%------------------------------------------------------------------------------
% File     : SYP116_1 : TPTP v9.3.1. Released v9.3.0.
% Domain   : Syntactic
% Problem  : Check correctness of Constraint Refutation rule implementation
% Version  : Especial.
% English  :

% Refs     : [Kru09] Kruglov (2009), Email to Geoff Sutcliffe
% Source   : [Kru09]
% Names    : CR.dfg [Kru09]

% Status   : Unsatisfiable
% Rating   : 0.00 v9.3.0
% Syntax   : Number of formulae    :   11 (   0 unt;   5 typ;   0 def)
%            Number of atoms       :   15 (   1 equ)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   10 (   1   ~;   0   |;   3   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number arithmetic     :   10 (   4 atm;   0 fun;   4 num;   2 var)
%            Number of types       :    2 (   0 usr;   1 ari;   0 dat;   0 cdt)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   3 usr;   2 prp; 0-2 aty)
%            Number of functors    :    3 (   2 usr;   3 con; 0-0 aty)
%            Number of variables   :    2 (   2   !;   0   ?;   2   :)
% SPC      : TF0_UNS_EQU_ARI_NDT

% Comments :
%------------------------------------------------------------------------------
tff(type_npa,type,
    npa: $int ).

tff(type_npb,type,
    npb: $int ).

tff(type_p,type,
    p: $int > $o ).

tff(type_q,type,
    q: $int > $o ).

tff(type_r,type,
    r: $int > $o ).

%----ge(npa,0) & P(npa) → false
tff(ax1,axiom,
    ( ( $greatereq(npa,0)
      & p(npa) )
   => $false ) ).

%----ge(npb,0) → P(npb)
tff(ax2,axiom,
    ( $greatereq(npb,0)
   => p(npb) ) ).

%----ls(npa,0) & Q(npa) → false
tff(ax3,axiom,
    ( ( $less(npa,0)
      & q(npa) )
   => $false ) ).

%----ls(npb,0) → Q(npb)
tff(ax4,axiom,
    ( $less(npb,0)
   => q(npb) ) ).

%----∀x. (¬(npa = npb) ∧ R(x)) → false
tff(ax5,axiom,
    ! [X: $int] :
      ( ( ( npa != npb )
        & r(X) )
     => $false ) ).

%----∀x. true → R(x)
tff(ax6,axiom,
    ! [X: $int] :
      ( $true
     => r(X) ) ).

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