mirror of
https://github.com/Z3Prover/z3
synced 2025-04-06 17:44:08 +00:00
313 lines
6.9 KiB
Plaintext
313 lines
6.9 KiB
Plaintext
Z3 4.0.0.0
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simple_example
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CONTEXT:
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(solver)END OF CONTEXT
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DeMorgan
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DeMorgan is valid
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find_model_example1
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model for: x xor y
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sat
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y -> false
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x -> true
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find_model_example2
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model for: x < y + 1, x > 2
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sat
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y -> 3
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x -> 3
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model for: x < y + 1, x > 2, not(x = y)
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sat
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y -> 4
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x -> 3
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prove_example1
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prove: x = y implies g(x) = g(y)
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valid
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disprove: x = y implies g(g(x)) = g(y)
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invalid
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counterexample:
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y -> U!val!0
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x -> U!val!0
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g -> {
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U!val!0 -> U!val!1
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U!val!1 -> U!val!2
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else -> U!val!1
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}
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prove_example2
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prove: not(g(g(x) - g(y)) = g(z)), x + z <= y <= x implies z < 0
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valid
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disprove: not(g(g(x) - g(y)) = g(z)), x + z <= y <= x implies z < -1
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invalid
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counterexample:
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z -> -1
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y -> -7719
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x -> -7719
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g -> {
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-7719 -> 0
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0 -> 2
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-1 -> 3
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else -> 0
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}
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push_pop_example1
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assert: x >= 'big number'
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push
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number of scopes: 1
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assert: x <= 3
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unsat
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pop
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number of scopes: 0
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sat
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x = 1000000000000000000000000000000000000000000000000000000:int
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function interpretations:
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assert: y > x
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sat
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y = 1000000000000000000000000000000000000000000000000000001:int
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x = 1000000000000000000000000000000000000000000000000000000:int
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function interpretations:
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quantifier_example1
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pattern: {(f #0 #1)}
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assert axiom:
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(forall (k!0 Int) (k!1 Int) (= (inv!0 (f k!1 k!0)) k!0) :pat {(f k!1 k!0)})
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prove: f(x, y) = f(w, v) implies y = v
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valid
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disprove: f(x, y) = f(w, v) implies x = w
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that is: not(f(x, y) = f(w, v) implies x = w) is satisfiable
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unknown
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potential model:
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w = 2:int
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v = 1:int
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y = 1:int
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x = 0:int
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function interpretations:
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f = {(0:int, 1:int|->3:int), (2:int, 1:int|->3:int), (else|->3:int)}
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inv!0 = {(3:int|->1:int), (else|->1:int)}
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reason for last failure: 7 (7 = quantifiers)
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array_example1
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prove: store(a1, i1, v1) = store(a2, i2, v2) implies (i1 = i3 or i2 = i3 or select(a1, i3) = select(a2, i3))
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(implies (= (store a1 i1 v1) (store a2 i2 v2))
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(or (= i1 i3) (= i2 i3) (= (select a1 i3) (select a2 i3))))
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valid
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array_example2
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n = 2
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(distinct k!0 k!1)
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sat
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#0 = (define as-array[k!0] (Array Bool Bool))
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#1 = (define as-array[k!1] (Array Bool Bool))
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function interpretations:
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#0 = {((define false Bool)|->(define true Bool)), (else|->(define true Bool))}
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#1 = {((define false Bool)|->(define false Bool)), (else|->(define false Bool))}
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n = 3
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(distinct k!0 k!1 k!2)
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sat
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#0 = (define as-array[k!0] (Array Bool Bool))
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#1 = (define as-array[k!1] (Array Bool Bool))
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#2 = (define as-array[k!2] (Array Bool Bool))
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function interpretations:
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#0 = {((define true Bool)|->(define true Bool)), ((define false Bool)|->(define false Bool)), (else|->(define true Bool))}
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#1 = {((define false Bool)|->(define true Bool)), (else|->(define true Bool))}
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#2 = {((define true Bool)|->(define false Bool)), ((define false Bool)|->(define false Bool)), (else|->(define false Bool))}
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n = 4
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(distinct k!0 k!1 k!2 k!3)
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sat
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#0 = (define as-array[k!0] (Array Bool Bool))
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#1 = (define as-array[k!1] (Array Bool Bool))
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#2 = (define as-array[k!2] (Array Bool Bool))
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#3 = (define as-array[k!3] (Array Bool Bool))
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function interpretations:
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#0 = {((define true Bool)|->(define false Bool)), ((define false Bool)|->(define true Bool)), (else|->(define false Bool))}
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#1 = {((define true Bool)|->(define true Bool)), ((define false Bool)|->(define false Bool)), (else|->(define true Bool))}
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#2 = {((define true Bool)|->(define true Bool)), ((define false Bool)|->(define true Bool)), (else|->(define true Bool))}
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#3 = {((define true Bool)|->(define false Bool)), ((define false Bool)|->(define false Bool)), (else|->(define false Bool))}
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n = 5
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(distinct k!0 k!1 k!2 k!3 k!4)
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unsat
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array_example3
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domain: int
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range: bool
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tuple_example1
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tuple_sort: (real, real)
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prove: get_x(mk_pair(x, y)) = 1 implies x = 1
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valid
