SET007 Axioms: SET007+509.ax


%------------------------------------------------------------------------------
% File     : SET007+509 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Algebraic and Arithmetic Lattices. Part I
% 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    : waybel13 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   38 (   0 unit)
%            Number of atoms       :  502 (  13 equality)
%            Maximal formula depth :   20 (  10 average)
%            Number of connectives :  518 (  54 ~  ;   0  |; 344  &)
%                                         (   9 <=>; 111 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   52 (   0 propositional; 1-3 arity)
%            Number of functors    :   20 (   0 constant; 1-4 arity)
%            Number of variables   :  108 (   0 singleton;  99 !;   9 ?)
%            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(rc1_waybel13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v1_waybel_0(B,A)
          & v12_waybel_0(B,A)
          & v14_waybel_0(B,A) ) ) )).

fof(cc1_waybel13,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v4_orders_2(B)
        & l1_orders_2(B) )
     => ! [C] :
          ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v23_waybel_0(C,A,B) )
           => ( ~ v1_xboole_0(C)
              & v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B))
              & v17_waybel_0(C,A,B)
              & v18_waybel_0(C,A,B)
              & v19_waybel_0(C,A,B)
              & v20_waybel_0(C,A,B)
              & v21_waybel_0(C,A,B)
              & v22_waybel_0(C,A,B) ) ) ) ) )).

fof(t1_waybel13,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_orders_2(A,B,C)
               => r1_tarski(k2_waybel_8(A,B),k2_waybel_8(A,C)) ) ) ) ) )).

fof(t2_waybel13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => m1_subset_1(k2_waybel_8(A,B),k1_zfmisc_1(u1_struct_0(k1_waybel_8(A)))) ) ) )).

fof(t3_waybel13,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_yellow_0(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).

fof(t4_waybel13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v1_xboole_0(u1_struct_0(A))
        & v1_waybel_0(u1_struct_0(A),A)
        & v12_waybel_0(u1_struct_0(A),A)
        & m1_subset_1(u1_struct_0(A),k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(t5_waybel13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(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) )
           => u1_struct_0(k1_waybel_8(A)) = u1_struct_0(k1_waybel_8(B)) ) ) ) )).

fof(t6_waybel13,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] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & v7_yellow_0(B,A)
            & v4_waybel_0(B,A)
            & m1_yellow_0(B,A) )
         => v2_waybel_8(B) ) ) )).

fof(t8_waybel13,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k2_yellow_1(k8_waybel_0(A)))
        & v4_yellow_0(k2_yellow_1(k8_waybel_0(A)),k3_yellow_1(u1_struct_0(A)))
        & v7_yellow_0(k2_yellow_1(k8_waybel_0(A)),k3_yellow_1(u1_struct_0(A)))
        & v4_waybel_0(k2_yellow_1(k8_waybel_0(A)),k3_yellow_1(u1_struct_0(A)))
        & m1_yellow_0(k2_yellow_1(k8_waybel_0(A)),k3_yellow_1(u1_struct_0(A))) ) ) )).

fof(t9_waybel13,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,k2_yellow_1(k8_waybel_0(A)))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))) )
         => k1_yellow_0(k2_yellow_1(k8_waybel_0(A)),B) = k3_tarski(B) ) ) )).

fof(t10_waybel13,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => v2_waybel_8(k2_yellow_1(k8_waybel_0(A))) ) )).

fof(t11_waybel13,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
         => ( v1_waybel_3(B,k2_yellow_1(k8_waybel_0(A)))
          <=> ( ~ v1_xboole_0(B)
              & v1_waybel_0(B,A)
              & v12_waybel_0(B,A)
              & v14_waybel_0(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) )).

fof(t12_waybel13,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
         => ( v1_waybel_3(B,k2_yellow_1(k8_waybel_0(A)))
          <=> ? [C] :
                ( m1_subset_1(C,u1_struct_0(A))
                & B = k6_waybel_0(A,C) ) ) ) ) )).

fof(t13_waybel13,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_waybel_8(k2_yellow_1(k8_waybel_0(A)))))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k1_waybel_8(k2_yellow_1(k8_waybel_0(A))))) )
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k1_waybel_0(A,k1_waybel_8(k2_yellow_1(k8_waybel_0(A))),B,C) = k6_waybel_0(A,C) )
           => v23_waybel_0(B,A,k1_waybel_8(k2_yellow_1(k8_waybel_0(A)))) ) ) ) )).

fof(t14_waybel13,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => v3_waybel_8(k2_yellow_1(k8_waybel_0(A))) ) )).

fof(t15_waybel13,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & l1_orders_2(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))
        & v1_yellow_0(k1_waybel_8(A))
        & l1_orders_2(k1_waybel_8(A)) ) ) )).

fof(t16_waybel13,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_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(k2_yellow_1(k8_waybel_0(k1_waybel_8(A)))))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(k1_waybel_8(A))))) )
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k1_waybel_0(A,k2_yellow_1(k8_waybel_0(k1_waybel_8(A))),B,C) = k2_waybel_8(A,C) )
           => v23_waybel_0(B,A,k2_yellow_1(k8_waybel_0(k1_waybel_8(A)))) ) ) ) )).

