SET007 Axioms: SET007+498.ax


%------------------------------------------------------------------------------
% File     : SET007+498 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Algebraic 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    : waybel_8 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   62 (   3 unit)
%            Number of atoms       :  596 (  24 equality)
%            Maximal formula depth :   27 (   9 average)
%            Number of connectives :  595 (  61 ~  ;   0  |; 394  &)
%                                         (  16 <=>; 124 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   55 (   1 propositional; 0-3 arity)
%            Number of functors    :   21 (   0 constant; 1-4 arity)
%            Number of variables   :  120 (   0 singleton; 116 !;   4 ?)
%            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(fc1_waybel_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k1_waybel_8(A))
        & v1_orders_2(k1_waybel_8(A))
        & v2_orders_2(k1_waybel_8(A))
        & v4_orders_2(k1_waybel_8(A))
        & v4_yellow_0(k1_waybel_8(A),A) ) ) )).

fof(fc2_waybel_8,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ~ v1_xboole_0(k2_waybel_8(A,B)) ) )).

fof(cc1_waybel_8,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v2_waybel_8(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v2_yellow_0(A)
          & v24_waybel_0(A)
          & v2_waybel_3(A)
          & v3_waybel_3(A) ) ) ) )).

fof(cc2_waybel_8,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v2_waybel_8(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v24_waybel_0(A)
          & v1_waybel_8(A) ) ) ) )).

fof(fc3_waybel_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( v1_orders_2(k1_waybel_8(A))
        & v2_orders_2(k1_waybel_8(A))
        & v3_orders_2(k1_waybel_8(A))
        & v4_orders_2(k1_waybel_8(A))
        & v4_yellow_0(k1_waybel_8(A),A)
        & v6_yellow_0(k1_waybel_8(A),A) ) ) )).

fof(cc3_waybel_8,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v3_waybel_8(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v2_yellow_0(A)
          & v24_waybel_0(A)
          & v2_waybel_3(A)
          & v3_waybel_3(A)
          & v1_waybel_8(A)
          & v2_waybel_8(A) ) ) ) )).

fof(cc4_waybel_8,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v2_yellow_0(A)
          & v24_waybel_0(A)
          & v2_waybel_3(A)
          & v3_waybel_3(A)
          & v1_waybel_8(A)
          & v2_waybel_8(A)
          & v3_waybel_8(A) ) ) ) )).

fof(rc1_waybel_8,axiom,(
    ? [A] :
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v1_orders_2(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(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)
      & v2_waybel_1(A)
      & v9_waybel_1(A)
      & v10_waybel_1(A)
      & v11_waybel_1(A)
      & v2_waybel_3(A)
      & v3_waybel_3(A)
      & v3_realset2(A)
      & v1_waybel_8(A)
      & v2_waybel_8(A)
      & v3_waybel_8(A) ) )).

fof(fc4_waybel_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) )).

fof(fc5_waybel_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) )).

fof(fc6_waybel_8,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v3_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) )).

fof(fc7_waybel_8,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v4_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) )).

fof(fc8_waybel_8,axiom,(
    ! [A] :
      ( ( v2_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v2_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) )).

fof(fc9_waybel_8,axiom,(
    ! [A] :
      ( ( v1_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v1_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) )).

fof(fc10_waybel_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v24_waybel_0(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v24_waybel_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) )).

fof(fc11_waybel_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & v2_waybel_8(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v4_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v24_waybel_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v1_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v2_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) )).

fof(fc12_waybel_8,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_waybel_8(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v3_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v4_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v1_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v2_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v2_yellow_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v24_waybel_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v2_waybel_3(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v3_waybel_3(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v1_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v2_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
        & v3_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) )).

fof(rc2_waybel_8,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v2_waybel_8(A)
        & l1_orders_2(A)
        & v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
        & v7_waybel_1(B,A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
     => ? [C] :
          ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_2(A,A,B))))
          & ~ v1_xboole_0(C)
          & v1_waybel_0(C,k2_yellow_2(A,A,B)) ) ) )).

