%------------------------------------------------------------------------------
% File     : SWX200+1 : TPTP v9.3.0. Released v9.3.0.
% Domain   : Software Verification
% Problem  : Faulty property about merge
% Version  : Especial.
% English  :

% Refs     : [CST26] Claessen et al. (2026), Email to Geoff Sutcliffe
% Source   : [CST26]
% Names    : MergeSort_prop_merge_ord_not3.p [CST26]

% Status   : Theorem
% Rating   : 0.22 v9.3.0
% Syntax   : Number of formulae    :   16 (  11 unt;   0 def)
%            Number of atoms       :   23 (   9 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   13 (   6   ~;   0   |;   1   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   0 prp; 1-2 aty)
%            Number of functors    :    8 (   8 usr;   2 con; 0-2 aty)
%            Number of variables   :   29 (  27   !;   2   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments :
%------------------------------------------------------------------------------
fof(axiom_001,axiom,
    ! [X,X2] : head(cons(X,X2)) = X ).

fof(axiom_002,axiom,
    ! [X,X2] : tail(cons(X,X2)) = X2 ).

fof(axiom_003,axiom,
    ! [X,X2] : nil != cons(X,X2) ).

fof(axiom_004,axiom,
    ! [X] : proj1S(s(X)) = X ).

fof(axiom_005,axiom,
    ! [X] : z != s(X) ).

fof(axiom_006,axiom,
    ! [Y] : leqNat(z,Y) ).

fof(axiom_007,axiom,
    ! [Z] : ~ leqNat(s(Z),z) ).

fof(axiom_008,axiom,
    ! [Z,M] :
      ( leqNat(s(Z),s(M))
    <=> leqNat(Z,M) ) ).

fof(axiom_009,axiom,
    ! [Y] : merge(nil,Y) = Y ).

fof(axiom_010,axiom,
    ! [Z,Xs] : merge(cons(Z,Xs),nil) = cons(Z,Xs) ).

fof(axiom_011,axiom,
    ! [Z,Xs,Y2,Ys] :
      ( leqNat(Z,Y2)
     => merge(cons(Z,Xs),cons(Y2,Ys)) = cons(Z,merge(Xs,cons(Y2,Ys))) ) ).

fof(axiom_012,axiom,
    ! [Z,Xs,Y2,Ys] :
      ( ~ leqNat(Z,Y2)
     => merge(cons(Z,Xs),cons(Y2,Ys)) = cons(Y2,merge(cons(Z,Xs),Ys)) ) ).

fof(axiom_013,axiom,
    ord(nil) ).

fof(axiom_014,axiom,
    ! [Y] : ord(cons(Y,nil)) ).

fof(axiom_015,axiom,
    ! [Y,Y2,Xs] :
      ( ord(cons(Y,cons(Y2,Xs)))
    <=> ( leqNat(Y,Y2)
        & ord(cons(Y2,Xs)) ) ) ).

fof(goal_016,conjecture,
    ? [Xs,Ys] :
      ~ ( ord(Xs)
       => ( ~ ord(Ys)
         => ord(merge(Xs,Ys)) ) ) ).

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