SET007 Axioms: SET007+490.ax


%------------------------------------------------------------------------------
% File     : SET007+490 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Auxiliary and Approximating Relations
% 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_4 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  142 (   4 unit)
%            Number of atoms       : 1417 (  59 equality)
%            Maximal formula depth :   27 (  10 average)
%            Number of connectives : 1366 (  91 ~  ;   0  |; 919  &)
%                                         (  41 <=>; 315 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   59 (   1 propositional; 0-4 arity)
%            Number of functors    :   49 (   1 constant; 0-5 arity)
%            Number of variables   :  352 (   0 singleton; 334 !;  18 ?)
%            Maximal term depth    :    6 (   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(cc1_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v5_waybel_4(B,A)
           => ( v1_waybel_4(B,A)
              & v2_waybel_4(B,A)
              & v3_waybel_4(B,A)
              & v4_waybel_4(B,A) ) ) ) ) )).

fof(cc2_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( ( v1_waybel_4(B,A)
              & v2_waybel_4(B,A)
              & v3_waybel_4(B,A)
              & v4_waybel_4(B,A) )
           => v5_waybel_4(B,A) ) ) ) )).

fof(rc1_waybel_4,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
          & v1_relat_1(B)
          & v1_waybel_4(B,A)
          & v2_waybel_4(B,A)
          & v3_waybel_4(B,A)
          & v4_waybel_4(B,A)
          & v5_waybel_4(B,A) ) ) )).

fof(cc3_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( ( v1_waybel_4(B,A)
              & v2_waybel_4(B,A) )
           => v8_relat_2(B) ) ) ) )).

fof(fc1_waybel_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v1_relat_1(k2_waybel_4(A))
        & v1_waybel_4(k2_waybel_4(A),A) ) ) )).

fof(fc2_waybel_4,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(k2_waybel_4(A))
        & v1_waybel_4(k2_waybel_4(A),A)
        & v2_waybel_4(k2_waybel_4(A),A) ) ) )).

fof(fc3_waybel_4,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(k2_waybel_4(A))
        & v1_waybel_4(k2_waybel_4(A),A)
        & v3_waybel_4(k2_waybel_4(A),A) ) ) )).

fof(fc4_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(k2_waybel_4(A))
        & v1_waybel_4(k2_waybel_4(A),A)
        & v4_waybel_4(k2_waybel_4(A),A) ) ) )).

fof(fc5_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ~ v1_xboole_0(k3_waybel_4(A)) ) )).

fof(fc6_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k2_yellow_1(k3_waybel_4(A)))
        & v1_orders_2(k2_yellow_1(k3_waybel_4(A)))
        & v2_orders_2(k2_yellow_1(k3_waybel_4(A)))
        & v3_orders_2(k2_yellow_1(k3_waybel_4(A)))
        & v4_orders_2(k2_yellow_1(k3_waybel_4(A)))
        & v2_yellow_0(k2_yellow_1(k3_waybel_4(A))) ) ) )).

fof(fc7_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(k4_waybel_4(A))
        & v8_relat_2(k4_waybel_4(A))
        & v1_waybel_4(k4_waybel_4(A),A)
        & v2_waybel_4(k4_waybel_4(A),A)
        & v3_waybel_4(k4_waybel_4(A),A)
        & v4_waybel_4(k4_waybel_4(A),A)
        & v5_waybel_4(k4_waybel_4(A),A) ) ) )).

fof(fc8_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k2_yellow_1(k3_waybel_4(A)))
        & v1_orders_2(k2_yellow_1(k3_waybel_4(A)))
        & v2_orders_2(k2_yellow_1(k3_waybel_4(A)))
        & v3_orders_2(k2_yellow_1(k3_waybel_4(A)))
        & v4_orders_2(k2_yellow_1(k3_waybel_4(A)))
        & v1_yellow_0(k2_yellow_1(k3_waybel_4(A)))
        & v2_yellow_0(k2_yellow_1(k3_waybel_4(A))) ) ) )).