fof(fc13_waybel_8,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,u1_struct_0(k3_yellow_1(A)))
     => ( ~ v1_xboole_0(k2_waybel_8(k3_yellow_1(A),B))
        & v1_waybel_0(k2_waybel_8(k3_yellow_1(A),B),k3_yellow_1(A))
        & v12_waybel_0(k2_waybel_8(k3_yellow_1(A),B),k3_yellow_1(A)) ) ) )).

fof(fc14_waybel_8,axiom,(
    ! [A] :
      ( ~ v3_struct_0(k3_yellow_1(A))
      & v1_orders_2(k3_yellow_1(A))
      & v2_orders_2(k3_yellow_1(A))
      & v3_orders_2(k3_yellow_1(A))
      & v4_orders_2(k3_yellow_1(A))
      & v1_lattice3(k3_yellow_1(A))
      & v2_lattice3(k3_yellow_1(A))
      & v3_lattice3(k3_yellow_1(A))
      & v1_yellow_0(k3_yellow_1(A))
      & v2_yellow_0(k3_yellow_1(A))
      & v3_yellow_0(k3_yellow_1(A))
      & v24_waybel_0(k3_yellow_1(A))
      & v25_waybel_0(k3_yellow_1(A))
      & v2_waybel_1(k3_yellow_1(A))
      & v9_waybel_1(k3_yellow_1(A))
      & v10_waybel_1(k3_yellow_1(A))
      & v11_waybel_1(k3_yellow_1(A))
      & v2_waybel_3(k3_yellow_1(A))
      & v3_waybel_3(k3_yellow_1(A))
      & v1_waybel_8(k3_yellow_1(A))
      & v2_waybel_8(k3_yellow_1(A)) ) )).

fof(d1_waybel_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_orders_2(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ( B = k1_waybel_8(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r2_hidden(C,u1_struct_0(B))
                <=> v1_waybel_3(C,A) ) ) ) ) ) )).

fof(t1_waybel_8,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r3_orders_2(A,B,D)
                      & r3_orders_2(A,D,C)
                      & r2_hidden(D,u1_struct_0(k1_waybel_8(A))) )
                   => r1_waybel_3(A,B,C) ) ) ) ) ) )).

fof(t2_waybel_8,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( ( ~ v1_xboole_0(k7_waybel_0(A,B))
              & v2_waybel_0(k7_waybel_0(A,B),A)
              & v13_waybel_0(k7_waybel_0(A,B),A)
              & v1_waybel_6(k7_waybel_0(A,B),A)
              & m1_subset_1(k7_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))) )
          <=> v1_waybel_3(B,A) ) ) ) )).

fof(t3_waybel_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ( v6_yellow_0(k1_waybel_8(A),A)
        & r2_hidden(k3_yellow_0(A),u1_struct_0(k1_waybel_8(A))) ) ) )).

fof(t4_waybel_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,k2_waybel_8(A,B))
              <=> ( r1_orders_2(A,C,B)
                  & v1_waybel_3(C,A) ) ) ) ) ) )).

fof(t5_waybel_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k2_waybel_8(A,B) = k3_xboole_0(k6_waybel_0(A,B),u1_struct_0(k1_waybel_8(A))) ) ) )).

fof(t6_waybel_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_tarski(k2_waybel_8(A,B),k1_waybel_3(A,B)) ) ) )).

fof(d3_waybel_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_waybel_8(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => B = k1_yellow_0(A,k2_waybel_8(A,B)) ) ) ) )).

fof(d4_waybel_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( v2_waybel_8(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ( ~ v1_xboole_0(k2_waybel_8(A,B))
                & v1_waybel_0(k2_waybel_8(A,B),A) ) )
          & v24_waybel_0(A)
          & v1_waybel_8(A) ) ) ) )).

