%------------------------------------------------------------------------------
% File     : ITP001_20 : TPTP v9.0.0. Released v8.2.0.
% Domain   : Interactive Theorem Proving
% Problem  : HOL4 set theory export of thm_2Ebool_2ETRUTH.p, bushy mode
% Version  : ITP001_2 with the conjecture removed
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [TPTP]
% Names    : 
%          : HL400001_2.p [TPAP]

% Status   : Satisfiable
% Rating   : 0.00 v8.2.0
% Syntax   : Number of formulae    :   29 (   6 unt;  15 typ;   0 def)
%            Number of atoms       :   54 (  10 equ)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :   17 (   0   ~;   0   |;   0   &)
%                                         (   3 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :   23 (  23 fml;   0 var)
%            Number of types       :    4 (   2 usr)
%            Number of type conns  :   13 (   9   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   2 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   4 con; 0-2 aty)
%            Number of variables   :   23 (  23   !;   0   ?;  23   :)
% SPC      : TX0_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP001_2.ax').
%------------------------------------------------------------------------------
tff(stp_o,type,
    tp__o: $tType ).

tff(stp_inj_o,type,
    inj__o: tp__o > $i ).

tff(stp_surj_o,type,
    surj__o: $i > tp__o ).

tff(stp_inj_surj_o,axiom,
    ! [X: tp__o] : ( surj__o(inj__o(X)) = X ) ).

tff(stp_inj_mem_o,axiom,
    ! [X: tp__o] : mem(inj__o(X),bool) ).

tff(stp_iso_mem_o,axiom,
    ! [X: $i] :
      ( mem(X,bool)
     => ( X = inj__o(surj__o(X)) ) ) ).

tff(tp_c_2Ebool_2ET,type,
    c_2Ebool_2ET: $i ).

tff(mem_c_2Ebool_2ET,axiom,
    mem(c_2Ebool_2ET,bool) ).

tff(stp_fo_c_2Ebool_2ET,type,
    fo__c_2Ebool_2ET: tp__o ).

tff(stp_eq_fo_c_2Ebool_2ET,axiom,
    inj__o(fo__c_2Ebool_2ET) = c_2Ebool_2ET ).

tff(ax_true_p,axiom,
    p(c_2Ebool_2ET) ).

tff(tp_c_2Emin_2E_3D,type,
    c_2Emin_2E_3D: del > $i ).

tff(mem_c_2Emin_2E_3D,axiom,
    ! [A_27a: del] : mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))) ).

tff(ax_eq_p,axiom,
    ! [A: del,X: $i] :
      ( mem(X,A)
     => ! [Y: $i] :
          ( mem(Y,A)
         => ( p(ap(ap(c_2Emin_2E_3D(A),X),Y))
          <=> ( X = Y ) ) ) ) ).

tff(ax_thm_2Ebool_2ET__DEF,axiom,
    ( $true
  <=> ( i(bool) = i(bool) ) ) ).

% tff(conj_thm_2Ebool_2ETRUTH,conjecture,
%     $true ).

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