%------------------------------------------------------------------------------
% File     : SWV389+1 : TPTP v9.0.0. Released v3.3.0.
% Domain   : Software Verification
% Problem  : Priority queue checker: lemma_not_min_elem_not_check_ind_steps 4
% 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_l025 [Pis06]

% Status   : Theorem
% Rating   : 0.03 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.08 v6.3.0, 0.04 v6.2.0, 0.12 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.04 v5.4.0, 0.14 v5.3.0, 0.15 v5.2.0, 0.05 v5.1.0, 0.10 v5.0.0, 0.12 v4.1.0, 0.17 v4.0.0, 0.21 v3.7.0, 0.30 v3.5.0, 0.47 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   :  123 ( 123   !;   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_04 (cpq_l040.p)
fof(l25_l40,lemma,
    ! [U,V,W] :
      ( ( check_cpq(removemin_cpq_eff(triple(U,V,W)))
        & ok(removemin_cpq_eff(triple(U,V,W))) )
     => check_cpq(triple(U,V,W)) ) ).

%----step4: removemin (conjecture)
fof(l25_co,conjecture,
    ! [U,V,W] :
      ( ~ check_cpq(triple(U,V,W))
     => ( ~ check_cpq(removemin_cpq_eff(triple(U,V,W)))
        | ~ ok(removemin_cpq_eff(triple(U,V,W))) ) ) ).

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