SET007 Axioms: SET007+655.ax


%------------------------------------------------------------------------------
% File     : SET007+655 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Order-consistent Topology of Complete and Uncomplete 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    : waybel32 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   63 (   4 unit)
%            Number of atoms       :  701 (  28 equality)
%            Maximal formula depth :   16 (  10 average)
%            Number of connectives :  731 (  93 ~  ;   1  |; 491  &)
%                                         (  15 <=>; 131 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   56 (   1 propositional; 0-3 arity)
%            Number of functors    :   31 (   0 constant; 1-4 arity)
%            Number of variables   :  155 (   0 singleton; 139 !;  16 ?)
%            Maximal term depth    :    4 (   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(rc1_waybel32,axiom,(
    ? [A] :
      ( l1_waybel_9(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)
      & v2_pre_topc(A)
      & v1_waybel_9(A)
      & v4_waybel11(A)
      & v1_lattice3(A)
      & v2_lattice3(A) ) )).

fof(cc1_waybel32,axiom,(
    ! [A] :
      ( l1_waybel_9(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v2_pre_topc(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v2_pre_topc(A)
          & v1_waybel32(A) ) ) ) )).

fof(rc2_waybel32,axiom,(
    ? [A] :
      ( l1_waybel_9(A)
      & ~ v3_struct_0(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v2_yellow_0(A)
      & v16_waybel_0(A)
      & v24_waybel_0(A)
      & v2_pre_topc(A)
      & v2_waybel_3(A)
      & v1_waybel_9(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_realset2(A)
      & v1_waybel32(A) ) )).

fof(cc2_waybel32,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) )
     => ! [B] :
          ( m1_yellow_9(B,A)
         => ( v4_waybel11(B)
           => ( ~ v3_struct_0(B)
              & v2_orders_2(B)
              & v3_orders_2(B)
              & v4_orders_2(B)
              & v24_waybel_0(B)
              & v2_pre_topc(B)
              & ~ v1_yellow_3(B) ) ) ) ) )).

fof(rc3_waybel32,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) )
     => ? [B] :
          ( m1_yellow_9(B,A)
          & ~ v3_struct_0(B)
          & v2_orders_2(B)
          & v3_orders_2(B)
          & v4_orders_2(B)
          & v24_waybel_0(B)
          & v2_pre_topc(B)
          & ~ v1_yellow_3(B)
          & v4_waybel11(B) ) ) )).

fof(rc4_waybel32,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v25_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_yellow_9(B,A)
          & ~ v3_struct_0(B)
          & v2_orders_2(B)
          & v3_orders_2(B)
          & v4_orders_2(B)
          & v24_waybel_0(B)
          & v2_pre_topc(B)
          & ~ v1_yellow_3(B)
          & v1_waybel_9(B)
          & v4_waybel11(B) ) ) )).

fof(cc3_waybel32,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) )
     => ! [B] :
          ( m1_yellow_9(B,A)
         => ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v24_waybel_0(B)
            & ~ v1_yellow_3(B) ) ) ) )).

fof(cc4_waybel32,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v12_waybel_0(B,A)
           => v3_waybel11(B,A) ) ) ) )).

fof(rc5_waybel32,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) )
     => ? [B] :
          ( m1_yellow_9(B,A)
          & ~ v3_struct_0(B)
          & v2_orders_2(B)
          & v3_orders_2(B)
          & v4_orders_2(B)
          & v24_waybel_0(B)
          & v2_pre_topc(B)
          & ~ v1_yellow_3(B)
          & v2_waybel32(B) ) ) )).

fof(rc6_waybel32,axiom,(
    ? [A] :
      ( l1_waybel_9(A)
      & ~ v3_struct_0(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)
      & v24_waybel_0(A)
      & v25_waybel_0(A)
      & v2_pre_topc(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v2_waybel32(A) ) )).

fof(fc1_waybel32,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v3_orders_2(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
        & m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
     => ( ~ v3_struct_0(k1_waybel32(A,B,C))
        & v3_orders_2(k1_waybel32(A,B,C))
        & v6_waybel_0(k1_waybel32(A,B,C),A) ) ) )).

fof(fc2_waybel32,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v7_waybel_0(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
        & m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
     => ( ~ v3_struct_0(k1_waybel32(A,B,C))
        & v6_waybel_0(k1_waybel32(A,B,C),A)
        & v7_waybel_0(k1_waybel32(A,B,C)) ) ) )).