fof(t7_waybel_8,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( v2_waybel_8(A)
      <=> ( v3_waybel_3(A)
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ~ ( r1_waybel_3(A,B,C)
                      & ! [D] :
                          ( m1_subset_1(D,u1_struct_0(A))
                         => ~ ( r2_hidden(D,u1_struct_0(k1_waybel_8(A)))
                              & r3_orders_2(A,B,D)
                              & r3_orders_2(A,D,C) ) ) ) ) ) ) ) ) )).

fof(d5_waybel_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( v3_waybel_8(A)
      <=> ( v2_waybel_8(A)
          & v5_yellow_0(k1_waybel_8(A),A) ) ) ) )).

fof(t8_waybel_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
              & v24_waybel_0(A) )
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(B))
                           => ( ( C = E
                                & D = F
                                & r1_waybel_3(A,C,D) )
                             => r1_waybel_3(B,E,F) ) ) ) ) ) ) ) ) )).

fof(t9_waybel_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
              & v24_waybel_0(A) )
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ( ( C = D
                        & v1_waybel_3(C,A) )
                     => v1_waybel_3(D,B) ) ) ) ) ) ) )).

fof(t10_waybel_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v4_orders_2(B)
            & v24_waybel_0(B)
            & l1_orders_2(B) )
         => ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ( C = D
                     => k2_waybel_8(A,C) = k2_waybel_8(B,D) ) ) ) ) ) ) )).

fof(t11_waybel_8,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ~ ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
              & ~ v3_struct_0(A)
              & v3_struct_0(B) ) ) ) )).

fof(t12_waybel_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
              & v2_orders_2(A) )
           => v2_orders_2(B) ) ) ) )).

fof(t13_waybel_8,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
              & v3_orders_2(A) )
           => v3_orders_2(B) ) ) ) )).

fof(t14_waybel_8,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
              & v4_orders_2(A) )
           => v4_orders_2(B) ) ) ) )).

fof(t15_waybel_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & l1_orders_2(B) )
         => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
              & v24_waybel_0(A) )
           => v24_waybel_0(B) ) ) ) )).

fof(t16_waybel_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v4_orders_2(B)
            & v24_waybel_0(B)
            & l1_orders_2(B) )
         => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
              & v1_waybel_8(A)
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ( ~ v1_xboole_0(k2_waybel_8(A,C))
                    & v1_waybel_0(k2_waybel_8(A,C),A) ) ) )
           => v1_waybel_8(B) ) ) ) )).

fof(t17_waybel_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
              & v2_waybel_8(A) )
           => v2_waybel_8(B) ) ) ) )).

fof(t18_waybel_8,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
              & v3_waybel_8(A) )
           => v3_waybel_8(B) ) ) ) )).

fof(t19_waybel_8,axiom,(
    $true )).

fof(t20_waybel_8,axiom,(
    $true )).

fof(t21_waybel_8,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v2_waybel_8(A)
        & l1_orders_2(A) )
     => ( v3_waybel_8(A)
      <=> ( v2_orders_2(k1_waybel_8(A))
          & v3_orders_2(k1_waybel_8(A))
          & v4_orders_2(k1_waybel_8(A))
          & v1_lattice3(k1_waybel_8(A))
          & v2_lattice3(k1_waybel_8(A))
          & l1_orders_2(k1_waybel_8(A)) ) ) ) )).

fof(t22_waybel_8,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_yellow_0(A)
        & v2_waybel_8(A)
        & l1_orders_2(A) )
     => ( v3_waybel_8(A)
      <=> v5_waybel_7(k1_waybel_4(A),A) ) ) )).

fof(t23_waybel_8,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_8(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v4_waybel_7(B,A)
           => v5_waybel_6(B,A) ) ) ) )).

fof(t24_waybel_8,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_yellow_0(A)
        & v2_waybel_1(A)
        & v2_waybel_8(A)
        & l1_orders_2(A) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ( v4_waybel_7(B,A)
             => v5_waybel_6(B,A) ) )
       => v3_waybel_8(A) ) ) )).

