## TPTP Axioms File: SWV007+4.ax

```%------------------------------------------------------------------------------
% File     : SWV007+4 : TPTP v7.5.0. Released v3.3.0.
% Domain   : Software Verification
% Axioms   : Priority queue checker: implementation function, Pi, Pi#
% Version  : [dNP05] axioms.
% English  :

% Refs     : [Pis06] Piskac (2006), Email to Geoff Sutcliffe
%          : [dNP05] de Nivelle & Piskac (2005), Verification of an Off-Lin
% Source   : [Pis06]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of formulae    :    9 (   2 unit)
%            Number of atoms       :   20 (   2 equality)
%            Maximal formula depth :    6 (   5 average)
%            Number of connectives :   11 (   0 ~  ;   0  |;   4  &)
%                                         (   7 <=>;   0 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   13 (   0 propositional; 1-2 arity)
%            Number of functors    :    7 (   2 constant; 0-3 arity)
%            Number of variables   :   21 (   0 singleton;  18 !;   3 ?)
%            Maximal term depth    :    5 (   1 average)
% SPC      :

% Comments : Requires SWV007+0 SWV007+1 SWV007+2 SWV007+3
%------------------------------------------------------------------------------
fof(ax54,axiom,(
! [U,V] : i(triple(U,create_slb,V)) = create_pq )).

fof(ax55,axiom,(
! [U,V,W,X,Y] : i(triple(U,insert_slb(V,pair(X,Y)),W)) = insert_pq(i(triple(U,V,W)),X) )).

%----All below here are definitions
fof(ax56,axiom,(
! [U,V] :
( pi_sharp_remove(U,V)
<=> contains_pq(U,V) ) )).

fof(ax57,axiom,(
! [U,V] :
( pi_remove(U,V)
<=> pi_sharp_remove(i(U),V) ) )).

fof(ax58,axiom,(
! [U,V] :
( pi_sharp_find_min(U,V)
<=> ( contains_pq(U,V)
& issmallestelement_pq(U,V) ) ) )).

fof(ax59,axiom,(
! [U] :
( pi_find_min(U)
<=> ? [V] : pi_sharp_find_min(i(U),V) ) )).

fof(ax60,axiom,(
! [U,V] :
( pi_sharp_removemin(U,V)
<=> ( contains_pq(U,V)
& issmallestelement_pq(U,V) ) ) )).

fof(ax61,axiom,(
! [U] :
( pi_removemin(U)
<=> ? [V] : pi_sharp_find_min(i(U),V) ) )).

fof(ax62,axiom,(
! [U] :
( phi(U)
<=> ? [V] :
( succ_cpq(U,V)
& ok(V)
& check_cpq(V) ) ) )).

%------------------------------------------------------------------------------
```