%------------------------------------------------------------------------------
% File     : SWV413+1 : TPTP v8.2.0. Released v3.3.0.
% Domain   : Software Verification
% Problem  : Priority queue checker: lemma_contains_update_02
% 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    : cpq_l049 [Pis06]

% Status   : Theorem
% Rating   : 0.03 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.08 v6.2.0, 0.16 v6.1.0, 0.07 v6.0.0, 0.09 v5.5.0, 0.04 v5.4.0, 0.07 v5.3.0, 0.15 v5.2.0, 0.05 v5.0.0, 0.08 v4.1.0, 0.13 v4.0.0, 0.12 v3.7.0, 0.15 v3.5.0, 0.16 v3.4.0, 0.11 v3.3.0
% Syntax   : Number of formulae    :   20 (   9 unt;   0 def)
%            Number of atoms       :   42 (  12 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   28 (   6   ~;   3   |;   9   &)
%                                         (   3 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   0 prp; 1-3 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-2 aty)
%            Number of variables   :   56 (  55   !;   1   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments :
%------------------------------------------------------------------------------
%----Include the axioms about priority queues and checked priority queues
include('Axioms/SWV007+0.ax').
include('Axioms/SWV007+2.ax').
%------------------------------------------------------------------------------
%----tmp_not_check_03_2 (cpq_l036.p, cpq_l037.p)
fof(l49_li3637,lemma,
    ! [U,V,W,X] :
      ( ( pair_in_list(U,V,W)
        & less_than(X,W) )
     => pair_in_list(update_slb(U,X),V,W) ) ).

%----lemma_contains_update_02 (conjecture)
fof(l49_co,conjecture,
    ! [U,V,W,X] :
      ( ( pair_in_list(U,V,W)
        & strictly_less_than(V,X)
        & less_than(X,W) )
     => ? [Y] :
          ( pair_in_list(update_slb(U,X),V,Y)
          & less_than(X,Y) ) ) ).

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