SET007 Axioms: SET007+488.ax


%------------------------------------------------------------------------------
% File     : SET007+488 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Meet - 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    : waybel_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   95 (   0 unit)
%            Number of atoms       : 1042 (  64 equality)
%            Maximal formula depth :   24 (  10 average)
%            Number of connectives : 1096 ( 149 ~  ;   0  |; 673  &)
%                                         (  21 <=>; 253 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   52 (   0 propositional; 1-4 arity)
%            Number of functors    :   58 (   2 constant; 0-4 arity)
%            Number of variables   :  265 (   0 singleton; 252 !;  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_waybel_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & ~ v1_xboole_0(D)
        & m1_subset_1(D,k1_zfmisc_1(A)) )
     => ~ v1_xboole_0(k9_relat_1(C,D)) ) )).

fof(cc1_waybel_2,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v16_waybel_0(A) )
       => ( ~ v3_struct_0(A)
          & v1_lattice3(A)
          & v2_lattice3(A) ) ) ) )).

fof(fc2_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v16_waybel_0(A)
        & l1_orders_2(A) )
     => ( ~ v1_xboole_0(k2_pre_topc(A))
        & v1_waybel_0(k2_pre_topc(A),A)
        & v2_waybel_0(k2_pre_topc(A),A)
        & v12_waybel_0(k2_pre_topc(A),A)
        & v13_waybel_0(k2_pre_topc(A),A) ) ) )).

fof(fc3_waybel_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v24_waybel_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v24_waybel_0(B)
        & l1_orders_2(B) )
     => ( ~ v3_struct_0(k3_yellow_3(A,B))
        & v1_orders_2(k3_yellow_3(A,B))
        & v2_orders_2(k3_yellow_3(A,B))
        & v24_waybel_0(k3_yellow_3(A,B))
        & ~ v1_yellow_3(k3_yellow_3(A,B)) ) ) )).

fof(cc2_waybel_2,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & ~ v1_yellow_3(A)
          & v2_waybel_1(A)
          & v10_waybel_1(A) ) ) ) )).

fof(rc1_waybel_2,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_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_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v2_waybel_1(A)
      & v9_waybel_1(A)
      & v10_waybel_1(A)
      & v11_waybel_1(A)
      & v3_realset2(A) ) )).

fof(fc4_waybel_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A)
        & v1_funct_1(C)
        & v1_funct_2(C,B,u1_struct_0(A))
        & m1_relset_1(C,B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k2_waybel_2(A,B,C))
        & v7_waybel_0(k2_waybel_2(A,B,C))
        & v8_waybel_0(k2_waybel_2(A,B,C),A)
        & v10_waybel_0(k2_waybel_2(A,B,C),A) ) ) )).

fof(fc5_waybel_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & ~ v3_struct_0(C)
        & l1_waybel_0(C,A) )
     => ( ~ v3_struct_0(k3_waybel_2(A,B,C))
        & v6_waybel_0(k3_waybel_2(A,B,C),A) ) ) )).

fof(fc6_waybel_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & ~ v3_struct_0(C)
        & v7_waybel_0(C)
        & l1_waybel_0(C,A) )
     => ( ~ v3_struct_0(k3_waybel_2(A,B,C))
        & v6_waybel_0(k3_waybel_2(A,B,C),A)
        & v7_waybel_0(k3_waybel_2(A,B,C)) ) ) )).

fof(fc7_waybel_2,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v1_xboole_0(k4_waybel_2(A))
        & v1_relat_1(k4_waybel_2(A))
        & v1_funct_1(k4_waybel_2(A))
        & v1_funct_2(k4_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A))
        & v5_orders_3(k4_waybel_2(A),k3_yellow_3(A,A),A)
        & v1_partfun1(k4_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A)) ) ) )).

fof(fc8_waybel_2,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v1_xboole_0(k5_waybel_2(A))
        & v1_relat_1(k5_waybel_2(A))
        & v1_funct_1(k5_waybel_2(A))
        & v1_funct_2(k5_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A))
        & v5_orders_3(k5_waybel_2(A),k3_yellow_3(A,A),A)
        & v1_partfun1(k5_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A)) ) ) )).

