%------------------------------------------------------------------------------
% File     : ITP002_5 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 set theory export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : min_2.ax [Gau20]
%          : HL4002_5.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   16 (   6 unt;   7 typ;   0 def)
%            Number of atoms       :   38 (   4 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :    8 (   0   ~;   0   |;   0   &)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :   21 (  21 fml;   0 var)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    6 (   5   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   6 usr;   2 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-2 aty)
%            Number of variables   :   12 (  12   !;   0   ?;  12   :)
% SPC      : TF0_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
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_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(tp_c_2Emin_2E_3D_3D_3E,type,
    c_2Emin_2E_3D_3D_3E: $i ).

tff(mem_c_2Emin_2E_3D_3D_3E,axiom,
    mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))) ).

tff(stp_fo_c_2Emin_2E_3D_3D_3E,type,
    fo__c_2Emin_2E_3D_3D_3E: ( tp__o * tp__o ) > tp__o ).

tff(stp_eq_fo_c_2Emin_2E_3D_3D_3E,axiom,
    ! [X0: tp__o,X1: tp__o] : ( inj__o(fo__c_2Emin_2E_3D_3D_3E(X0,X1)) = ap(ap(c_2Emin_2E_3D_3D_3E,inj__o(X0)),inj__o(X1)) ) ).

tff(ax_imp_p,axiom,
    ! [Q: $i] :
      ( mem(Q,bool)
     => ! [R: $i] :
          ( mem(R,bool)
         => ( p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R))
          <=> ( p(Q)
             => p(R) ) ) ) ) ).

tff(tp_c_2Emin_2E_40,type,
    c_2Emin_2E_40: del > $i ).

tff(mem_c_2Emin_2E_40,axiom,
    ! [A_27a: del] : mem(c_2Emin_2E_40(A_27a),arr(arr(A_27a,bool),A_27a)) ).

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