fof(fc3_waybel32,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v3_orders_2(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A) )
     => ( ~ v3_struct_0(k2_waybel32(A,B))
        & v3_orders_2(k2_waybel32(A,B))
        & v6_waybel_0(k2_waybel32(A,B),A)
        & v7_waybel_0(k2_waybel32(A,B)) ) ) )).

fof(fc4_waybel32,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v3_orders_2(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A) )
     => ( ~ v3_struct_0(k2_waybel32(A,B))
        & v3_orders_2(k2_waybel32(A,B))
        & v6_waybel_0(k2_waybel32(A,B),A)
        & v7_waybel_0(k2_waybel32(A,B)) ) ) )).

fof(fc5_waybel32,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & v25_waybel_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v3_orders_2(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A) )
     => ( ~ v3_struct_0(k2_waybel32(A,B))
        & v3_orders_2(k2_waybel32(A,B))
        & v6_waybel_0(k2_waybel32(A,B),A)
        & v7_waybel_0(k2_waybel32(A,B))
        & v8_waybel_0(k2_waybel32(A,B),A)
        & v10_waybel_0(k2_waybel32(A,B),A) ) ) )).

fof(fc6_waybel32,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & v25_waybel_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v3_orders_2(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A) )
     => ( ~ v3_struct_0(k2_waybel32(A,B))
        & v3_orders_2(k2_waybel32(A,B))
        & v6_waybel_0(k2_waybel32(A,B),A)
        & v7_waybel_0(k2_waybel32(A,B))
        & v8_waybel_0(k2_waybel32(A,B),A)
        & v10_waybel_0(k2_waybel32(A,B),A) ) ) )).

fof(d2_waybel32,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v2_pre_topc(A)
        & l1_waybel_9(A) )
     => ( v2_waybel32(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ( k6_waybel_0(A,B) = k6_pre_topc(A,k1_struct_0(A,B))
              & ! [C] :
                  ( ( ~ v3_struct_0(C)
                    & v3_orders_2(C)
                    & v7_waybel_0(C)
                    & v10_waybel_0(C,A)
                    & l1_waybel_0(C,A) )
                 => ( B = k1_waybel_2(A,C)
                   => ! [D] :
                        ( m1_connsp_2(D,A,B)
                       => r1_waybel_0(A,C,D) ) ) ) ) ) ) ) )).

fof(t1_waybel32,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v2_pre_topc(A)
        & v1_waybel32(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_pre_topc(B,A)
           => v13_waybel_0(B,A) ) ) ) )).

fof(t2_waybel32,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v2_pre_topc(A)
        & l1_waybel_9(A) )
     => ( v1_waybel32(A)
       => v2_waybel32(A) ) ) )).

fof(t3_waybel32,axiom,(
    $true )).

fof(t4_waybel32,axiom,(
    $true )).

fof(t5_waybel32,axiom,(
    $true )).

fof(t6_waybel32,axiom,(
    $true )).

fof(t7_waybel32,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) )
     => ? [B] :
          ( m1_yellow_9(B,A)
          & v4_waybel11(B) ) ) )).

fof(t8_waybel32,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) )
     => ! [B] :
          ( m1_yellow_9(B,A)
         => ( v4_waybel11(B)
           => v2_pre_topc(B) ) ) ) )).

fof(t9_waybel32,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k6_pre_topc(A,k1_struct_0(A,B)) = k6_waybel_0(A,B) ) ) )).

fof(t10_waybel32,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v2_pre_topc(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => v2_waybel32(A) ) )).

fof(t12_waybel32,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v25_waybel_0(A)
        & v2_lattice3(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,B)
               => r3_orders_2(A,k2_yellow_0(A,B),C) ) ) ) ) )).

fof(t13_waybel32,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v25_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & v8_waybel_0(B,A)
            & l1_waybel_0(B,A) )
         => k1_waybel11(A,B) = k1_waybel_2(A,B) ) ) )).

fof(t14_waybel32,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v25_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( r2_hidden(B,u1_pre_topc(k14_yellow_6(A,k2_waybel11(A))))
          <=> ( v1_waybel11(B,A)
              & v13_waybel_0(B,A) ) ) ) ) )).

fof(t15_waybel32,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v25_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_yellow_9(B,A)
         => ( u1_pre_topc(B) = k5_waybel11(A)
           => v4_waybel11(B) ) ) ) )).