fof(cc3_waybel_2,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & ~ v1_yellow_3(A)
          & v1_waybel_2(A) ) ) ) )).

fof(cc4_waybel_2,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v2_waybel_2(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v24_waybel_0(A)
          & ~ v1_yellow_3(A)
          & v1_waybel_2(A) ) ) ) )).

fof(cc5_waybel_2,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v24_waybel_0(A)
          & v1_waybel_2(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & ~ v1_yellow_3(A)
          & v2_waybel_2(A) ) ) ) )).

fof(rc2_waybel_2,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_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_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v2_waybel_1(A)
      & v9_waybel_1(A)
      & v10_waybel_1(A)
      & v11_waybel_1(A)
      & v3_realset2(A)
      & v1_waybel_2(A)
      & v2_waybel_2(A) ) )).

fof(fc9_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v1_xboole_0(k3_yellow_2(A))
        & v1_relat_1(k3_yellow_2(A))
        & v1_funct_1(k3_yellow_2(A))
        & v1_funct_2(k3_yellow_2(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A))
        & v5_orders_3(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A)
        & v20_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A)
        & v1_partfun1(k3_yellow_2(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A)) ) ) )).

fof(fc10_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v2_waybel_2(A)
        & l1_orders_2(A) )
     => ( ~ v1_xboole_0(k3_yellow_2(A))
        & v1_relat_1(k3_yellow_2(A))
        & v1_funct_1(k3_yellow_2(A))
        & v1_funct_2(k3_yellow_2(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A))
        & v5_orders_3(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A)
        & v19_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A)
        & v20_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A)
        & v1_partfun1(k3_yellow_2(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A)) ) ) )).

fof(fc11_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & v2_waybel_2(A)
        & l1_orders_2(A) )
     => ( ~ v1_xboole_0(k4_waybel_2(A))
        & v1_relat_1(k4_waybel_2(A))
        & v1_funct_1(k4_waybel_2(A))
        & v1_funct_2(k4_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A))
        & v5_orders_3(k4_waybel_2(A),k3_yellow_3(A,A),A)
        & v22_waybel_0(k4_waybel_2(A),k3_yellow_3(A,A),A)
        & v1_partfun1(k4_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A)) ) ) )).

fof(fc12_waybel_2,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & v2_waybel_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v1_xboole_0(k4_waybel_1(A,B))
        & v1_relat_1(k4_waybel_1(A,B))
        & v1_funct_1(k4_waybel_1(A,B))
        & v1_funct_2(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A))
        & v5_orders_3(k4_waybel_1(A,B),A,A)
        & v22_waybel_0(k4_waybel_1(A,B),A,A)
        & v1_partfun1(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(cc6_waybel_2,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v3_lattice3(A)
          & v9_waybel_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v24_waybel_0(A)
          & ~ v1_yellow_3(A)
          & v2_waybel_1(A)
          & v1_waybel_2(A)
          & v2_waybel_2(A) ) ) ) )).

fof(cc7_waybel_2,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v3_lattice3(A)
          & v2_waybel_1(A)
          & v2_waybel_2(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v2_yellow_0(A)
          & ~ v1_yellow_3(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v2_waybel_1(A)
          & v9_waybel_1(A) ) ) ) )).

fof(t1_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(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))
             => r1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,C),B)) ) ) ) )).

fof(t2_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v1_lattice3(A)
        & l1_orders_2(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))
             => r1_yellow_0(A,k2_yellow_4(A,k1_struct_0(A,C),B)) ) ) ) )).

fof(t3_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_waybel_0(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => r2_lattice3(A,B,k1_yellow_0(A,k2_yellow_4(A,B,C))) ) ) ) )).

fof(t4_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_waybel_0(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => k1_yellow_0(A,k2_yellow_4(A,B,C)) = k13_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) ) ) ) )).

fof(t11_waybel_2,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) )
         => ( v24_waybel_0(k3_yellow_3(A,B))
           => ( v24_waybel_0(A)
              & v24_waybel_0(B) ) ) ) ) )).

