%--------------------------------------------------------------------------
% File     : SWC071+1 : TPTP v9.0.0. Released v2.4.0.
% Domain   : Software Creation
% Problem  : cond_id_segment_total2_x_pivot
% Version  : [Wei00] axioms.
% English  : Find components in a software library that match a given target
%            specification given in first-order logic. The components are
%            specified in first-order logic as well. The problem represents
%            a test of one library module specification against a target
%            specification.

% Refs     : [Wei00] Weidenbach (2000), Software Reuse of List Functions Ve
%          : [FSS98] Fischer et al. (1998), Deduction-Based Software Compon
% Source   : [Wei00]
% Names    : cond_id_segment_total2_x_pivot [Wei00]

% Status   : Theorem
% Rating   : 0.52 v9.0.0, 0.53 v7.4.0, 0.40 v7.3.0, 0.52 v7.2.0, 0.48 v7.1.0, 0.52 v7.0.0, 0.50 v6.4.0, 0.54 v6.2.0, 0.64 v6.1.0, 0.67 v6.0.0, 0.65 v5.5.0, 0.74 v5.4.0, 0.68 v5.3.0, 0.70 v5.2.0, 0.65 v5.1.0, 0.67 v5.0.0, 0.62 v4.1.0, 0.61 v4.0.1, 0.65 v4.0.0, 0.62 v3.7.0, 0.65 v3.5.0, 0.63 v3.3.0, 0.57 v3.2.0, 0.55 v3.1.0, 0.67 v2.7.0, 0.50 v2.4.0
% Syntax   : Number of formulae    :   96 (   9 unt;   0 def)
%            Number of atoms       :  419 (  79 equ)
%            Maximal formula atoms :   25 (   4 avg)
%            Number of connectives :  353 (  30   ~;  16   |;  47   &)
%                                         (  26 <=>; 234  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   20 (  19 usr;   0 prp; 1-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :  213 ( 197   !;  16   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments :
%--------------------------------------------------------------------------
%----Include list specification axioms
include('Axioms/SWC001+0.ax').
%--------------------------------------------------------------------------
fof(co1,conjecture,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ! [X] :
                  ( ssList(X)
                 => ( V != X
                    | U != W
                    | ? [Y] :
                        ( ssList(Y)
                        & neq(Y,nil)
                        & segmentP(V,Y)
                        & segmentP(U,Y) )
                    | ( nil = V
                      & nil = U )
                    | ( ! [Z] :
                          ( ssItem(Z)
                         => ! [X1] :
                              ( ssList(X1)
                             => ! [X2] :
                                  ( ssList(X2)
                                 => ( cons(Z,nil) != W
                                    | app(app(X1,W),X2) != X
                                    | ? [X3] :
                                        ( ssItem(X3)
                                        & memberP(X1,X3)
                                        & lt(Z,X3) )
                                    | ? [X4] :
                                        ( ssItem(X4)
                                        & memberP(X2,X4)
                                        & lt(X4,Z) ) ) ) ) )
                      & ( nil != X
                        | nil != W ) ) ) ) ) ) ) ).

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