fof(t17_waybel13,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & v2_waybel_8(A)
        & l1_orders_2(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),k1_waybel_8(A))
              & v12_waybel_0(k2_waybel_8(A,B),k1_waybel_8(A))
              & v14_waybel_0(k2_waybel_8(A,B),k1_waybel_8(A))
              & m1_subset_1(k2_waybel_8(A,B),k1_zfmisc_1(u1_struct_0(k1_waybel_8(A)))) )
          <=> v1_waybel_3(B,A) ) ) ) )).

fof(t18_waybel13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
                     => ( v23_waybel_0(E,A,B)
                       => ( r1_lattice3(A,C,D)
                        <=> r1_lattice3(B,k4_pre_topc(A,B,E,C),k1_waybel_0(A,B,E,D)) ) ) ) ) ) ) ) )).

fof(t19_waybel13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
                     => ( v23_waybel_0(E,A,B)
                       => ( r2_lattice3(A,C,D)
                        <=> r2_lattice3(B,k4_pre_topc(A,B,E,C),k1_waybel_0(A,B,E,D)) ) ) ) ) ) ) ) )).

fof(t20_waybel13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v23_waybel_0(C,A,B)
               => ( v17_waybel_0(C,A,B)
                  & v18_waybel_0(C,A,B) ) ) ) ) ) )).

fof(t21_waybel13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_orders_2(C)
                & v4_orders_2(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ~ ( v17_waybel_0(D,A,B)
                      & v4_yellow_0(B,C)
                      & v7_yellow_0(B,C)
                      & m1_yellow_0(B,C)
                      & v3_lattice3(C)
                      & ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
                            & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
                         => ~ ( D = E
                              & v17_waybel_0(E,A,C) ) ) ) ) ) ) ) )).

fof(t22_waybel13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_orders_2(C)
                & v4_orders_2(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ~ ( v5_orders_3(D,A,B)
                      & v22_waybel_0(D,A,B)
                      & v4_yellow_0(B,C)
                      & v4_waybel_0(B,C)
                      & m1_yellow_0(B,C)
                      & v3_lattice3(C)
                      & ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
                            & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
                         => ~ ( D = E
                              & v22_waybel_0(E,A,C) ) ) ) ) ) ) ) )).

fof(t23_waybel13,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k2_yellow_1(k8_waybel_0(k1_waybel_8(A))))
        & v4_yellow_0(k2_yellow_1(k8_waybel_0(k1_waybel_8(A))),k3_yellow_1(u1_struct_0(k1_waybel_8(A))))
        & v7_yellow_0(k2_yellow_1(k8_waybel_0(k1_waybel_8(A))),k3_yellow_1(u1_struct_0(k1_waybel_8(A))))
        & v4_waybel_0(k2_yellow_1(k8_waybel_0(k1_waybel_8(A))),k3_yellow_1(u1_struct_0(k1_waybel_8(A))))
        & m1_yellow_0(k2_yellow_1(k8_waybel_0(k1_waybel_8(A))),k3_yellow_1(u1_struct_0(k1_waybel_8(A)))) ) ) )).

fof(t24_waybel13,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(k3_yellow_1(u1_struct_0(k1_waybel_8(A)))))
          & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_yellow_1(u1_struct_0(k1_waybel_8(A)))))
          & v17_waybel_0(B,A,k3_yellow_1(u1_struct_0(k1_waybel_8(A))))
          & v22_waybel_0(B,A,k3_yellow_1(u1_struct_0(k1_waybel_8(A))))
          & v2_funct_1(B)
          & ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_waybel_0(A,k3_yellow_1(u1_struct_0(k1_waybel_8(A))),B,C) = k2_waybel_8(A,C) ) ) ) )).

fof(t25_waybel13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_yellow_1(B)
            & v4_waybel_3(B)
            & v5_waybel_3(B)
            & m1_pboole(B,A) )
         => ( ! [C] :
                ( m1_subset_1(C,A)
               => ( v2_orders_2(k6_waybel_3(A,B,C))
                  & v3_orders_2(k6_waybel_3(A,B,C))
                  & v4_orders_2(k6_waybel_3(A,B,C))
                  & v1_lattice3(k6_waybel_3(A,B,C))
                  & v2_lattice3(k6_waybel_3(A,B,C))
                  & v1_yellow_0(k6_waybel_3(A,B,C))
                  & v2_waybel_8(k6_waybel_3(A,B,C))
                  & l1_orders_2(k6_waybel_3(A,B,C)) ) )
           => ( v2_orders_2(k5_yellow_1(A,B))
              & v3_orders_2(k5_yellow_1(A,B))
              & v4_orders_2(k5_yellow_1(A,B))
              & v1_lattice3(k5_yellow_1(A,B))
              & v2_lattice3(k5_yellow_1(A,B))
              & v1_yellow_0(k5_yellow_1(A,B))
              & v2_waybel_8(k5_yellow_1(A,B))
              & l1_orders_2(k5_yellow_1(A,B)) ) ) ) ) )).