fof(t12_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,k3_yellow_3(A,A))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
         => k1_yellow_0(k3_yellow_3(A,A),B) = k7_yellow_3(A,A,k1_yellow_0(A,k4_yellow_3(A,A,B)),k1_yellow_0(A,k5_yellow_3(A,A,B))) ) ) )).

fof(t13_waybel_2,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [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)
                   => r1_tarski(k4_pre_topc(A,B,D,k4_waybel_0(A,C)),k4_waybel_0(B,k4_pre_topc(A,B,D,C))) ) ) ) ) ) )).

fof(t14_waybel_2,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [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)
                   => r1_tarski(k4_pre_topc(A,B,D,k5_waybel_0(A,C)),k5_waybel_0(B,k4_pre_topc(A,B,D,C))) ) ) ) ) ) )).

fof(t15_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v1_finset_1(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,B),C)) = k12_lattice3(A,B,k1_yellow_0(A,C)) ) ) ) )).

fof(t16_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v1_finset_1(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => k2_yellow_0(A,k2_yellow_4(A,k1_struct_0(A,B),C)) = k13_lattice3(A,B,k2_yellow_0(A,C)) ) ) ) )).

fof(t17_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v2_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v1_finset_1(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => r4_waybel_0(A,A,k4_waybel_1(A,B),C) ) ) ) )).

fof(t18_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ( v10_waybel_0(B,A)
           => v1_waybel_0(k8_yellow_2(u1_struct_0(B),A,k2_waybel_0(A,B)),A) ) ) ) )).

fof(t19_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,B,u1_struct_0(A))
                & m2_relset_1(C,B,u1_struct_0(A)) )
             => ( ~ v3_struct_0(g1_waybel_0(A,B,k1_toler_1(u1_orders_2(A),B),C))
                & v7_waybel_0(g1_waybel_0(A,B,k1_toler_1(u1_orders_2(A),B),C))
                & l1_waybel_0(g1_waybel_0(A,B,k1_toler_1(u1_orders_2(A),B),C),A) ) ) ) ) )).

fof(t20_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,B,u1_struct_0(A))
                & m2_relset_1(C,B,u1_struct_0(A)) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v7_waybel_0(D)
                    & l1_waybel_0(D,A) )
                 => ( ( C = k6_partfun1(B)
                      & D = g1_waybel_0(A,B,k1_toler_1(u1_orders_2(A),B),C) )
                   => v10_waybel_0(D,A) ) ) ) ) ) )).

fof(d1_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( l1_waybel_0(B,A)
         => k1_waybel_2(A,B) = k5_yellow_2(A,u1_waybel_0(A,B)) ) ) )).

fof(d2_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B,C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,u1_struct_0(A))
            & m2_relset_1(C,B,u1_struct_0(A)) )
         => ! [D] :
              ( ( ~ v3_struct_0(D)
                & v7_waybel_0(D)
                & l1_waybel_0(D,A) )
             => ( D = k2_waybel_2(A,B,C)
              <=> ? [E] :
                    ( v1_funct_1(E)
                    & v1_funct_2(E,k5_finsub_1(B),u1_struct_0(A))
                    & m2_relset_1(E,k5_finsub_1(B),u1_struct_0(A))
                    & ! [F] :
                        ( m1_subset_1(F,k5_finsub_1(B))
                       => ( k7_yellow_2(k5_finsub_1(B),A,E,F) = k1_yellow_0(A,k2_funct_2(B,u1_struct_0(A),C,F))
                          & D = g1_waybel_0(A,k5_finsub_1(B),k1_yellow_1(k5_finsub_1(B)),E) ) ) ) ) ) ) ) )).

fof(t21_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B,C,D] :
          ( ( v1_funct_1(D)
            & v1_funct_2(D,B,u1_struct_0(A))
            & m2_relset_1(D,B,u1_struct_0(A)) )
         => ( m1_subset_1(C,u1_struct_0(k2_waybel_2(A,B,D)))
          <=> m1_subset_1(C,k5_finsub_1(B)) ) ) ) )).