fof(t25_waybel_8,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v2_waybel_8(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v7_waybel_1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v22_waybel_0(B,A,A)
           => r1_tarski(k4_pre_topc(A,A,B,k2_pre_topc(k1_waybel_8(A))),k2_pre_topc(k1_waybel_8(k2_yellow_2(A,A,B)))) ) ) ) )).

fof(t26_waybel_8,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_yellow_0(A)
        & v2_waybel_8(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v7_waybel_1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v22_waybel_0(B,A,A)
           => ( v2_orders_2(k2_yellow_2(A,A,B))
              & v3_orders_2(k2_yellow_2(A,A,B))
              & v4_orders_2(k2_yellow_2(A,A,B))
              & v1_lattice3(k2_yellow_2(A,A,B))
              & v2_lattice3(k2_yellow_2(A,A,B))
              & v2_waybel_8(k2_yellow_2(A,A,B))
              & l1_orders_2(k2_yellow_2(A,A,B)) ) ) ) ) )).

fof(t27_waybel_8,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_yellow_0(A)
        & v2_waybel_8(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v7_waybel_1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v22_waybel_0(B,A,A)
           => k4_pre_topc(A,A,B,k2_pre_topc(k1_waybel_8(A))) = k2_pre_topc(k1_waybel_8(k2_yellow_2(A,A,B))) ) ) ) )).

fof(t28_waybel_8,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,u1_struct_0(k3_yellow_1(A)))
    <=> r1_tarski(B,A) ) )).

fof(t29_waybel_8,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,u1_struct_0(k3_yellow_1(A)))
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(k3_yellow_1(A)))
         => ( r1_waybel_3(k3_yellow_1(A),B,C)
          <=> ! [D] :
                ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A)))
               => ~ ( r1_tarski(C,k5_setfam_1(A,D))
                    & ! [E] :
                        ( ( v1_finset_1(E)
                          & m1_subset_1(E,k1_zfmisc_1(D)) )
                       => ~ r1_tarski(B,k3_tarski(E)) ) ) ) ) ) ) )).

fof(t30_waybel_8,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,u1_struct_0(k3_yellow_1(A)))
     => ( v1_finset_1(B)
      <=> v1_waybel_3(B,k3_yellow_1(A)) ) ) )).

fof(t32_waybel_8,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ( r2_hidden(B,u1_struct_0(k1_waybel_8(k3_yellow_1(A))))
      <=> v1_finset_1(B) ) ) )).

fof(t33_waybel_8,axiom,(
    ! [A] : v2_waybel_8(k3_yellow_1(A)) )).

fof(dt_k1_waybel_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_orders_2(k1_waybel_8(A))
        & v4_yellow_0(k1_waybel_8(A),A)
        & m1_yellow_0(k1_waybel_8(A),A) ) ) )).

fof(dt_k2_waybel_8,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k2_waybel_8(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(d2_waybel_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k2_waybel_8(A,B) = a_2_0_waybel_8(A,B) ) ) )).

fof(t31_waybel_8,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,u1_struct_0(k3_yellow_1(A)))
     => k2_waybel_8(k3_yellow_1(A),B) = a_2_1_waybel_8(A,B) ) )).

fof(fraenkel_a_2_0_waybel_8,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v2_orders_2(B)
        & l1_orders_2(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_0_waybel_8(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & r1_orders_2(B,D,C)
            & v1_waybel_3(D,B) ) ) ) )).

fof(fraenkel_a_2_1_waybel_8,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,u1_struct_0(k3_yellow_1(B)))
     => ( r2_hidden(A,a_2_1_waybel_8(B,C))
      <=> ? [D] :
            ( v1_finset_1(D)
            & m1_subset_1(D,k1_zfmisc_1(C))
            & A = D ) ) ) )).
%------------------------------------------------------------------------------