fof(t26_waybel13,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))
           => r5_waybel_1(A,B) ) ) ) )).

fof(t27_waybel13,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] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v24_waybel_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v23_waybel_0(C,A,B)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( r1_waybel_3(A,D,E)
                        <=> r1_waybel_3(B,k1_waybel_0(A,B,C,D),k1_waybel_0(A,B,C,E)) ) ) ) ) ) ) ) )).

fof(t28_waybel13,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] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v24_waybel_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v23_waybel_0(C,A,B)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( v1_waybel_3(D,A)
                    <=> v1_waybel_3(k1_waybel_0(A,B,C,D),B) ) ) ) ) ) ) )).

fof(t29_waybel13,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] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v24_waybel_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v23_waybel_0(C,A,B)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k4_pre_topc(A,B,C,k2_waybel_8(A,D)) = k2_waybel_8(B,k1_waybel_0(A,B,C,D)) ) ) ) ) ) )).

fof(t30_waybel13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ( ( r5_waybel_1(A,B)
              & v24_waybel_0(A) )
           => v24_waybel_0(B) ) ) ) )).

fof(t31_waybel13,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ( ( r5_waybel_1(A,B)
              & v3_lattice3(A)
              & v1_waybel_8(A) )
           => v1_waybel_8(B) ) ) ) )).

fof(t32_waybel13,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_lattice3(B)
            & l1_orders_2(B) )
         => ( ( r5_waybel_1(A,B)
              & v1_yellow_0(A)
              & v2_waybel_8(A) )
           => v2_waybel_8(B) ) ) ) )).

fof(t33_waybel13,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ( v17_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A)
        & v18_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A) ) ) )).

fof(t34_waybel13,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ( ~ ( v2_waybel_8(A)
            & ! [B] :
                ( ~ v1_xboole_0(B)
               => ! [C] :
                    ( ( v4_yellow_0(C,k3_yellow_1(B))
                      & m1_yellow_0(C,k3_yellow_1(B)) )
                   => ~ ( v7_yellow_0(C,k3_yellow_1(B))
                        & v4_waybel_0(C,k3_yellow_1(B))
                        & r5_waybel_1(A,C) ) ) ) )
        & ( ? [B,C] :
              ( v4_yellow_0(C,k3_yellow_1(B))
              & m1_yellow_0(C,k3_yellow_1(B))
              & v7_yellow_0(C,k3_yellow_1(B))
              & v4_waybel_0(C,k3_yellow_1(B))
              & r5_waybel_1(A,C) )
         => v2_waybel_8(A) ) ) ) )).

fof(t35_waybel13,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ( ~ ( v2_waybel_8(A)
            & ! [B] :
                ( ~ v1_xboole_0(B)
               => ! [C] :
                    ( ( v1_funct_1(C)
                      & v1_funct_2(C,u1_struct_0(k3_yellow_1(B)),u1_struct_0(k3_yellow_1(B)))
                      & v7_waybel_1(C,k3_yellow_1(B))
                      & m2_relset_1(C,u1_struct_0(k3_yellow_1(B)),u1_struct_0(k3_yellow_1(B))) )
                   => ~ ( v22_waybel_0(C,k3_yellow_1(B),k3_yellow_1(B))
                        & r5_waybel_1(A,k2_yellow_2(k3_yellow_1(B),k3_yellow_1(B),C)) ) ) ) )
        & ( ? [B,C] :
              ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(k3_yellow_1(B)),u1_struct_0(k3_yellow_1(B)))
              & v7_waybel_1(C,k3_yellow_1(B))
              & m2_relset_1(C,u1_struct_0(k3_yellow_1(B)),u1_struct_0(k3_yellow_1(B)))
              & v22_waybel_0(C,k3_yellow_1(B),k3_yellow_1(B))
              & r5_waybel_1(A,k2_yellow_2(k3_yellow_1(B),k3_yellow_1(B),C)) )
         => v2_waybel_8(A) ) ) ) )).

fof(t7_waybel13,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(C)
        & v4_yellow_0(C,k3_yellow_1(A))
        & v7_yellow_0(C,k3_yellow_1(A))
        & v4_waybel_0(C,k3_yellow_1(A))
        & m1_yellow_0(C,k3_yellow_1(A)) )
     => ( r2_hidden(B,u1_struct_0(k1_waybel_8(C)))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(k3_yellow_1(A)))
            & v1_finset_1(D)
            & B = k1_setfam_1(a_3_0_waybel13(A,C,D))
            & r1_tarski(D,B) ) ) ) )).

fof(fraenkel_a_3_0_waybel13,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(C)
        & v4_yellow_0(C,k3_yellow_1(B))
        & v7_yellow_0(C,k3_yellow_1(B))
        & v4_waybel_0(C,k3_yellow_1(B))
        & m1_yellow_0(C,k3_yellow_1(B))
        & m1_subset_1(D,u1_struct_0(k3_yellow_1(B))) )
     => ( r2_hidden(A,a_3_0_waybel13(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(C))
            & A = E
            & r1_tarski(D,E) ) ) ) )).
%------------------------------------------------------------------------------