%------------------------------------------------------------------------------
% File     : SWV387+1 : TPTP v8.2.0. Released v3.3.0.
% Domain   : Software Verification
% Problem  : Priority queue checker: lemma_not_min_elem_not_check_ind_steps 2
% 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_l023 [Pis06]

% Status   : Theorem
% Rating   : 0.06 v7.4.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.2.0, 0.20 v6.1.0, 0.13 v5.5.0, 0.07 v5.4.0, 0.14 v5.3.0, 0.15 v5.2.0, 0.10 v5.0.0, 0.12 v4.1.0, 0.17 v4.0.0, 0.21 v3.7.0, 0.20 v3.5.0, 0.26 v3.4.0, 0.21 v3.3.0
% Syntax   : Number of formulae    :   43 (  16 unt;   0 def)
%            Number of atoms       :   88 (  29 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   61 (  16   ~;   4   |;  13   &)
%                                         (   7 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   18 (  18 usr;   3 con; 0-3 aty)
%            Number of variables   :  125 ( 125   !;   0   ?)
% 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').
include('Axioms/SWV007+3.ax').
%------------------------------------------------------------------------------
%----goal: fof(l21_li2225, lemma, (! [U,V,W] : (~(check_cpq(triple(U,V,W))) =>
%----     (~(check_cpq(im_succ_cpq(triple(U,V,W)))) |
%----    ~(ok(im_succ_cpq(triple(U,V,W)))))))).

%----tmp_not_check_02 (cpq_l027.p)
fof(l23_l027,lemma,
    ! [U,V,W,X] :
      ( ( check_cpq(remove_cpq(triple(U,V,W),X))
        & ok(remove_cpq(triple(U,V,W),X)) )
     => check_cpq(triple(U,V,W)) ) ).

%----step2: remove (conjecture)
fof(l23_co,conjecture,
    ! [U,V,W] :
      ( ~ check_cpq(triple(U,V,W))
     => ! [X] :
          ( ~ check_cpq(remove_cpq(triple(U,V,W),X))
          | ~ ok(remove_cpq(triple(U,V,W),X)) ) ) ).

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