%------------------------------------------------------------------------------
% File     : SWX204+1 : TPTP v9.3.0. Released v9.3.0.
% Domain   : Software Verification
% Problem  : Faulty property about multiplication of natural numbers
% Version  : Especial.
% English  :

% Refs     : [CST26] Claessen et al. (2026), Email to Geoff Sutcliffe
% Source   : [CST26]
% Names    : Nat_mul_idem.p [CST26]

% Status   : Theorem
% Rating   : 0.00 v9.3.0
% Syntax   : Number of formulae    :    7 (   7 unt;   0 def)
%            Number of atoms       :    7 (   7 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   3 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :    9 (   8   !;   1   ?)
% SPC      : FOF_THM_RFO_PEQ

% Comments :
%------------------------------------------------------------------------------
fof(axiom_001,axiom,
    ! [X] : proj1S(s(X)) = X ).

fof(axiom_002,axiom,
    ! [X] : z != s(X) ).

fof(axiom_003,axiom,
    ! [Y] : x2(z,Y) = Y ).

fof(axiom_004,axiom,
    ! [Y,N] : x2(s(N),Y) = s(x2(N,Y)) ).

fof(axiom_005,axiom,
    ! [Y] : x22(z,Y) = z ).

fof(axiom_006,axiom,
    ! [Y,N] : x22(s(N),Y) = x2(Y,x22(N,Y)) ).

fof(goal_007,conjecture,
    ? [X] : x22(X,X) != X ).

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