clause([P(A), R(A), Q(B)]).subsumes(Clause([Q(B), P(A)])))
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False
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>>> print(Clause([P(x)]).subsumes(Clause([P(A)])))
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True
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>>> print(Clause([P(A)]).subsumes(Clause([P(x)])))
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True
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------------
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Test prove()
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------------
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>>> print(ResolutionProverCommand(read_expr('man(x)')).prove())
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False
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>>> print(ResolutionProverCommand(read_expr('(man(x) -> man(x))')).prove())
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True
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>>> print(ResolutionProverCommand(read_expr('(man(x) -> --man(x))')).prove())
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True
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>>> print(ResolutionProverCommand(read_expr('-(man(x) & -man(x))')).prove())
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True
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>>> print(ResolutionProverCommand(read_expr('(man(x) | -man(x))')).prove())
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True
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>>> print(ResolutionProverCommand(read_expr('(man(x) -> man(x))')).prove())
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True
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>>> print(ResolutionProverCommand(read_expr('-(man(x) & -man(x))')).prove())
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True
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>>> print(ResolutionProverCommand(read_expr('(man(x) | -man(x))')).prove())
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True
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>>> print(ResolutionProverCommand(read_expr('(man(x) -> man(x))')).prove())
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True
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>>> print(ResolutionProverCommand(read_expr('(man(x) <-> man(x))')).prove())
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True
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>>> print(ResolutionProverCommand(read_expr('-(man(x) <-> -man(x))')).prove())
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True
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>>> print(ResolutionProverCommand(read_expr('all x.man(x)')).prove())
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False
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>>> print(ResolutionProverCommand(read_expr('-all x.some y.F(x,y) & some x.all y.(-F(x,y))')).prove())
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False
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>>> print(ResolutionProverCommand(read_expr('some x.all y.sees(x,y)')).prove())
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False
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>>> p1 = read_expr('all x.(man(x) -> mortal(x))')
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>>> p2 = read_expr('man(Socrates)')
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>>> c = read_expr('mortal(Socrates)')
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>>> ResolutionProverCommand(c, [p1,p2]).prove()
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True
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>>> p1 = read_expr('all x.(man(x) -> walks(x))')
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>>> p2 = read_expr('man(John)')
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>>> c = read_expr('some y.walks(y)')
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>>> ResolutionProverCommand(c, [p1,p2]).prove()
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True
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>>> p = read_expr('some e1.some e2.(believe(e1,john,e2) & walk(e2,mary))')
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>>> c = read_expr('some e0.walk(e0,mary)')
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>>> ResolutionProverCommand(c, [p]).prove()
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True
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------------
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Test proof()
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------------
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>>> p1 = read_expr('all x.(man(x) -> mortal(x))')
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>>> p2 = read_expr('man(Socrates)')
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>>> c = read_expr('mortal(Socrates)')
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>>> logic._counter._value = 0
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>>> tp = ResolutionProverCommand(c, [p1,p2])
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>>> tp.prove()
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True
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>>> print(tp.proof())
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[1] {-mortal(Socrates)} A
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[2] {-man(z2), mortal(z2)} A
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[3] {man(Socrates)} A
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[4] {-man(Socrates)} (1, 2)
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[5] {mortal(Socrates)} (2, 3)
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[6] {} (1, 5)
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<BLANKLINE>
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------------------
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Question Answering
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------------------
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One answer
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>>> p1 = read_expr('father_of(art,john)')
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>>> p2 = read_expr('father_of(bob,kim)')
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>>> p3 = read_expr('all x.all y.(father_of(x,y) -> parent_of(x,y))')
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>>> c = read_expr('all x.(parent_of(x,john) -> ANSWER(x))')
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>>> logic._counter._value = 0
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>>> tp = ResolutionProverCommand(None, [p1,p2,p3,c])
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>>> sorted(tp.find_answers())
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[<ConstantExpression art>]
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>>> print(tp.proof()) # doctest: +SKIP
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[1] {father_of(art,john)} A
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[2] {father_of(bob,kim)} A
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[3] {-father_of(z3,z4), parent_of(z3,z4)} A
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[4] {-parent_of(z6,john), ANSWER(z6)} A
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[5] {parent_of(art,john)} (1, 3)
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[6] {parent_of(bob,kim)} (2, 3)
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[7] {ANSWER(z6), -father_of(z6,john)} (3, 4)
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[8] {ANSWER(art)} (1, 7)
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[9] {ANSWER(art)} (4, 5)
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<BLANKLINE>
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Multiple answers
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>>> p1 = read_expr('father_of(art,john)')
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>>> p2 = read_expr('mother_of(ann,john)')
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>>> p3 = read_expr('all x.all y.(father_of(x,y) -> parent_of(x,y))')
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>>> p4 = read_expr('all x.all y.(mother_of(x,y) -> parent_of(x,y))')
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>>> c = read_expr('all x.(parent_of(x,john) -> ANSWER(x))')
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>>> logic._counter._value = 0
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>>> tp = ResolutionProverCommand(None, [p1,p2,p3,p4,c])
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>>> sorted(tp.find_answers())
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[<ConstantExpression ann>, <ConstantExpression art>]
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>>> print(tp.proof()) # doctest: +SKIP
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[ 1] {father_of(art,john)} A
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[ 2] {mother_of(ann,john)} A
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[ 3] {-father_of(z3,z4), parent_of(z3,z4)} A
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[ 4] {-mother_of(z7,z8), parent_of(z7,z8)} A
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[ 5] {-parent_of(z10,john), ANSWER(z10)} A
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[ 6] {parent_of(art,john)} (1, 3)
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[ 7] {parent_of(ann,john)} (2, 4)
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[ 8] {ANSWER(z10), -father_of(z10,john)} (3, 5)
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[ 9] {ANSWER(art)} (1, 8)
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[10] {ANSWER(z10), -mother_of(z10,john)} (4, 5)
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[11] {ANSWER(ann)} (2, 10)
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[12] {ANSWER(art)} (5, 6)
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[13] {ANSWER(ann)} (5, 7)
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<BLANKLINE>
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