%------------------------------------------------------------------------------
% File     : ITP006_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    : normalForms_2.ax [Gau20]
%          : HL4006_5.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :    8 (   2 unt;   2 typ;   0 def)
%            Number of atoms       :   51 (   4 equ)
%            Maximal formula atoms :    4 (   6 avg)
%            Number of connectives :   12 (   0   ~;   0   |;   0   &)
%                                         (   2 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :   33 (  33 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   6 usr;   2 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   0 con; 1-2 aty)
%            Number of variables   :   17 (  17   !;   0   ?;  17   :)
% SPC      : TF0_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tp_c_2EnormalForms_2EEXT__POINT,type,
    c_2EnormalForms_2EEXT__POINT: ( del * del ) > $i ).

tff(mem_c_2EnormalForms_2EEXT__POINT,axiom,
    ! [A_27a: del,A_27b: del] : mem(c_2EnormalForms_2EEXT__POINT(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,A_27b),A_27a))) ).

tff(tp_c_2EnormalForms_2EUNIV__POINT,type,
    c_2EnormalForms_2EUNIV__POINT: del > $i ).

tff(mem_c_2EnormalForms_2EUNIV__POINT,axiom,
    ! [A_27a: del] : mem(c_2EnormalForms_2EUNIV__POINT(A_27a),arr(arr(A_27a,bool),A_27a)) ).

tff(ax_thm_2EnormalForms_2EEXT__POINT__DEF,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( mem(V0f,arr(A_27a,A_27b))
     => ! [V1g: $i] :
          ( mem(V1g,arr(A_27a,A_27b))
         => ( ( ap(V0f,ap(ap(c_2EnormalForms_2EEXT__POINT(A_27a,A_27b),V0f),V1g)) = ap(V1g,ap(ap(c_2EnormalForms_2EEXT__POINT(A_27a,A_27b),V0f),V1g)) )
           => ( V0f = V1g ) ) ) ) ).

tff(conj_thm_2EnormalForms_2EEXT__POINT,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( mem(V0f,arr(A_27a,A_27b))
     => ! [V1g: $i] :
          ( mem(V1g,arr(A_27a,A_27b))
         => ( ( ap(V0f,ap(ap(c_2EnormalForms_2EEXT__POINT(A_27a,A_27b),V0f),V1g)) = ap(V1g,ap(ap(c_2EnormalForms_2EEXT__POINT(A_27a,A_27b),V0f),V1g)) )
          <=> ( V0f = V1g ) ) ) ) ).

tff(ax_thm_2EnormalForms_2EUNIV__POINT__DEF,axiom,
    ! [A_27a: del,V0p: $i] :
      ( mem(V0p,arr(A_27a,bool))
     => ( p(ap(V0p,ap(c_2EnormalForms_2EUNIV__POINT(A_27a),V0p)))
       => ! [V1x: $i] :
            ( mem(V1x,A_27a)
           => p(ap(V0p,V1x)) ) ) ) ).

tff(conj_thm_2EnormalForms_2EUNIV__POINT,axiom,
    ! [A_27a: del,V0p: $i] :
      ( mem(V0p,arr(A_27a,bool))
     => ( p(ap(V0p,ap(c_2EnormalForms_2EUNIV__POINT(A_27a),V0p)))
      <=> ! [V1x: $i] :
            ( mem(V1x,A_27a)
           => p(ap(V0p,V1x)) ) ) ) ).

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