def test_problem_15(self):
prover = Prover()
prover.add_formula("forall(x,forall(y,forall(z,if(and(L(x,y),L(y,z)),"
"L(x,z)))))")
prover.add_formula("forall(x,forall(y,if(L(x,y),L(y,x))))")
prover.add_goal("forall(x,L(x,x))")
self.assertFalse(prover.run_prover())
def test_problem_15(self):
prover = Prover()
prover.add_formula('if(L, M)')
prover.add_formula('if(M, N)')
prover.add_formula('if(N, L)')
prover.add_goal('or(L, N)')
self.assertFalse(prover.run_prover())
def test_problem_16(self):
prover = Prover()
prover.add_formula('if(S, T)')
prover.add_formula('if(S, not(T))')
prover.add_formula('if(not(T), S)')
prover.add_goal('or(S, not(T))')
self.assertFalse(prover.run_prover())
def test_problem_06(self):
prover = Prover()
prover.add_formula("or(A, and(B, C))")
prover.add_formula("if(A, D)")
prover.add_formula("if(D, C)")
prover.add_goal("C")
self.assertTrue(prover.run_prover())
def test_problem_04(self):
prover = Prover()
prover.add_formula("exists(x,and(A(x),not(B(x))))")
prover.add_formula("exists(x,and(A(x),not(C(x))))")
prover.add_formula("exists(x,and(not(B(x)),D(x)))")
prover.add_goal("exists(x,and(and(A(x),not(B(x))),D(x)))")
self.assertFalse(prover.run_prover())
def test_problem_17(self):
prover = Prover()
prover.add_formula("and(A, and(B, C))")
prover.add_formula("if(A, or(D, E))")
prover.add_formula("if(B, or(D, F))")
prover.add_goal("or(D, and(E, F))")
self.assertTrue(prover.run_prover())
def test_problem_15(self):
prover = Prover()
prover.add_formula("if(or(not(A), B), and(C, D))")
prover.add_formula("not(or(A, E))")
prover.add_formula("if(F, not(D))")
prover.add_goal("not(F)")
self.assertTrue(prover.run_prover())
def test_problem_03(self):
prover = Prover()
prover.add_formula('not(iff(A, B))')
prover.add_formula('not(A)')
prover.add_formula('not(B)')
prover.add_goal('and(C, not(C))')
self.assertTrue(prover.run_prover())
def test_problem_02(self):
prover = Prover()
prover.add_formula('if(K, H)')
prover.add_formula('if(H, L)')
prover.add_formula('if(L, M)')
prover.add_goal('if(K, M)')
self.assertTrue(prover.run_prover())
def test_problem_17(self):
prover = Prover()
prover.add_formula('if(W, X)')
prover.add_formula('if(X, W)')
prover.add_formula('if(X, Y)')
prover.add_formula('if(Y, X)')
prover.add_goal('iff(W, Y)')
self.assertTrue(prover.run_prover())
def test_get_proof(self):
prover = Prover()
prover.add_formula("and(a,b)")
prover.add_goal("a")
prover.run_prover()
proof = prover.get_proof()
expected = [' 1) a '
' Assumption',
' 3) ~a '
' Assumption',
' 4) $$FALSE '
' resolve(1,3)']
self.assertEqual(expected, proof)
def test_problem_12(self):
prover = Prover()
prover.add_formula("if(A, B)")
prover.add_formula("if(not(B), not(C))")
prover.add_formula("not(and(not(C), not(A)))")
prover.add_goal("B")
self.assertTrue(prover.run_prover())
def test_problem_05(self):
prover = Prover()
prover.add_formula("forall(x,if(A(x),F(x)))")
prover.add_formula("if(exists(x,F(x)),not(exists(y,G(y))))")
prover.add_goal("forall(x,if(exists(y,A(y)),not(G(x))))")
self.assertTrue(prover.run_prover())
def test_problem_02(self):
prover = Prover()
prover.add_formula("forall(x,if(A(x),and(B(x),C(x))))")
prover.add_formula("forall(x,if(A(x),not(C(x))))")
prover.add_goal("not(A(a))")
self.assertTrue(prover.run_prover())
def test_problem_03(self):
prover = Prover()
prover.add_formula("forall(x,if(A(x),B(x)))")
prover.add_formula("forall(x,if(not(A(x)),C(x)))")
prover.add_goal("forall(x,if(not(B(x)),not(C(x))))")
self.assertFalse(prover.run_prover())
def test_problem_17(self):
prover = Prover()
prover.add_formula("forall(x,forall(y,if(and(A(x),B(y)),C(x,y))))")
