SET007 Axioms: SET007+639.ax


%------------------------------------------------------------------------------
% File     : SET007+639 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Weights of Continuous Lattices
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : waybel31 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   53 (   3 unit)
%            Number of atoms       :  517 (  38 equality)
%            Maximal formula depth :   26 (   9 average)
%            Number of connectives :  492 (  28 ~  ;   1  |; 356  &)
%                                         (  10 <=>;  97 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   48 (   1 propositional; 0-2 arity)
%            Number of functors    :   36 (   7 constant; 0-3 arity)
%            Number of variables   :  111 (   0 singleton;  98 !;  13 ?)
%            Maximal term depth    :    5 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_waybel31,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A)
        & v6_waybel23(B,A)
        & m1_waybel23(B,A) )
     => ( ~ v3_struct_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
        & v1_orders_2(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
        & v2_orders_2(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
        & v3_orders_2(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
        & v4_orders_2(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
        & v1_yellow_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
        & v2_yellow_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
        & v3_yellow_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
        & v24_waybel_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
        & v25_waybel_0(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
        & ~ v1_yellow_3(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
        & v1_waybel_2(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
        & v2_waybel_2(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
        & v1_waybel_8(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
        & v2_waybel_8(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
        & v1_lattice3(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
        & v2_lattice3(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
        & v3_lattice3(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
        & v2_waybel_3(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B))))
        & v3_waybel_3(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))) ) ) )).

fof(cc1_waybel31,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( v6_group_1(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v2_yellow_0(A)
          & v24_waybel_0(A)
          & ~ v1_yellow_3(A)
          & v1_waybel_8(A)
          & v2_waybel_8(A)
          & v3_waybel_8(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v2_waybel_3(A)
          & v3_waybel_3(A) ) ) ) )).

fof(rc1_waybel31,axiom,(
    ? [A] :
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v6_group_1(A)
      & v1_orders_2(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_yellow_0(A)
      & v2_yellow_0(A)
      & v3_yellow_0(A)
      & v16_waybel_0(A)
      & v24_waybel_0(A)
      & v25_waybel_0(A)
      & ~ v1_yellow_3(A)
      & v1_waybel_2(A)
      & v2_waybel_2(A)
      & v1_waybel_8(A)
      & v2_waybel_8(A)
      & v3_waybel_8(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v2_waybel_3(A)
      & v3_waybel_3(A)
      & v3_realset2(A) ) )).

fof(fc2_waybel31,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k2_yellow_1(k5_waybel11(A)))
        & v1_orders_2(k2_yellow_1(k5_waybel11(A)))
        & v2_orders_2(k2_yellow_1(k5_waybel11(A)))
        & v3_orders_2(k2_yellow_1(k5_waybel11(A)))
        & v4_orders_2(k2_yellow_1(k5_waybel11(A)))
        & v2_yellow_0(k2_yellow_1(k5_waybel11(A)))
        & v24_waybel_0(k2_yellow_1(k5_waybel11(A)))
        & ~ v1_yellow_3(k2_yellow_1(k5_waybel11(A)))
        & v1_lattice3(k2_yellow_1(k5_waybel11(A)))
        & v2_waybel_3(k2_yellow_1(k5_waybel11(A)))
        & v3_waybel_3(k2_yellow_1(k5_waybel11(A))) ) ) )).

fof(t1_waybel31,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_cantor_1(B,A)
         => r1_ordinal1(k2_waybel23(A),k1_card_1(B)) ) ) )).

fof(t2_waybel31,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ? [B] :
          ( m1_cantor_1(B,A)
          & k1_card_1(B) = k2_waybel23(A) ) ) )).

fof(t3_waybel31,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v6_waybel23(B,A)
            & m1_waybel23(B,A) )
         => r1_ordinal1(k1_waybel31(A),k1_card_1(B)) ) ) )).

fof(t4_waybel31,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( v6_waybel23(B,A)
          & m1_waybel23(B,A)
          & k1_card_1(B) = k1_waybel31(A) ) ) )).

fof(t5_waybel31,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v2_waybel_8(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => k1_waybel31(A) = k1_card_1(u1_struct_0(k1_waybel_8(A))) ) )).

fof(t6_waybel31,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_lattice3(B)
            & v3_waybel_3(B)
            & l1_orders_2(B) )
         => ( k2_yellow_1(u1_pre_topc(A)) = B
           => ! [C] :
                ( ( v6_waybel23(C,B)
                  & m1_waybel23(C,B) )
               => m1_cantor_1(C,A) ) ) ) ) )).

fof(t7_waybel31,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_waybel_3(B)
            & l1_orders_2(B) )
         => ( k2_yellow_1(u1_pre_topc(A)) = B
           => ! [C] :
                ( m1_cantor_1(C,A)
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                   => ( C = D
                     => ( v6_waybel23(k12_waybel_0(B,D),B)
                        & m1_waybel23(k12_waybel_0(B,D),B) ) ) ) ) ) ) ) )).