fof(d3_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_waybel_0(C,A) )
             => ! [D] :
                  ( ( v6_waybel_0(D,A)
                    & l1_waybel_0(D,A) )
                 => ( D = k3_waybel_2(A,B,C)
                  <=> ( g1_orders_2(u1_struct_0(D),u1_orders_2(D)) = g1_orders_2(u1_struct_0(C),u1_orders_2(C))
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(D))
                         => ? [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                              & F = k1_funct_1(u1_waybel_0(A,C),E)
                              & k1_funct_1(u1_waybel_0(A,D),E) = k11_lattice3(A,B,F) ) ) ) ) ) ) ) ) )).

fof(t22_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                <=> m1_subset_1(D,u1_struct_0(k3_waybel_2(A,C,B))) ) ) ) ) )).

fof(t23_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_waybel_0(C,A) )
             => k8_yellow_2(u1_struct_0(k3_waybel_2(A,B,C)),A,u1_waybel_0(A,k3_waybel_2(A,B,C))) = k3_yellow_4(A,k1_struct_0(A,B),k8_yellow_2(u1_struct_0(C),A,u1_waybel_0(A,C))) ) ) ) )).

fof(t24_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B,C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,u1_struct_0(A))
            & m2_relset_1(C,B,u1_struct_0(A)) )
         => ( ! [D] : r1_yellow_0(A,k2_funct_2(B,u1_struct_0(A),C,D))
           => r1_tarski(k8_yellow_2(u1_struct_0(k2_waybel_2(A,B,C)),A,k2_waybel_0(A,k2_waybel_2(A,B,C))),k12_waybel_0(A,k8_yellow_2(B,A,C))) ) ) ) )).

fof(t25_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B,C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,u1_struct_0(A))
            & m2_relset_1(C,B,u1_struct_0(A)) )
         => r1_tarski(k8_yellow_2(B,A,C),k8_yellow_2(u1_struct_0(k2_waybel_2(A,B,C)),A,k2_waybel_0(A,k2_waybel_2(A,B,C)))) ) ) )).

fof(t26_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B,C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,u1_struct_0(A))
            & m2_relset_1(C,B,u1_struct_0(A)) )
         => ( ( r1_yellow_0(A,k8_yellow_2(B,A,C))
              & r1_yellow_0(A,k8_yellow_2(u1_struct_0(k2_waybel_2(A,B,C)),A,k2_waybel_0(A,k2_waybel_2(A,B,C))))
              & ! [D] :
                  ( m1_subset_1(D,k5_finsub_1(B))
                 => r1_yellow_0(A,k2_funct_2(B,u1_struct_0(A),C,D)) ) )
           => k5_yellow_2(A,C) = k1_waybel_2(A,k2_waybel_2(A,B,C)) ) ) ) )).

fof(t27_waybel_2,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( v10_waybel_0(B,A)
               => v10_waybel_0(k3_waybel_2(A,C,B),A) ) ) ) ) )).

fof(t28_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v1_waybel_0(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => ( r3_orders_2(A,B,k1_yellow_0(A,C))
                 => r3_orders_2(A,B,k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,B),C))) ) ) )
       => ! [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))
               => k12_lattice3(A,C,k1_yellow_0(A,B)) = k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,C),B)) ) ) ) ) )).

fof(t29_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( ! [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))
               => k11_lattice3(A,C,k1_yellow_0(A,B)) = k1_yellow_0(A,k3_yellow_4(A,k1_struct_0(A,C),B)) ) )
       => ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r1_yellow_0(A,B)
                 => k11_lattice3(A,C,k1_yellow_0(A,B)) = k1_yellow_0(A,k3_yellow_4(A,k1_struct_0(A,C),k12_waybel_0(A,B))) ) ) ) ) ) )).

fof(t30_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v1_lattice3(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))
               => k12_lattice3(A,C,k1_yellow_0(A,B)) = k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,C),k12_waybel_0(A,B))) ) )
       => ! [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))
               => k12_lattice3(A,C,k1_yellow_0(A,B)) = k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,C),B)) ) ) ) ) )).