prover.add_formula("exists(y,and(F(y),forall(z,if(H(z),C(y,z)))))")
prover.add_formula("forall(x,forall(y,forall(z,if(and(L(x,y),L(y,z)),"
"L(x,z)))))")
prover.add_formula("forall(x,if(F(x),B(x)))")
prover.add_goal("forall(z,forall(y,if(and(A(z),H(y)),C(z,y))))")
self.assertFalse(prover.run_prover())
def test_problem_18(self):
self.skipTest('Should work')
prover = Prover()
prover.add_formula("forall(x,if(exists(y,and(A(y),B(x,y))),C(x)))")
prover.add_formula(
"exists(y,and(D(y),exists(x,and(F(x),and(G(x),B(y,x))))))")
prover.add_formula("forall(x,if(F(x),A(x)))")
prover.add_formula(
"if(exists(x,and(C(x),D(x))),if(exists(y,and(D(y),exists(z,B(y,z)))),forall(x,F(x))))"
)
prover.add_goal("forall(x,A(x))")
self.assertTrue(prover.run_prover())
def test_problem_13(self):
prover = Prover()
prover.add_formula("if(A, B)")
prover.add_formula("if(not(C), not(B))")
prover.add_formula("iff(C, D)")
prover.add_goal("if(A, D)")
self.assertTrue(prover.run_prover())
def test_prover_formula_error(self):
prover = Prover()
with self.assertRaises(TypeError):
prover.add_formula(None)
def test_problem_08(self):
prover = Prover()
prover.add_formula("forall(x,exists(y,and(F(x),G(x,y))))")
prover.add_goal("exists(y,forall(x,and(F(x),G(x,y))))")
self.assertFalse(prover.run_prover())
def test_problem_06(self):
prover = Prover()
prover.add_formula("exists(x,or(A(x),not(B(x))))")
prover.add_formula("forall(x,if(and(A(x),not(B(x))),C(x)))")
prover.add_goal("exists(x,C(x))")
self.assertFalse(prover.run_prover())
def test_prover_no_goal_error(self):
prover = Prover()
with self.assertRaises(Exception):
prover.run_prover()
def test_problem_07(self):
prover = Prover()
prover.add_formula("forall(x,not(F(x,x)))")
prover.add_formula("if(not(forall(x,G(x))),exists(y,F(y,a)))")
prover.add_goal("exists(z,and(G(z),F(z,z)))")
self.assertFalse(prover.run_prover())
def test_problem_10(self):
prover = Prover()
prover.add_formula("or(F(a),exists(y,G(y,a)))")
prover.add_formula("or(F(b),exists(y,not(G(y,a))))")
prover.add_goal("exists(y,G(y,a))")
self.assertFalse(prover.run_prover())
def test_problem_09(self):
prover = Prover()
prover.add_formula("exists(x,and(F(x),forall(y,if(G(y),L(x,y)))))")
prover.add_formula("forall(x,if(F(x),forall(y,if(M(y),not(L(x,y))))))")
prover.add_goal("forall(x,if(G(x),not(M(x))))")
self.assertTrue(prover.run_prover())
def test_problem_12(self):
prover = Prover()
prover.add_formula("forall(z,iff(L(z),H(z)))")
prover.add_formula("forall(x,not(or(H(x),not(B(x)))))")
prover.add_goal("not(L(b))")
self.assertTrue(prover.run_prover())
def test_problem_11(self):
prover = Prover()
prover.add_formula("forall(x,not(J(x)))")
prover.add_formula("if(exists(y,or(H(b,y),R(y,y))),exists(x,J(x)))")
prover.add_goal("forall(y,not(or(H(b,y),R(y,y))))")
self.assertTrue(prover.run_prover())
def test_problem_01(self):
prover = Prover()
prover.add_formula("forall(x,if(A(x),B(x)))")
prover.add_formula("forall(x,if(B(x),C(x)))")
prover.add_goal("forall(x,if(A(x),C(x)))")
self.assertTrue(prover.run_prover())
def test_problem_13(self):
prover = Prover()
prover.add_formula("or(not(forall(x,K(x,x))),forall(y,H(y,y)))")
prover.add_goal("exists(z,if(not(H(z,z)),not(K(z,z))))")
self.assertTrue(prover.run_prover())
def test_problem_16(self):
prover = Prover()
prover.add_formula("forall(x,if(S(x),exists(y,and(S(y),forall(z,"
"iff(B(z,y),and(B(z,x),B(z,z))))))))")
prover.add_formula("forall(x,not(B(x,x)))")
prover.add_formula("exists(x,S(x))")
prover.add_goal("exists(x,and(S(x),forall(y,not(B(y,x)))))")
self.assertTrue(prover.run_prover())