fof(t8_waybel31,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_t_0topsp(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v3_waybel_3(B)
            & l1_orders_2(B) )
         => ( k2_yellow_1(u1_pre_topc(A)) = B
           => ( v6_group_1(A)
              | k2_waybel23(A) = k1_waybel31(B) ) ) ) ) )).

fof(t9_waybel31,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_t_0topsp(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_lattice3(B)
            & v3_waybel_3(B)
            & l1_orders_2(B) )
         => ( k2_yellow_1(u1_pre_topc(A)) = B
           => r1_ordinal1(k1_card_1(u1_struct_0(A)),k1_card_1(u1_struct_0(B))) ) ) ) )).

fof(t10_waybel31,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_t_0topsp(A)
        & l1_pre_topc(A) )
     => ( v6_group_1(A)
       => k2_waybel23(A) = k1_card_1(u1_struct_0(A)) ) ) )).

fof(t11_waybel31,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_waybel_3(B)
            & l1_orders_2(B) )
         => ( ( k2_yellow_1(u1_pre_topc(A)) = B
              & v6_group_1(A) )
           => k1_waybel31(B) = k1_card_1(u1_struct_0(B)) ) ) ) )).

fof(t13_waybel31,axiom,(
    $true )).

fof(t14_waybel31,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & l1_orders_2(A) )
     => ( v6_group_1(A)
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => r2_hidden(B,k2_waybel_8(A,B)) ) ) ) )).

fof(t15_waybel31,axiom,(
    ! [A] :
      ( ( v6_group_1(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => v3_waybel_8(A) ) )).

fof(t16_waybel31,axiom,(
    ! [A] :
      ( ( v6_group_1(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v6_waybel23(B,A)
            & m1_waybel23(B,A) )
         => ( k1_card_1(B) = k1_waybel31(A)
          <=> B = u1_struct_0(k1_waybel_8(A)) ) ) ) )).

fof(d2_waybel31,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_waybel31(A,B,C) = k6_subset_1(u1_struct_0(A),k2_waybel_3(A,C),k5_waybel_0(A,B)) ) ) ) )).

fof(t17_waybel31,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k2_waybel31(A,k1_pre_topc(A),B) = k2_waybel_3(A,B) ) ) )).

fof(t18_waybel31,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,k5_waybel_0(A,B))
               => k2_waybel31(A,B,C) = k1_xboole_0 ) ) ) ) )).

fof(t19_waybel31,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_group_1(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => v1_finset_1(k8_waybel_0(A)) ) )).

fof(t20_waybel31,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ( ~ v6_group_1(A)
       => ! [B] :
            ( ( v6_waybel23(B,A)
              & m1_waybel23(B,A) )
           => ~ v1_finset_1(B) ) ) ) )).

fof(t21_waybel31,axiom,(
    $true )).

fof(t22_waybel31,axiom,(
    $true )).

fof(t23_waybel31,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v1_waybel_3(B,A)
           => B = k2_yellow_0(A,k2_waybel_3(A,B)) ) ) ) )).

fof(t25_waybel31,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel19(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v1_finset_1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( v3_pre_topc(k3_subset_1(u1_struct_0(A),k5_waybel_0(A,B)),A)
            & v3_pre_topc(k3_subset_1(u1_struct_0(A),k4_waybel_0(A,B)),A) ) ) ) )).

fof(t29_waybel31,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(B,A) )
         => k1_waybel31(A) = k2_waybel23(B) ) ) )).

fof(t30_waybel31,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & v2_waybel19(B)
            & m1_yellow_9(B,A) )
         => k1_waybel31(A) = k2_waybel23(B) ) ) )).

fof(t31_waybel31,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ( r5_waybel_1(A,B)
           => k1_card_1(u1_struct_0(A)) = k1_card_1(u1_struct_0(B)) ) ) ) )).

fof(t32_waybel31,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v6_waybel23(B,A)
            & m1_waybel23(B,A) )
         => ( k1_card_1(B) = k1_waybel31(A)
           => k1_waybel31(A) = k1_waybel31(k2_yellow_1(k8_waybel_0(k5_yellow_0(A,B)))) ) ) ) )).

fof(t33_waybel31,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => r1_ordinal1(k1_waybel31(A),k1_waybel31(k2_yellow_1(k5_waybel11(A)))) ) )).

fof(t34_waybel31,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ( ~ v6_group_1(A)
       => k1_waybel31(A) = k1_waybel31(k2_yellow_1(k5_waybel11(A))) ) ) )).

fof(dt_k1_waybel31,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => v1_card_1(k1_waybel31(A)) ) )).

fof(dt_k2_waybel31,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k2_waybel31(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(d1_waybel31,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => k1_waybel31(A) = k1_setfam_1(a_1_0_waybel31(A)) ) )).

fof(t12_waybel31,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(B,A) )
         => ! [C] :
              ( ( v2_pre_topc(C)
                & v2_waybel19(C)
                & m1_yellow_9(C,A) )
             => ! [D] :
                  ( m1_cantor_1(D,C)
                 => m1_cantor_1(a_3_0_waybel31(A,C,D),B) ) ) ) ) )).