fof(d4_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A)) )
         => ( B = k4_waybel_2(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k7_yellow_2(u1_struct_0(k3_yellow_3(A,A)),A,B,k7_yellow_3(A,A,C,D)) = k11_lattice3(A,C,D) ) ) ) ) ) )).

fof(t31_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k3_yellow_3(A,A)))
         => k7_yellow_2(u1_struct_0(k3_yellow_3(A,A)),A,k4_waybel_2(A),B) = k11_lattice3(A,k8_yellow_3(A,A,B),k9_yellow_3(A,A,B)) ) ) )).

fof(t32_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k4_pre_topc(k3_yellow_3(A,A),A,k4_waybel_2(A),k6_yellow_3(A,A,B,C)) = k3_yellow_4(A,B,C) ) ) ) )).

fof(t33_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,k3_yellow_3(A,A))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
         => k1_yellow_0(A,k4_pre_topc(k3_yellow_3(A,A),A,k4_waybel_2(A),B)) = k1_yellow_0(A,k4_yellow_4(A,k4_yellow_3(A,A,B),k5_yellow_3(A,A,B))) ) ) )).

fof(d5_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A)) )
         => ( B = k5_waybel_2(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k7_yellow_2(u1_struct_0(k3_yellow_3(A,A)),A,B,k7_yellow_3(A,A,C,D)) = k10_lattice3(A,C,D) ) ) ) ) ) )).

fof(t34_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k3_yellow_3(A,A)))
         => k7_yellow_2(u1_struct_0(k3_yellow_3(A,A)),A,k5_waybel_2(A),B) = k10_lattice3(A,k8_yellow_3(A,A,B),k9_yellow_3(A,A,B)) ) ) )).

fof(t35_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k4_pre_topc(k3_yellow_3(A,A),A,k5_waybel_2(A),k6_yellow_3(A,A,B,C)) = k1_yellow_4(A,B,C) ) ) ) )).

fof(t36_waybel_2,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] :
          ( ( ~ v1_xboole_0(B)
            & v2_waybel_0(B,k3_yellow_3(A,A))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
         => k2_yellow_0(A,k4_pre_topc(k3_yellow_3(A,A),A,k5_waybel_2(A),B)) = k2_yellow_0(A,k2_yellow_4(A,k4_yellow_3(A,A,B),k5_yellow_3(A,A,B))) ) ) )).

fof(d6_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_waybel_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v1_waybel_0(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => k11_lattice3(A,B,k1_yellow_0(A,C)) = k1_yellow_0(A,k3_yellow_4(A,k1_struct_0(A,B),C)) ) ) ) ) )).

fof(d7_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( v2_waybel_2(A)
      <=> ( v24_waybel_0(A)
          & v1_waybel_2(A) ) ) ) )).

fof(t38_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( v19_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A)
       => ! [B] :
            ( ( ~ v1_xboole_0(B)
              & v1_waybel_0(B,A)
              & v12_waybel_0(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v1_waybel_0(C,A)
                  & v12_waybel_0(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => k12_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) = k1_yellow_0(A,k4_yellow_4(A,B,C)) ) ) ) ) )).

fof(t39_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( ! [B] :
            ( ( ~ v1_xboole_0(B)
              & v1_waybel_0(B,A)
              & v12_waybel_0(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v1_waybel_0(C,A)
                  & v12_waybel_0(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => k12_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) = k1_yellow_0(A,k4_yellow_4(A,B,C)) ) )
       => v19_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A) ) ) )).

fof(t40_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( ! [B] :
            ( ( ~ v1_xboole_0(B)
              & v1_waybel_0(B,A)
              & v12_waybel_0(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v1_waybel_0(C,A)
                  & v12_waybel_0(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => k12_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) = k1_yellow_0(A,k4_yellow_4(A,B,C)) ) )
       => ! [B] :
            ( ( ~ v1_xboole_0(B)
              & v1_waybel_0(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v1_waybel_0(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => k12_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) = k1_yellow_0(A,k4_yellow_4(A,B,C)) ) ) ) ) )).

