%------------------------------------------------------------------------------
% File     : ITP104+5 : TPTP v8.2.0. 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    :    9 (   1 unt;   0 def)
%            Number of atoms       :   19 (   2 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   13 (   3   ~;   0   |;   0   &)
%                                         (   1 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   0 prp; 1-2 aty)
%            Number of functors    :   16 (  16 usr;   2 con; 0-2 aty)
%            Number of variables   :   11 (  11   !;   0   ?)
% SPC      : FOF_SAT_RFO_SEQ

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(mem_c_2Eucord_2Eomega1,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => mem(c_2Eucord_2Eomega1(A_27a),ty_2Eordinal_2Eordinal(ty_2Esum_2Esum(A_27a,arr(ty_2Enum_2Enum,bool)))) ) ).

fof(conj_thm_2Eucord_2Eucinf__uncountable,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ~ 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)))))) ) ).

fof(conj_thm_2Eucord_2EUnum__cardlt__ucinf,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ~ 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))) ) ).

fof(conj_thm_2Eucord_2EUnum__cardle__ucinf,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => 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)))))) ) ).

fof(lameq_f2279,axiom,
    ! [A_27a,V0a] : 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))) ).

fof(conj_thm_2Eucord_2Eucord__sup__exists__lemma,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => 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)))))) ) ).

fof(ax_thm_2Eucord_2Eomega1__def,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => 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))) ) ).

fof(conj_thm_2Eucord_2Ex__lt__omega1__countable,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0x] :
          ( 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))) ) ) ) ).

fof(conj_thm_2Eucord_2Eomega1__not__countable,axiom,
    ! [A_27a] :
      ( ne(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))),c_2Eucord_2Eomega1(A_27a)))) ) ).

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