%------------------------------------------------------------------------------
% File     : ITP104_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    : ucord_2.ax [Gau20]
%          : HL4104_5.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   11 (   8 unt;   2 typ;   0 def)
%            Number of atoms       :  181 (   2 equ)
%            Maximal formula atoms :    3 (  16 avg)
%            Number of connectives :    5 (   3   ~;   0   |;   0   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :  170 ( 170 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  17 usr;   3 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   0 con; 1-1 aty)
%            Number of variables   :   11 (  11   !;   0   ?;  11   :)
% SPC      : TF0_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tp_c_2Eucord_2Eomega1,type,
    c_2Eucord_2Eomega1: del > $i ).

tff(mem_c_2Eucord_2Eomega1,axiom,
    ! [A_27a: del] : mem(c_2Eucord_2Eomega1(A_27a),ty_2Eordinal_2Eordinal(ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool)))) ).

tff(conj_thm_2Eucord_2Eucinf__uncountable,axiom,
    ! [A_27a: del] : ~ p(ap(c_2Epred__set_2Ecountable(ty_2Esum_2Esum(ty_2Enum_2Enum,ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool)))),c_2Epred__set_2EUNIV(ty_2Esum_2Esum(ty_2Enum_2Enum,ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool)))))) ).

tff(conj_thm_2Eucord_2EUnum__cardlt__ucinf,axiom,
    ! [A_27a: del] : ~ p(ap(ap(c_2Ecardinal_2Ecardleq(ty_2Esum_2Esum(ty_2Enum_2Enum,ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool))),ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Esum_2Esum(ty_2Enum_2Enum,ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool))))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))) ).

tff(conj_thm_2Eucord_2EUnum__cardle__ucinf,axiom,
    ! [A_27a: del] : p(ap(ap(c_2Ecardinal_2Ecardleq(ty_2Enum_2Enum,ty_2Esum_2Esum(ty_2Enum_2Enum,ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool)))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Esum_2Esum(ty_2Enum_2Enum,ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool)))))) ).

tff(lamtp_f2279,type,
    f2279: del > $i ).

tff(lameq_f2279,axiom,
    ! [A_27a: del,V0a: $i] : ( ap(f2279(A_27a),V0a) = ap(ap(c_2Epair_2E_2C(ty_2Eordinal_2Eordinal(ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool))),bool),V0a),ap(c_2Epred__set_2Ecountable(ty_2Eordinal_2Eordinal(ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool)))),ap(c_2Eordinal_2Epreds(ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool))),V0a))) ) ).

tff(conj_thm_2Eucord_2Eucord__sup__exists__lemma,axiom,
    ! [A_27a: del] : p(ap(ap(c_2Ecardinal_2Ecardleq(ty_2Eordinal_2Eordinal(ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool))),ty_2Esum_2Esum(ty_2Enum_2Enum,ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool)))),ap(c_2Epred__set_2EGSPEC(ty_2Eordinal_2Eordinal(ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool))),ty_2Eordinal_2Eordinal(ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool)))),f2279(A_27a))),c_2Epred__set_2EUNIV(ty_2Esum_2Esum(ty_2Enum_2Enum,ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool)))))) ).

tff(ax_thm_2Eucord_2Eomega1__def,axiom,
    ! [A_27a: del] : ( c_2Eucord_2Eomega1(A_27a) = ap(c_2Eordinal_2Esup(ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool))),ap(c_2Epred__set_2EGSPEC(ty_2Eordinal_2Eordinal(ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool))),ty_2Eordinal_2Eordinal(ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool)))),f2279(A_27a))) ) ).

tff(conj_thm_2Eucord_2Ex__lt__omega1__countable,axiom,
    ! [A_27a: del,V0x: $i] :
      ( mem(V0x,ty_2Eordinal_2Eordinal(ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool))))
     => ( p(ap(ap(c_2Eordinal_2Eordlt(ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool))),V0x),c_2Eucord_2Eomega1(A_27a)))
      <=> p(ap(c_2Epred__set_2Ecountable(ty_2Eordinal_2Eordinal(ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool)))),ap(c_2Eordinal_2Epreds(ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool))),V0x))) ) ) ).

tff(conj_thm_2Eucord_2Eomega1__not__countable,axiom,
    ! [A_27a: del] : ~ p(ap(c_2Epred__set_2Ecountable(ty_2Eordinal_2Eordinal(ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool)))),ap(c_2Eordinal_2Epreds(ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool))),c_2Eucord_2Eomega1(A_27a)))) ).

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