fof(t41_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_waybel_2(A)
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( ( ~ v3_struct_0(C)
                  & v7_waybel_0(C)
                  & l1_waybel_0(C,A) )
               => ( v10_waybel_0(C,A)
                 => k11_lattice3(A,B,k1_waybel_2(A,C)) = k1_yellow_0(A,k3_yellow_4(A,k1_struct_0(A,B),k8_yellow_2(u1_struct_0(C),A,k2_waybel_0(A,C)))) ) ) ) ) ) )).

fof(t42_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( ( ~ v3_struct_0(C)
                  & v7_waybel_0(C)
                  & l1_waybel_0(C,A) )
               => ( v10_waybel_0(C,A)
                 => k11_lattice3(A,B,k1_waybel_2(A,C)) = k1_yellow_0(A,k3_yellow_4(A,k1_struct_0(A,B),k8_yellow_2(u1_struct_0(C),A,k2_waybel_0(A,C)))) ) ) )
       => v1_waybel_2(A) ) ) )).

fof(t43_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & l1_orders_2(A) )
     => ( v22_waybel_0(k4_waybel_2(A),k3_yellow_3(A,A),A)
       => ! [B] :
            ( ( ~ v1_xboole_0(B)
              & v1_waybel_0(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v1_waybel_0(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => k11_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) = k1_yellow_0(A,k3_yellow_4(A,B,C)) ) ) ) ) )).

fof(t44_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( ! [B] :
            ( ( ~ v1_xboole_0(B)
              & v1_waybel_0(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v1_waybel_0(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => k11_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) = k1_yellow_0(A,k3_yellow_4(A,B,C)) ) )
       => v1_waybel_2(A) ) ) )).

fof(t45_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & v1_waybel_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_waybel_0(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( r3_orders_2(A,B,k1_yellow_0(A,C))
               => B = k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,B),C)) ) ) ) ) )).

fof(t46_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v1_waybel_0(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => ( r3_orders_2(A,B,k1_yellow_0(A,C))
                 => r3_orders_2(A,B,k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,B),C))) ) ) )
       => v22_waybel_0(k4_waybel_2(A),k3_yellow_3(A,A),A) ) ) )).

fof(t47_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( ( ~ v3_struct_0(C)
                  & v7_waybel_0(C)
                  & l1_waybel_0(C,A) )
               => ( v10_waybel_0(C,A)
                 => k12_lattice3(A,B,k1_waybel_2(A,C)) = k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,B),k8_yellow_2(u1_struct_0(C),A,k2_waybel_0(A,C)))) ) ) )
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C,D] :
                ( ( v1_funct_1(D)
                  & v1_funct_2(D,C,u1_struct_0(A))
                  & m2_relset_1(D,C,u1_struct_0(A)) )
               => k12_lattice3(A,B,k5_yellow_2(A,D)) = k1_waybel_2(A,k3_waybel_2(A,B,k2_waybel_2(A,C,D))) ) ) ) ) )).

fof(t48_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C,D] :
                ( ( v1_funct_1(D)
                  & v1_funct_2(D,C,u1_struct_0(A))
                  & m2_relset_1(D,C,u1_struct_0(A)) )
               => k12_lattice3(A,B,k5_yellow_2(A,D)) = k1_waybel_2(A,k3_waybel_2(A,B,k2_waybel_2(A,C,D))) ) )
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( ( ~ v3_struct_0(C)
                  & v7_waybel_0(C)
                  & l1_waybel_0(C,A) )
               => ( v10_waybel_0(C,A)
                 => k12_lattice3(A,B,k1_waybel_2(A,C)) = k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,B),k8_yellow_2(u1_struct_0(C),A,k2_waybel_0(A,C)))) ) ) ) ) ) )).

fof(t49_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( v2_waybel_2(A)
      <=> ( v19_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A)
          & v20_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A) ) ) ) )).

fof(t50_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( v2_waybel_2(A)
      <=> ! [B] :
            ( ( ~ v1_xboole_0(B)
              & v1_waybel_0(B,A)
              & v12_waybel_0(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v1_waybel_0(C,A)
                  & v12_waybel_0(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => k12_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) = k1_yellow_0(A,k4_yellow_4(A,B,C)) ) ) ) ) )).