fof(t16_waybel32,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v25_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(B,A) )
         => k5_waybel11(A) = u1_pre_topc(B) ) ) )).

fof(t17_waybel32,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_t_0topsp(A)
        & l1_pre_topc(A) ) ) )).

fof(t18_waybel32,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) )
     => ! [B] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( ( v13_waybel_0(D,B)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
                 => ( ~ r2_hidden(C,D)
                   => m2_connsp_2(k3_subset_1(u1_struct_0(B),k6_waybel_0(B,C)),B,D) ) ) ) ) ) )).

fof(t19_waybel32,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(B,A) )
         => ! [C] :
              ( ( v13_waybel_0(C,B)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
             => ? [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B))))
                  & C = k6_setfam_1(u1_struct_0(B),D)
                  & ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
                     => ( r2_hidden(E,D)
                       => m2_connsp_2(E,B,C) ) ) ) ) ) ) )).

fof(t20_waybel32,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_pre_topc(B,A)
          <=> ( v13_waybel_0(B,A)
              & v3_waybel11(B,A) ) ) ) ) )).

fof(t21_waybel32,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,B)
               => r3_orders_2(A,C,k1_yellow_0(A,B)) ) ) ) ) )).

fof(t22_waybel32,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v6_group_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => v1_waybel11(B,A) ) ) )).

fof(t23_waybel32,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v16_waybel_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => v3_pre_topc(k3_subset_1(u1_struct_0(B),k6_waybel_0(B,C)),B) ) ) ) )).

fof(t25_waybel32,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => k6_waybel_0(A,C) = k6_pre_topc(A,k1_struct_0(A,C)) )
              & v3_pre_topc(B,A) )
           => v13_waybel_0(B,A) ) ) ) )).

fof(t26_waybel32,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k6_waybel_0(A,C) = k6_pre_topc(A,k1_struct_0(A,C)) )
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( v4_pre_topc(C,A)
                 => v12_waybel_0(C,A) ) ) ) ) ) )).

fof(t27_waybel32,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v25_waybel_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => k1_waybel11(A,k6_waybel_9(A,B,C)) = k1_waybel11(A,B) ) ) ) )).

fof(d3_waybel32,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v6_waybel_0(D,A)
                    & l1_waybel_0(D,A) )
                 => ( D = k1_waybel32(A,B,C)
                  <=> ( g1_orders_2(u1_struct_0(D),u1_orders_2(D)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
                      & u1_waybel_0(A,D) = C ) ) ) ) ) ) )).

fof(t29_waybel32,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v25_waybel_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => k1_waybel_2(A,k2_waybel32(A,B)) = k1_waybel11(A,B) ) ) )).

fof(t30_waybel32,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v25_waybel_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => k1_waybel_2(A,k2_waybel32(A,B)) = k1_waybel11(A,k6_waybel_9(A,B,C)) ) ) ) )).

fof(t31_waybel32,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v25_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( ( v13_waybel_0(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( r1_waybel_0(A,k2_waybel32(A,B),C)
               => r1_waybel_0(A,B,C) ) ) ) ) )).

fof(t32_waybel32,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v25_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( ( v12_waybel_0(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( r1_waybel_0(A,B,C)
               => r1_waybel_0(A,k2_waybel32(A,B),C) ) ) ) ) )).

fof(t33_waybel32,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v25_waybel_0(A)
        & v2_pre_topc(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v2_waybel32(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_orders_2(A,C,k1_waybel11(A,B))
               => r3_waybel_9(A,B,C) ) ) ) ) )).

fof(t34_waybel32,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v25_waybel_0(A)
        & v2_pre_topc(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v2_waybel32(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & v10_waybel_0(B,A)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_orders_2(A,C,k1_waybel11(A,B))
              <=> r3_waybel_9(A,B,C) ) ) ) ) )).

fof(dt_k1_waybel32,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
        & m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
     => ( ~ v3_struct_0(k1_waybel32(A,B,C))
        & v6_waybel_0(k1_waybel32(A,B,C),A)
        & l1_waybel_0(k1_waybel32(A,B,C),A) ) ) )).

fof(dt_k2_waybel32,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A) )
     => ( ~ v3_struct_0(k2_waybel32(A,B))
        & v6_waybel_0(k2_waybel32(A,B),A)
        & v7_waybel_0(k2_waybel32(A,B))
        & l1_waybel_0(k2_waybel32(A,B),A) ) ) )).

