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Diffstat (limited to 'unit-tests/Tests_zchaff_tactics.v')
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diff --git a/unit-tests/Tests_zchaff_tactics.v b/unit-tests/Tests_zchaff_tactics.v new file mode 100644 index 0000000..c6ed4e3 --- /dev/null +++ b/unit-tests/Tests_zchaff_tactics.v @@ -0,0 +1,397 @@ +(**************************************************************************) +(* *) +(* SMTCoq *) +(* Copyright (C) 2011 - 2019 *) +(* *) +(* See file "AUTHORS" for the list of authors *) +(* *) +(* This file is distributed under the terms of the CeCILL-C licence *) +(* *) +(**************************************************************************) + + +Add Rec LoadPath "../src" as SMTCoq. + +Require Import SMTCoq. +Require Import Bool PArray Int63 List ZArith. + +Local Open Scope int63_scope. + + +(* First a tactic, to test the universe computation in an empty + environment. *) + +Lemma check_univ (x1: bool): + (x1 && (negb x1)) = false. +Proof. + zchaff. +Qed. + + +(* zChaff tactic *) + +Goal forall a, a || negb a. + zchaff. +Qed. + +Goal forall a, negb (a || negb a) = false. + zchaff. +Qed. + +Goal forall a, negb (negb (a || negb a)). + zchaff. +Qed. + +Goal forall a, (a && negb a) = false. + zchaff. +Qed. + +Goal forall a, negb (a && negb a). + zchaff. +Qed. + +Goal forall a, implb a a. + zchaff. +Qed. + +Goal forall a, negb (implb a a) = false. + zchaff. +Qed. + +Goal forall a , (xorb a a) || negb (xorb a a). + zchaff. +Qed. + +Goal forall a, (a||negb a) || negb (a||negb a). + zchaff. +Qed. + +Goal true. + zchaff. +Qed. + +Goal negb false. + zchaff. +Qed. + +Goal forall a, Bool.eqb a a. +Proof. + zchaff. +Qed. + +Goal forall (a:bool), a = a. + zchaff. +Qed. + + +(* sat2.smt *) +(* ((a ∧ b) ∨ (b ∧ c)) ∧ ¬b = ⊥ *) + +Goal forall a b c, (((a && b) || (b && c)) && (negb b)) = false. +Proof. + zchaff. +Qed. + + +(* sat3.smt *) +(* (a ∨ a) ∧ ¬a = ⊥ *) + +Goal forall a, ((a || a) && (negb a)) = false. +Proof. + zchaff. +Qed. + + +(* sat4.smt *) +(* ¬(a ∨ ¬a) = ⊥ *) + +Goal forall a, (negb (a || (negb a))) = false. +Proof. + zchaff. +Qed. + + +(* sat5.smt *) +(* (a ∨ b ∨ c) ∧ (¬a ∨ ¬b ∨ ¬c) ∧ (¬a ∨ b) ∧ (¬b ∨ c) ∧ (¬c ∨ a) = ⊥ *) + +Goal forall a b c, + (a || b || c) && ((negb a) || (negb b) || (negb c)) && ((negb a) || b) && ((negb b) || c) && ((negb c) || a) = false. +Proof. + zchaff. +Qed. + + +(* The same, but with a, b and c being concrete terms *) + +Goal forall i j k, + ((i == j) || (j == k) || (k == i)) && ((negb (i == j)) || (negb (j == k)) || (negb (k == i))) && ((negb (i == j)) || (j == k)) && ((negb (j == k)) || (k == i)) && ((negb (k == i)) || (i == j)) = false. +Proof. + zchaff. +Qed. + +Goal forall i j k, + let a := i == j in + let b := j == k in + let c := k == i in + (a || b || c) && ((negb a) || (negb b) || (negb c)) && ((negb a) || b) && ((negb b) || c) && ((negb c) || a) = false. +Proof. + zchaff. +Qed. + + +(* sat6.smt *) +(* (a ∧ b) ∧ (c ∨ d) ∧ ¬(c ∨ (a ∧ b ∧ d)) = ⊥ *) + +Goal forall a b c d, ((a && b) && (c || d) && (negb (c || (a && b && d)))) = false. +Proof. + zchaff. +Qed. + + +(* sat7.smt *) +(* a ∧ b ∧ c ∧ (¬a ∨ ¬b ∨ d) ∧ (¬d ∨ ¬c) = ⊥ *) + +Goal forall a b c d, (a && b && c && ((negb a) || (negb b) || d) && ((negb d) || (negb c))) = false. +Proof. + zchaff. +Qed. + + +(* Other connectives *) + +Goal (false || true) && false = false. +Proof. + zchaff. +Qed. + + +Goal negb true = false. +Proof. + zchaff. +Qed. + + +Goal false = false. +Proof. + zchaff. +Qed. + + +Goal forall x y, Bool.eqb (xorb x y) ((x && (negb y)) || ((negb x) && y)). +Proof. + zchaff. +Qed. + + +Goal forall x y, Bool.eqb (implb x y) ((x && y) || (negb x)). +Proof. + zchaff. +Qed. + + +Goal forall x y z, Bool.eqb (ifb x y z) ((x && y) || ((negb x) && z)). +Proof. + zchaff. +Qed. + + +(* Multiple negations *) + +Goal forall a, orb a (negb (negb (negb a))) = true. +Proof. + zchaff. +Qed. + + +(* Polarities *) + +Goal forall a b, andb (orb a b) (negb (orb a b)) = false. +Proof. + zchaff. +Qed. + + +Goal forall a b, andb (orb a b) (andb (negb a) (negb b)) = false. +Proof. + zchaff. +Qed. + + +(* Pigeon hole: 4 holes, 5 pigeons. xij stands for "pidgeon i goes to + hole j". *) + +Goal forall x11 x12 x13 x14 x15 x21 x22 x23 x24 x25 x31 x32 x33 x34 x35 x41 x42 x43 x44 x45, ( + (orb (negb x11) (negb x21)) && + (orb (negb x11) (negb x31)) && + (orb (negb x11) (negb x41)) && + (orb (negb x21) (negb x31)) && + (orb (negb x21) (negb x41)) && + (orb (negb x31) (negb x41)) && + + (orb (negb x12) (negb x22)) && + (orb (negb x12) (negb x32)) && + (orb (negb x12) (negb x42)) && + (orb (negb x22) (negb x32)) && + (orb (negb x22) (negb x42)) && + (orb (negb x32) (negb x42)) && + + (orb (negb x13) (negb x23)) && + (orb (negb x13) (negb x33)) && + (orb (negb x13) (negb x43)) && + (orb (negb x23) (negb x33)) && + (orb (negb x23) (negb x43)) && + (orb (negb x33) (negb x43)) && + + (orb (negb x14) (negb x24)) && + (orb (negb x14) (negb x34)) && + (orb (negb x14) (negb x44)) && + (orb (negb x24) (negb x34)) && + (orb (negb x24) (negb x44)) && + (orb (negb x34) (negb x44)) && + + (orb (negb x15) (negb x25)) && + (orb (negb x15) (negb x35)) && + (orb (negb x15) (negb x45)) && + (orb (negb x25) (negb x35)) && + (orb (negb x25) (negb x45)) && + (orb (negb x35) (negb x45)) && + + + (orb (negb x11) (negb x12)) && + (orb (negb x11) (negb x13)) && + (orb (negb x11) (negb x14)) && + (orb (negb x11) (negb x15)) && + (orb (negb x12) (negb x13)) && + (orb (negb x12) (negb x14)) && + (orb (negb x12) (negb x15)) && + (orb (negb x13) (negb x14)) && + (orb (negb x13) (negb x15)) && + (orb (negb x14) (negb x15)) && + + (orb (negb x21) (negb x22)) && + (orb (negb x21) (negb x23)) && + (orb (negb x21) (negb x24)) && + (orb (negb x21) (negb x25)) && + (orb (negb x22) (negb x23)) && + (orb (negb x22) (negb x24)) && + (orb (negb x22) (negb x25)) && + (orb (negb x23) (negb x24)) && + (orb (negb x23) (negb x25)) && + (orb (negb x24) (negb x25)) && + + (orb (negb x31) (negb