fof(fc9_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k2_yellow_1(k3_waybel_4(A)))
        & v1_orders_2(k2_yellow_1(k3_waybel_4(A)))
        & v2_orders_2(k2_yellow_1(k3_waybel_4(A)))
        & v3_orders_2(k2_yellow_1(k3_waybel_4(A)))
        & v4_orders_2(k2_yellow_1(k3_waybel_4(A)))
        & v1_yellow_0(k2_yellow_1(k3_waybel_4(A)))
        & v2_yellow_0(k2_yellow_1(k3_waybel_4(A)))
        & v2_lattice3(k2_yellow_1(k3_waybel_4(A))) ) ) )).

fof(fc10_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k2_yellow_1(k3_waybel_4(A)))
        & v1_orders_2(k2_yellow_1(k3_waybel_4(A)))
        & v2_orders_2(k2_yellow_1(k3_waybel_4(A)))
        & v3_orders_2(k2_yellow_1(k3_waybel_4(A)))
        & v4_orders_2(k2_yellow_1(k3_waybel_4(A)))
        & v1_yellow_0(k2_yellow_1(k3_waybel_4(A)))
        & v2_yellow_0(k2_yellow_1(k3_waybel_4(A)))
        & v3_yellow_0(k2_yellow_1(k3_waybel_4(A)))
        & v24_waybel_0(k2_yellow_1(k3_waybel_4(A)))
        & v25_waybel_0(k2_yellow_1(k3_waybel_4(A)))
        & v1_lattice3(k2_yellow_1(k3_waybel_4(A)))
        & v2_lattice3(k2_yellow_1(k3_waybel_4(A)))
        & v3_lattice3(k2_yellow_1(k3_waybel_4(A))) ) ) )).

fof(fc11_waybel_4,axiom,(
    ! [A,B,C] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & v4_waybel_4(C,A)
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
     => ~ v1_xboole_0(k5_waybel_4(A,B,C)) ) )).

fof(fc12_waybel_4,axiom,(
    ! [A,B,C] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & v2_waybel_4(C,A)
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
     => v12_waybel_0(k5_waybel_4(A,B,C),A) ) )).

fof(fc13_waybel_4,axiom,(
    ! [A,B,C] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & v3_waybel_4(C,A)
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
     => v1_waybel_0(k5_waybel_4(A,B,C),A) ) )).

fof(fc14_waybel_4,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & v2_waybel_4(B,A)
        & v3_waybel_4(B,A)
        & v4_waybel_4(B,A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
     => ( v1_relat_1(k7_waybel_4(A,B))
        & v1_funct_1(k7_waybel_4(A,B))
        & v1_funct_2(k7_waybel_4(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
        & v5_orders_3(k7_waybel_4(A,B),A,k2_yellow_1(k8_waybel_0(A))) ) ) )).

fof(fc15_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k8_waybel_4(A))
        & v1_orders_2(k8_waybel_4(A)) ) ) )).

fof(fc16_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k8_waybel_4(A))
        & v1_orders_2(k8_waybel_4(A))
        & v2_yellow_0(k8_waybel_4(A)) ) ) )).

fof(fc17_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(k9_waybel_4(A))
        & v1_funct_1(k9_waybel_4(A))
        & v1_funct_2(k9_waybel_4(A),u1_struct_0(k2_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A)))
        & v5_orders_3(k9_waybel_4(A),k2_yellow_1(k3_waybel_4(A)),k8_waybel_4(A)) ) ) )).

fof(fc18_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(k10_waybel_4(A))
        & v1_funct_1(k10_waybel_4(A))
        & v1_funct_2(k10_waybel_4(A),u1_struct_0(k8_waybel_4(A)),u1_struct_0(k2_yellow_1(k3_waybel_4(A))))
        & v5_orders_3(k10_waybel_4(A),k8_waybel_4(A),k2_yellow_1(k3_waybel_4(A))) ) ) )).

fof(fc19_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(k9_waybel_4(A))
        & v1_funct_1(k9_waybel_4(A))
        & v2_funct_1(k9_waybel_4(A))
        & v1_funct_2(k9_waybel_4(A),u1_struct_0(k2_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A)))
        & v5_orders_3(k9_waybel_4(A),k2_yellow_1(k3_waybel_4(A)),k8_waybel_4(A)) ) ) )).