fof(d1_waybel32,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_waybel_9(A) )
     => ( v1_waybel32(A)
      <=> m2_cantor_1(a_1_0_waybel32(A),A) ) ) )).

fof(t11_waybel32,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v25_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( C = a_2_0_waybel32(A,B)
               => ( ~ v1_xboole_0(C)
                  & v1_waybel_0(C,A) ) ) ) ) ) )).

fof(t24_waybel32,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v16_waybel_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ( v3_pre_topc(C,B)
              <=> ( C = u1_struct_0(B)
                  | r2_hidden(C,a_2_1_waybel32(A,B)) ) ) ) ) ) )).

fof(d4_waybel32,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_waybel_0(C,A)
                & v7_waybel_0(C)
                & l1_waybel_0(C,A) )
             => ( C = k2_waybel32(A,B)
              <=> ? [D] :
                    ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A))
                    & C = k1_waybel32(A,B,D)
                    & ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => k3_yellow_6(u1_struct_0(B),A,D,E) = k2_yellow_0(A,a_3_1_waybel32(A,B,E)) ) ) ) ) ) ) )).

fof(t28_waybel32,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => k5_relset_1(u1_struct_0(k2_waybel32(A,B)),u1_struct_0(A),u1_waybel_0(A,k2_waybel32(A,B))) = a_2_2_waybel32(A,B) ) ) )).

fof(fraenkel_a_1_0_waybel32,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l1_waybel_9(B) )
     => ( r2_hidden(A,a_1_0_waybel32(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(B))
            & A = k3_subset_1(u1_struct_0(B),k6_waybel_0(B,C)) ) ) ) )).

fof(fraenkel_a_2_0_waybel32,axiom,(
    ! [A,B,C] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v25_waybel_0(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & ~ v3_struct_0(C)
        & v3_orders_2(C)
        & v7_waybel_0(C)
        & l1_waybel_0(C,B) )
     => ( r2_hidden(A,a_2_0_waybel32(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(C))
            & A = k2_yellow_0(B,a_3_0_waybel32(B,C,D)) ) ) ) )).

fof(fraenkel_a_3_0_waybel32,axiom,(
    ! [A,B,C,D] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v25_waybel_0(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & ~ v3_struct_0(C)
        & v3_orders_2(C)
        & v7_waybel_0(C)
        & l1_waybel_0(C,B)
        & m1_subset_1(D,u1_struct_0(C)) )
     => ( r2_hidden(A,a_3_0_waybel32(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(C))
            & A = k3_waybel_0(B,C,E)
            & r1_orders_2(C,D,E) ) ) ) )).

fof(fraenkel_a_2_1_waybel32,axiom,(
    ! [A,B,C] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v16_waybel_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v3_lattice3(B)
        & l1_orders_2(B)
        & v4_waybel11(C)
        & m1_yellow_9(C,B) )
     => ( r2_hidden(A,a_2_1_waybel32(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(C))
            & A = k3_subset_1(u1_struct_0(C),k6_waybel_0(C,D)) ) ) ) )).

fof(fraenkel_a_3_1_waybel32,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & l1_orders_2(B)
        & ~ v3_struct_0(C)
        & v7_waybel_0(C)
        & l1_waybel_0(C,B)
        & m1_subset_1(D,u1_struct_0(C)) )
     => ( r2_hidden(A,a_3_1_waybel32(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(C))
            & A = k3_waybel_0(B,C,E)
            & r1_orders_2(C,D,E) ) ) ) )).

fof(fraenkel_a_2_2_waybel32,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & l1_orders_2(B)
        & ~ v3_struct_0(C)
        & v3_orders_2(C)
        & v7_waybel_0(C)
        & l1_waybel_0(C,B) )
     => ( r2_hidden(A,a_2_2_waybel32(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(C))
            & A = k2_yellow_0(B,a_3_2_waybel32(B,C,D)) ) ) ) )).

fof(fraenkel_a_3_2_waybel32,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & l1_orders_2(B)
        & ~ v3_struct_0(C)
        & v3_orders_2(C)
        & v7_waybel_0(C)
        & l1_waybel_0(C,B)
        & m1_subset_1(D,u1_struct_0(C)) )
     => ( r2_hidden(A,a_3_2_waybel32(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(C))
            & A = k3_waybel_0(B,C,E)
            & r1_orders_2(C,D,E) ) ) ) )).
%------------------------------------------------------------------------------