%--------------------------------------------------------------------------
% File     : SWC326+1 : TPTP v9.0.0. Released v2.4.0.
% Domain   : Software Creation
% Problem  : cond_run_eq_front2_x_run_eq_front1
% 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_run_eq_front2_x_run_eq_front1 [Wei00]

% Status   : Theorem
% Rating   : 1.00 v2.4.0
% Syntax   : Number of formulae    :   96 (   9 unt;   0 def)
%            Number of atoms       :  417 (  78 equ)
%            Maximal formula atoms :   23 (   4 avg)
%            Number of connectives :  352 (  31   ~;  15   |;  46   &)
%                                         (  26 <=>; 234  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   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   :  212 ( 197   !;  15   ?)
% 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
                    | ~ frontsegP(X,W)
                    | ~ equalelemsP(W)
                    | ? [Y] :
                        ( ssList(Y)
                        & neq(W,Y)
                        & frontsegP(X,Y)
                        & segmentP(Y,W)
                        & equalelemsP(Y) )
                    | ( ? [Z] :
                          ( ssList(Z)
                          & app(U,Z) = V
                          & ! [X1] :
                              ( ssItem(X1)
                             => ! [X2] :
                                  ( ssList(X2)
                                 => ( app(cons(X1,nil),X2) != Z
                                    | ! [X3] :
                                        ( ssList(X3)
                                       => app(X3,cons(X1,nil)) != U ) ) ) )
                          & equalelemsP(U) )
                      & ( nil != U
                        | nil = V ) ) ) ) ) ) ) ).

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