fof(t24_waybel31,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ( ~ v6_group_1(A)
       => ! [B] :
            ( ( v6_waybel23(B,A)
              & m1_waybel23(B,A) )
           => r1_ordinal1(k1_card_1(a_2_0_waybel31(A,B)),k1_card_1(B)) ) ) ) )).

fof(t26_waybel31,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & v2_waybel19(B)
            & m1_yellow_9(B,A) )
         => ! [C] :
              ( ( v6_waybel23(C,A)
                & m1_waybel23(C,A) )
             => m1_cantor_1(a_2_0_waybel31(A,C),B) ) ) ) )).

fof(t27_waybel31,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(B,A) )
         => ! [C] :
              ( m1_cantor_1(C,B)
             => m1_cantor_1(a_3_1_waybel31(A,B,C),B) ) ) ) )).

fof(t28_waybel31,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(B,A) )
         => ! [C] :
              ( m1_cantor_1(C,B)
             => ~ ( ~ v1_finset_1(C)
                  & v1_finset_1(a_3_2_waybel31(A,B,C)) ) ) ) ) )).

fof(s1_waybel31,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(f1_s1_waybel31))))
     => ( A = a_0_0_waybel31
       => k5_waybel_0(f1_s1_waybel31,k5_setfam_1(u1_struct_0(f1_s1_waybel31),A)) = k3_tarski(a_0_1_waybel31) ) ) )).

fof(s2_waybel31,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(f1_s2_waybel31))))
     => ( A = a_0_2_waybel31
       => k4_waybel_0(f1_s2_waybel31,k5_setfam_1(u1_struct_0(f1_s2_waybel31),A)) = k3_tarski(a_0_3_waybel31) ) ) )).

fof(fraenkel_a_1_0_waybel31,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & v3_waybel_3(B)
        & l1_orders_2(B) )
     => ( r2_hidden(A,a_1_0_waybel31(B))
      <=> ? [C] :
            ( v6_waybel23(C,B)
            & m1_waybel23(C,B)
            & A = k1_card_1(C) ) ) ) )).

fof(fraenkel_a_3_0_waybel31,axiom,(
    ! [A,B,C,D] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v3_waybel_3(B)
        & l1_orders_2(B)
        & v2_pre_topc(C)
        & v2_waybel19(C)
        & m1_yellow_9(C,B)
        & m1_cantor_1(D,C) )
     => ( r2_hidden(A,a_3_0_waybel31(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C)))
            & A = k5_waybel_0(C,E)
            & r2_hidden(E,D) ) ) ) )).

fof(fraenkel_a_2_0_waybel31,axiom,(
    ! [A,B,C] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v3_waybel_3(B)
        & l1_orders_2(B)
        & v6_waybel23(C,B)
        & m1_waybel23(C,B) )
     => ( r2_hidden(A,a_2_0_waybel31(B,C))
      <=> ? [D,E] :
            ( m1_subset_1(D,u1_struct_0(B))
            & v1_finset_1(E)
            & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
            & A = k2_waybel31(B,E,D)
            & r2_hidden(D,C)
            & r1_tarski(E,C) ) ) ) )).

fof(fraenkel_a_3_1_waybel31,axiom,(
    ! [A,B,C,D] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v3_waybel_3(B)
        & l1_orders_2(B)
        & v4_waybel11(C)
        & m1_yellow_9(C,B)
        & m1_cantor_1(D,C) )
     => ( r2_hidden(A,a_3_1_waybel31(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C)))
            & A = k2_waybel_3(C,k2_yellow_0(C,E))
            & r2_hidden(E,D) ) ) ) )).

fof(fraenkel_a_3_2_waybel31,axiom,(
    ! [A,B,C,D] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v3_waybel_3(B)
        & l1_orders_2(B)
        & v4_waybel11(C)
        & m1_yellow_9(C,B)
        & m1_cantor_1(D,C) )
     => ( r2_hidden(A,a_3_2_waybel31(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C)))
            & A = k2_yellow_0(C,E)
            & r2_hidden(E,D) ) ) ) )).

fof(fraenkel_a_0_0_waybel31,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_waybel31)
    <=> ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s1_waybel31)))
          & A = B
          & p1_s1_waybel31(B) ) ) )).

fof(fraenkel_a_0_1_waybel31,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_1_waybel31)
    <=> ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s1_waybel31)))
          & A = k5_waybel_0(f1_s1_waybel31,B)
          & p1_s1_waybel31(B) ) ) )).

fof(fraenkel_a_0_2_waybel31,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_2_waybel31)
    <=> ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s2_waybel31)))
          & A = B
          & p1_s2_waybel31(B) ) ) )).

fof(fraenkel_a_0_3_waybel31,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_3_waybel31)
    <=> ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s2_waybel31)))
          & A = k4_waybel_0(f1_s2_waybel31,B)
          & p1_s2_waybel31(B) ) ) )).
%------------------------------------------------------------------------------