%------------------------------------------------------------------------------
% File     : SWV366+1 : TPTP v8.2.0. Released v3.3.0.
% Domain   : Software Verification
% Problem  : Priority queue checker: lemma_I_s induction
% 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_l002 [Pis06]

% Status   : Theorem
% Rating   : 0.31 v8.2.0, 0.28 v8.1.0, 0.33 v7.5.0, 0.34 v7.4.0, 0.17 v7.3.0, 0.28 v7.2.0, 0.31 v7.1.0, 0.26 v7.0.0, 0.27 v6.3.0, 0.25 v6.2.0, 0.36 v6.1.0, 0.37 v6.0.0, 0.26 v5.5.0, 0.37 v5.4.0, 0.43 v5.3.0, 0.48 v5.2.0, 0.50 v5.1.0, 0.48 v5.0.0, 0.46 v4.1.0, 0.43 v4.0.1, 0.39 v4.0.0, 0.38 v3.7.0, 0.35 v3.5.0, 0.37 v3.4.0, 0.32 v3.3.0
% Syntax   : Number of formulae    :   63 (  23 unt;   0 def)
%            Number of atoms       :  130 (  42 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   83 (  16   ~;   4   |;  21   &)
%                                         (  16 <=>;  26  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   21 (  19 usr;   1 prp; 0-3 aty)
%            Number of functors    :   26 (  26 usr;   4 con; 0-3 aty)
%            Number of variables   :  174 ( 171   !;   3   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments :
%------------------------------------------------------------------------------
%----Include the axioms about priority queues and checked priority queues
include('Axioms/SWV007+0.ax').
include('Axioms/SWV007+1.ax').
include('Axioms/SWV007+2.ax').
include('Axioms/SWV007+3.ax').
include('Axioms/SWV007+4.ax').
%------------------------------------------------------------------------------
%----goal: fof(lemma_I_s, conjecture,
%----    (! [U,V,W,X,Y] : (i(triple(U,W,X)) = i(triple(V,W,Y))))).

%----induction step:
fof(l2_co,conjecture,
    ! [U] :
      ( ! [V,W,X,Y] : i(triple(V,U,X)) = i(triple(W,U,Y))
     => ! [Z,X1,X2,X3,X4,X5] : i(triple(Z,insert_slb(U,pair(X4,X5)),X2)) = i(triple(X1,insert_slb(U,pair(X4,X5)),X3)) ) ).

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