x32)) && + (orb (negb x31) (negb x33)) && + (orb (negb x31) (negb x34)) && + (orb (negb x31) (negb x35)) && + (orb (negb x32) (negb x33)) && + (orb (negb x32) (negb x34)) && + (orb (negb x32) (negb x35)) && + (orb (negb x33) (negb x34)) && + (orb (negb x33) (negb x35)) && + (orb (negb x34) (negb x35)) && + + (orb (negb x41) (negb x42)) && + (orb (negb x41) (negb x43)) && + (orb (negb x41) (negb x44)) && + (orb (negb x41) (negb x45)) && + (orb (negb x42) (negb x43)) && + (orb (negb x42) (negb x44)) && + (orb (negb x42) (negb x45)) && + (orb (negb x43) (negb x44)) && + (orb (negb x43) (negb x45)) && + (orb (negb x44) (negb x45)) && + + + (orb (orb (orb x11 x21) x31) x41) && + (orb (orb (orb x12 x22) x32) x42) && + (orb (orb (orb x13 x23) x33) x43) && + (orb (orb (orb x14 x24) x34) x44) && + (orb (orb (orb x15 x25) x35) x45)) = false. +Proof. + zchaff. +Qed. + + +(* Counter examples *) + +(* +Goal forall x, x && (negb x). +Proof. + zchaff. +Abort. + +Goal forall x y, (implb (implb x y) (implb y x)). +Proof. + zchaff. +Abort. + +(* Pigeon hole: 4 holes, 4 pigeons. xij stands for "pidgeon i goes to + hole j". *) + +Goal forall x11 x12 x13 x14 x21 x22 x23 x24 x31 x32 x33 x34 x41 x42 x43 x44, ( + (orb (negb x11) (negb x21)) && + (orb (negb x11) (negb x31)) && + (orb (negb x11) (negb x41)) && + (orb (negb x21) (negb x31)) && + (orb (negb x21) (negb x41)) && + (orb (negb x31) (negb x41)) && + + (orb (negb x12) (negb x22)) && + (orb (negb x12) (negb x32)) && + (orb (negb x12) (negb x42)) && + (orb (negb x22) (negb x32)) && + (orb (negb x22) (negb x42)) && + (orb (negb x32) (negb x42)) && + + (orb (negb x13) (negb x23)) && + (orb (negb x13) (negb x33)) && + (orb (negb x13) (negb x43)) && + (orb (negb x23) (negb x33)) && + (orb (negb x23) (negb x43)) && + (orb (negb x33) (negb x43)) && + + (orb (negb x14) (negb x24)) && + (orb (negb x14) (negb x34)) && + (orb (negb x14) (negb x44)) && + (orb (negb x24) (negb x34)) && + (orb (negb x24) (negb x44)) && + (orb (negb x34) (negb x44)) && + + + (orb (negb x11) (negb x12)) && + (orb (negb x11) (negb x13)) && + (orb (negb x11) (negb x14)) && + (orb (negb x12) (negb x13)) && + (orb (negb x12) (negb x14)) && + (orb (negb x13) (negb x14)) && + + (orb (negb x21) (negb x22)) && + (orb (negb x21) (negb x23)) && + (orb (negb x21) (negb x24)) && + (orb (negb x22) (negb x23)) && + (orb (negb x22) (negb x24)) && + (orb (negb x23) (negb x24)) && + + (orb (negb x31) (negb x32)) && + (orb (negb x31) (negb x33)) && + (orb (negb x31) (negb x34)) && + (orb (negb x32) (negb x33)) && + (orb (negb x32) (negb x34)) && + (orb (negb x33) (negb x34)) && + + (orb (negb x41) (negb x42)) && + (orb (negb x41) (negb x43)) && + (orb (negb x41) (negb x44)) && + (orb (negb x42) (negb x43)) && + (orb (negb x42) (negb x44)) && + (orb (negb x43) (negb x44)) && + + + (orb (orb (orb x11 x21) x31) x41) && + (orb (orb (orb x12 x22) x32) x42) && + (orb (orb (orb x13 x23) x33) x43) && + (orb (orb (orb x14 x24) x34) x44)) = false. +Proof. + zchaff. +Abort. +*) |