fof(t51_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( v2_waybel_2(A)
      <=> ! [B] :
            ( ( ~ v1_xboole_0(B)
              & v1_waybel_0(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v1_waybel_0(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => k12_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) = k1_yellow_0(A,k4_yellow_4(A,B,C)) ) ) ) ) )).

fof(t52_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( v2_waybel_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v1_waybel_0(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => ( r3_orders_2(A,B,k1_yellow_0(A,C))
                 => B = k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,B),C)) ) ) ) ) ) )).

fof(t53_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( v2_waybel_2(A)
      <=> v22_waybel_0(k4_waybel_2(A),k3_yellow_3(A,A),A) ) ) )).

fof(t54_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( v2_waybel_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( ( ~ v3_struct_0(C)
                  & v7_waybel_0(C)
                  & l1_waybel_0(C,A) )
               => ( v10_waybel_0(C,A)
                 => k12_lattice3(A,B,k1_waybel_2(A,C)) = k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,B),k8_yellow_2(u1_struct_0(C),A,k2_waybel_0(A,C)))) ) ) ) ) ) )).

fof(t55_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ( v2_waybel_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C,D] :
                ( ( v1_funct_1(D)
                  & v1_funct_2(D,C,u1_struct_0(A))
                  & m2_relset_1(D,C,u1_struct_0(A)) )
               => k12_lattice3(A,B,k5_yellow_2(A,D)) = k1_waybel_2(A,k3_waybel_2(A,B,k2_waybel_2(A,C,D))) ) ) ) ) )).

fof(t56_waybel_2,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) )
     => ( v9_waybel_1(A)
      <=> ( v2_waybel_2(A)
          & v2_waybel_1(A) ) ) ) )).

fof(s1_waybel_2,axiom,(
    ? [A] :
      ( ~ v3_struct_0(A)
      & v7_waybel_0(A)
      & l1_waybel_0(A,f1_s1_waybel_2)
      & g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(f2_s1_waybel_2),u1_orders_2(f2_s1_waybel_2))
      & ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k7_yellow_2(u1_struct_0(A),f1_s1_waybel_2,u1_waybel_0(f1_s1_waybel_2,A),B) = f3_s1_waybel_2(k1_funct_1(u1_waybel_0(f1_s1_waybel_2,f2_s1_waybel_2),B)) ) ) )).

fof(dt_k1_waybel_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & l1_waybel_0(B,A) )
     => m1_subset_1(k1_waybel_2(A,B),u1_struct_0(A)) ) )).

fof(dt_k2_waybel_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & v1_funct_1(C)
        & v1_funct_2(C,B,u1_struct_0(A))
        & m1_relset_1(C,B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k2_waybel_2(A,B,C))
        & v7_waybel_0(k2_waybel_2(A,B,C))
        & l1_waybel_0(k2_waybel_2(A,B,C),A) ) ) )).

fof(dt_k3_waybel_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & ~ v3_struct_0(C)
        & l1_waybel_0(C,A) )
     => ( v6_waybel_0(k3_waybel_2(A,B,C),A)
        & l1_waybel_0(k3_waybel_2(A,B,C),A) ) ) )).

fof(dt_k4_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v1_funct_1(k4_waybel_2(A))
        & v1_funct_2(k4_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A))
        & m2_relset_1(k4_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A)) ) ) )).

fof(dt_k5_waybel_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v1_funct_1(k5_waybel_2(A))
        & v1_funct_2(k5_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A))
        & m2_relset_1(k5_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A)) ) ) )).

fof(t5_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,k3_yellow_3(A,A))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
         => a_2_0_waybel_2(A,B) = a_2_1_waybel_2(A,B) ) ) )).

fof(t6_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,k3_yellow_3(A,A))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
         => k3_tarski(a_2_2_waybel_2(A,B)) = k4_yellow_4(A,k4_yellow_3(A,A,B),k5_yellow_3(A,A,B)) ) ) )).

