%------------------------------------------------------------------------------
% File     : ITP001+2 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 set theory export, bushy and chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% Source   : [BG+19]
% Names    : HL4001+2.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :    8 (   2 unt;   0 def)
%            Number of atoms       :   22 (   5 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   14 (   0   ~;   0   |;   0   &)
%                                         (   1 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   0 prp; 1-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   18 (  18   !;   0   ?)
% SPC      : FOF_SAT_RFO_SEQ

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(bool_ne,axiom,
    ne(bool) ).

fof(ind_ne,axiom,
    ne(ind) ).

fof(arr_ne,axiom,
    ! [A] :
      ( ne(A)
     => ! [B] :
          ( ne(B)
         => ne(arr(A,B)) ) ) ).

fof(ap_tp,axiom,
    ! [A,B,F] :
      ( mem(F,arr(A,B))
     => ! [X] :
          ( mem(X,A)
         => mem(ap(F,X),B) ) ) ).

fof(boolext,axiom,
    ! [Q] :
      ( mem(Q,bool)
     => ! [R] :
          ( mem(R,bool)
         => ( ( p(Q)
            <=> p(R) )
           => Q = R ) ) ) ).

fof(funcext,axiom,
    ! [A,B,F] :
      ( mem(F,arr(A,B))
     => ! [G] :
          ( mem(G,arr(A,B))
         => ( ! [X] :
                ( mem(X,A)
               => ap(F,X) = ap(G,X) )
           => F = G ) ) ) ).

fof(kbeta,axiom,
    ! [A,Y,X] :
      ( mem(X,A)
     => ap(k(A,Y),X) = Y ) ).

fof(ibeta,axiom,
    ! [A,X] :
      ( mem(X,A)
     => ap(i(A),X) = X ) ).

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