## TPTP Axioms File: SWV007+0.ax

```%------------------------------------------------------------------------------
% File     : SWV007+0 : TPTP v8.1.0. Released v3.3.0.
% Domain   : Software Verification
% Axioms   : Priority queue checker: quasi-order set with bottom element
% 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    :    5 (   2 unt;   0 def)
%            Number of atoms       :   10 (   0 equ)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :    6 (   1   ~;   1   |;   2   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    2 (   2 usr;   0 prp; 2-2 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :    9 (   9   !;   0   ?)
% SPC      :

%------------------------------------------------------------------------------
fof(transitivity,axiom,
! [U,V,W] :
( ( less_than(U,V)
& less_than(V,W) )
=> less_than(U,W) ) ).

fof(totality,axiom,
! [U,V] :
( less_than(U,V)
| less_than(V,U) ) ).

fof(reflexivity,axiom,
! [U] : less_than(U,U) ).

fof(stricly_smaller_definition,axiom,
! [U,V] :
( strictly_less_than(U,V)
<=> ( less_than(U,V)
& ~ less_than(V,U) ) ) ).

fof(bottom_smallest,axiom,
! [U] : less_than(bottom,U) ).

%------------------------------------------------------------------------------

```