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const x: int;
const y: int;
const z: int;
const r: real;
const s: real;
const t: real;
const P: bool;
const Q: bool;
const R: bool;
axiom x * (y + z) == x + y * z;
axiom x * y + z == (x + y) * z;
axiom x * y * z == x * y * z;
axiom x * y * z * x == x * y * z;
axiom x div y div z == x div (y div z);
axiom x div y div (z div x) == x div y div z;
axiom x + y mod z == y mod z + x;
axiom (x + y) mod z == x mod z + y mod z;
axiom x / y / z == x / (y / z);
axiom x / y / (z / x) == x / y / z;
axiom x / s / z == x / (s / z);
axiom x / s / (z / x) == x / s / z;
axiom r / s / t == r / (s / t);
axiom r / s / (t / r) == r / s / t;
axiom r * s / t == r * s / t;
axiom r / s * t == r / s * t;
axiom (r * s) ** t == r ** t * s ** t;
axiom r ** (s + t) == r ** s * r ** t;
axiom int(real(x)) == x;
axiom r >= 0e0 ==> real(int(r)) <= r;
axiom int(0e0 - 2e-2) == 0;
axiom int(0e0 - 35e0) == -35;
axiom int(27e-1) == 2;
axiom x - y - z == x - (y - z);
axiom x - y - (z - x) == x - y - z;
axiom x + y - z - x + y == 0;
axiom x + y - z - x + y == x + y - (z - (x + y));
axiom P ==> Q ==> R <==> P ==> Q ==> R;
axiom (P ==> Q) ==> R ==> P <==> (P ==> Q) ==> R;
axiom P <==> Q <==> R;
axiom P ==> Q <==> Q ==> R <==> R ==> P;
axiom (P && Q) || (Q && R);
axiom (P || Q) && (Q || R);
axiom P || Q || Q || R;
axiom P && Q && Q && R;
function f(int) : int;
axiom (forall x: int :: {:xname "hello"} {:weight 5} {:ValueFunc f(x + 1)} { f(x + x) } { f(x) * f(x) } {:nopats f(x + x + x) } f(f(x)) < 200);
Boogie program verifier finished with 0 verified, 0 errors
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