fof(t7_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,k3_yellow_3(A,A))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
         => r1_yellow_0(A,k3_tarski(a_2_3_waybel_2(A,B))) ) ) )).

fof(t8_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,k3_yellow_3(A,A))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
         => r1_yellow_0(A,a_2_1_waybel_2(A,B)) ) ) )).

fof(t9_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,k3_yellow_3(A,A))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
         => r3_orders_2(A,k1_yellow_0(A,a_2_1_waybel_2(A,B)),k1_yellow_0(A,k3_tarski(a_2_3_waybel_2(A,B)))) ) ) )).

fof(t10_waybel_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,k3_yellow_3(A,A))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
         => k1_yellow_0(A,a_2_1_waybel_2(A,B)) = k1_yellow_0(A,k3_tarski(a_2_3_waybel_2(A,B))) ) ) )).

fof(t37_waybel_2,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))
               => k11_lattice3(A,C,k1_yellow_0(A,B)) = k1_yellow_0(A,a_3_0_waybel_2(A,B,C)) ) )
       => v1_waybel_2(A) ) ) )).

fof(fraenkel_a_2_0_waybel_2,axiom,(
    ! [A,B,C] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v24_waybel_0(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & ~ v1_xboole_0(C)
        & v1_waybel_0(C,k3_yellow_3(B,B))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) )
     => ( r2_hidden(A,a_2_0_waybel_2(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = k1_yellow_0(B,k4_yellow_4(B,k1_struct_0(B,D),k5_yellow_3(B,B,C)))
            & r2_hidden(D,k4_yellow_3(B,B,C)) ) ) ) )).

fof(fraenkel_a_2_1_waybel_2,axiom,(
    ! [A,B,C] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v24_waybel_0(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & ~ v1_xboole_0(C)
        & v1_waybel_0(C,k3_yellow_3(B,B))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) )
     => ( r2_hidden(A,a_2_1_waybel_2(B,C))
      <=> ? [D] :
            ( ~ v1_xboole_0(D)
            & v1_waybel_0(D,B)
            & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = k1_yellow_0(B,D)
            & ? [E] :
                ( m1_subset_1(E,u1_struct_0(B))
                & D = k4_yellow_4(B,k1_struct_0(B,E),k5_yellow_3(B,B,C))
                & r2_hidden(E,k4_yellow_3(B,B,C)) ) ) ) ) )).

fof(fraenkel_a_2_2_waybel_2,axiom,(
    ! [A,B,C] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & ~ v1_xboole_0(C)
        & v1_waybel_0(C,k3_yellow_3(B,B))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) )
     => ( r2_hidden(A,a_2_2_waybel_2(B,C))
      <=> ? [D] :
            ( ~ v1_xboole_0(D)
            & v1_waybel_0(D,B)
            & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = D
            & ? [E] :
                ( m1_subset_1(E,u1_struct_0(B))
                & D = k4_yellow_4(B,k1_struct_0(B,E),k5_yellow_3(B,B,C))
                & r2_hidden(E,k4_yellow_3(B,B,C)) ) ) ) ) )).

fof(fraenkel_a_2_3_waybel_2,axiom,(
    ! [A,B,C] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v24_waybel_0(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & ~ v1_xboole_0(C)
        & v1_waybel_0(C,k3_yellow_3(B,B))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) )
     => ( r2_hidden(A,a_2_3_waybel_2(B,C))
      <=> ? [D] :
            ( ~ v1_xboole_0(D)
            & v1_waybel_0(D,B)
            & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = D
            & ? [E] :
                ( m1_subset_1(E,u1_struct_0(B))
                & D = k4_yellow_4(B,k1_struct_0(B,E),k5_yellow_3(B,B,C))
                & r2_hidden(E,k4_yellow_3(B,B,C)) ) ) ) ) )).

fof(fraenkel_a_3_0_waybel_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & v2_orders_2(B)
        & l1_orders_2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_0_waybel_2(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = k11_lattice3(B,D,E)
            & r2_hidden(E,C) ) ) ) )).
%------------------------------------------------------------------------------