%--------------------------------------------------------------------------
% File     : SWC319+1 : TPTP v8.2.0. Released v2.4.0.
% Domain   : Software Creation
% Problem  : cond_rot_r_total1_x_rot_r_total3
% 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_rot_r_total1_x_rot_r_total3 [Wei00]

% Status   : Theorem
% Rating   : 1.00 v2.4.0
% Syntax   : Number of formulae    :   96 (   9 unt;   0 def)
%            Number of atoms       :  421 (  84 equ)
%            Maximal formula atoms :   27 (   4 avg)
%            Number of connectives :  355 (  30   ~;  14   |;  54   &)
%                                         (  26 <=>; 231  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (   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 ( 194   !;  19   ?)
% 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] :
                        ( ssItem(Y)
                        & ? [Z] :
                            ( ssList(Z)
                            & app(cons(Y,nil),Z) != W
                            & app(Z,cons(Y,nil)) = X ) )
                    | ( nil != W
                      & nil = X )
                    | ( ( nil != V
                        | nil = U )
                      & ( ~ neq(V,nil)
                        | ( ? [X1] :
                              ( ssList(X1)
                              & V = X1
                              & ? [X2] :
                                  ( ssList(X2)
                                  & ? [X3] :
                                      ( ssList(X3)
                                      & tl(U) = X2
                                      & app(X2,X3) = X1
                                      & ? [X4] :
                                          ( ssItem(X4)
                                          & cons(X4,nil) = X3
                                          & hd(U) = X4
                                          & neq(nil,U) )
                                      & neq(nil,U) ) ) )
                          & neq(U,nil) ) ) ) ) ) ) ) ) ).

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