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disprove: get_x(mk_pair(x, y)) = 1 implies y = 1
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invalid
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counterexample:
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y -> 0
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x -> 1
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prove: get_x(p1) = get_x(p2) and get_y(p1) = get_y(p2) implies p1 = p2
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valid
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disprove: get_x(p1) = get_x(p2) implies p1 = p2
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invalid
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counterexample:
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p1 -> (mk_pair 1 0)
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p2 -> (mk_pair 1 2)
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prove: p2 = update(p1, 0, 10) implies get_x(p2) = 10
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valid
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disprove: p2 = update(p1, 0, 10) implies get_y(p2) = 10
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invalid
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counterexample:
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p2 -> (mk_pair 10 1)
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p1 -> (mk_pair 0 1)
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bitvector_example1
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disprove: x - 10 <= 0 IFF x <= 10 for (32-bit) machine integers
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invalid
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counterexample:
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x -> bv2147483656[32]
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bitvector_example2
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find values of x and y, such that x ^ y - 103 == x * y
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sat
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y -> bv3905735879[32]
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x -> bv3787456528[32]
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eval_example1
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MODEL:
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y -> 4
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x -> 3
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evaluating x+y
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result = 7:int
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two_contexts_example1
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k!0
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error_code_example1
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last call succeeded.
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last call failed.
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error_code_example2
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before Z3_mk_iff
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Z3 error: type error.
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parser_example1
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formula 0: (> x y)
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formula 1: (> x 0)
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sat
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y -> 0
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x -> 1
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parser_example2
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formula: (> x y)
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sat
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y -> -1
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x -> 0
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parser_example3
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assert axiom:
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(forall (x Int) (y Int) (= (g x y) (g y x)) :qid {k!1})
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formula: (forall (x Int) (y Int) (implies (= x y) (= (g x 0) (g 0 y))) :qid {k!1})
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valid
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parser_example4
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declaration 0: (define y Int)
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declaration 1: (define sk_hack Bool Bool)
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declaration 2: (define x Int)
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assumption 0: (= x 20)
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formula 0: (> x y)
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formula 1: (> x 0)
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parser_example5
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Z3 error: parser error.
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Error message: 'ERROR: line 1 column 41: could not find sort symbol 'y'.
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'.
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ite_example
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term: (if false 1 0)
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enum_example
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(define apple[fruit:0] fruit)
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(define banana[fruit:1] fruit)
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(define orange[fruit:2] fruit)
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(define is_apple[fruit:0] fruit Bool)
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(define is_banana[fruit:1] fruit Bool)
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(define is_orange[fruit:2] fruit Bool)
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valid
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valid
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invalid
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counterexample:
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valid
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valid
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unsat_core_and_proof_example
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unsat
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proof: [unit-resolution
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[def-axiom (or (or (not PredA) PredC (not PredB)) (not PredC))]
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[unit-resolution
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[def-axiom (or (or (not PredA) (not PredB) (not PredC)) PredC)]
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[unit-resolution
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[mp
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[asserted (or (and PredA PredB PredC) P1)]
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[monotonicity
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[rewrite
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(iff (and PredA PredB PredC)
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(not (or (not PredA) (not PredB) (not PredC))))]
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(iff (or (and PredA PredB PredC) P1)
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(or (not (or (not PredA) (not PredB) (not PredC))) P1))]
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(or (not (or (not PredA) (not PredB) (not PredC))) P1)]
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[asserted (not P1)]
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(not (or (not PredA) (not PredB) (not PredC)))]
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PredC]
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[unit-resolution
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[mp
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[asserted (or (and PredA (not PredC) PredB) P2)]
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[monotonicity
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[rewrite
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(iff (and PredA (not PredC) PredB)
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(not (or (not PredA) PredC (not PredB))))]
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(iff (or (and PredA (not PredC) PredB) P2)
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(or (not (or (not PredA) PredC (not PredB))) P2))]
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(or (not (or (not PredA) PredC (not PredB))) P2)]
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[asserted (not P2)]
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(not (or (not PredA) PredC (not PredB)))]
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false]
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core:
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(not P2)
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(not P1)
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abstract_example
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formula: (> x y)
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abstracted formula: (> #0 y)
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get_implied_equalities example
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Class a |-> 0
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Class b |-> 0
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Class c |-> 0
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Class d |-> 3
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Class (f a) |-> 0
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Class (f b) |-> 0
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Class (f c) |-> 0
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asserting f(a) <= b
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Class a |-> 0
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Class b |-> 0
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Class c |-> 0
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Class d |-> 3
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Class (f a) |-> 0
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Class (f b) |-> 0
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Class (f c) |-> 0
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