fof(cc4_waybel_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_yellow_0(A)
          & v3_waybel_3(A)
          & v1_lattice3(A)
          & v2_lattice3(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_yellow_0(A)
          & v2_yellow_0(A)
          & v3_yellow_0(A)
          & v24_waybel_0(A)
          & v25_waybel_0(A)
          & ~ v1_yellow_3(A)
          & v1_waybel_2(A)
          & v2_waybel_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v3_lattice3(A) ) ) ) )).

fof(fc20_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(k1_waybel_4(A))
        & v1_waybel_4(k1_waybel_4(A),A) ) ) )).

fof(fc21_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(k1_waybel_4(A))
        & v2_waybel_4(k1_waybel_4(A),A) ) ) )).

fof(fc22_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(k1_waybel_4(A))
        & v1_waybel_4(k1_waybel_4(A),A)
        & v2_waybel_4(k1_waybel_4(A),A)
        & v3_waybel_4(k1_waybel_4(A),A) ) ) )).

fof(fc23_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v25_waybel_0(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(k1_waybel_4(A))
        & v1_waybel_4(k1_waybel_4(A),A)
        & v2_waybel_4(k1_waybel_4(A),A)
        & v3_waybel_4(k1_waybel_4(A),A) ) ) )).

fof(fc24_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(k1_waybel_4(A))
        & v1_waybel_4(k1_waybel_4(A),A)
        & v4_waybel_4(k1_waybel_4(A),A) ) ) )).

fof(fc25_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(k1_waybel_4(A))
        & v8_relat_2(k1_waybel_4(A))
        & v1_waybel_4(k1_waybel_4(A),A)
        & v2_waybel_4(k1_waybel_4(A),A)
        & v3_waybel_4(k1_waybel_4(A),A)
        & v4_waybel_4(k1_waybel_4(A),A)
        & v5_waybel_4(k1_waybel_4(A),A)
        & v6_waybel_4(k1_waybel_4(A),A) ) ) )).

fof(rc2_waybel_4,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_relset_1(B,u1_struct_0(A),u1_struct_0(A))
          & v1_relat_1(B)
          & v8_relat_2(B)
          & v1_waybel_4(B,A)
          & v2_waybel_4(B,A)
          & v3_waybel_4(B,A)
          & v4_waybel_4(B,A)
          & v5_waybel_4(B,A)
          & v6_waybel_4(B,A) ) ) )).

fof(fc26_waybel_4,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) )
     => ~ v1_xboole_0(k12_waybel_4(A)) ) )).

fof(cc5_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v8_waybel_4(B,A)
           => v9_waybel_4(B,A) ) ) ) )).

fof(fc27_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(k1_waybel_4(A))
        & v8_relat_2(k1_waybel_4(A))
        & v1_waybel_4(k1_waybel_4(A),A)
        & v2_waybel_4(k1_waybel_4(A),A)
        & v3_waybel_4(k1_waybel_4(A),A)
        & v4_waybel_4(k1_waybel_4(A),A)
        & v5_waybel_4(k1_waybel_4(A),A)
        & v6_waybel_4(k1_waybel_4(A),A)
        & v8_waybel_4(k1_waybel_4(A),A)
        & v9_waybel_4(k1_waybel_4(A),A) ) ) )).

fof(cc6_waybel_4,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_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( ( v5_waybel_4(B,A)
              & v6_waybel_4(B,A)
              & v9_waybel_4(B,A) )
           => ( v8_relat_2(B)
              & v1_waybel_4(B,A)
              & v2_waybel_4(B,A)
              & v3_waybel_4(B,A)
              & v4_waybel_4(B,A)
              & v5_waybel_4(B,A)
              & v6_waybel_4(B,A)
              & v8_waybel_4(B,A)
              & v9_waybel_4(B,A) ) ) ) ) )).

fof(d1_waybel_4,axiom,(
    $true )).

fof(d2_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( B = k1_waybel_4(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(k4_tarski(C,D),B)
                    <=> r1_waybel_3(A,C,D) ) ) ) ) ) ) )).

fof(d3_waybel_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => k2_waybel_4(A) = u1_orders_2(A) ) )).

fof(d4_waybel_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v1_waybel_4(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(k4_tarski(C,D),B)
                     => r1_orders_2(A,C,D) ) ) ) ) ) ) )).

fof(d5_waybel_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v2_waybel_4(B,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(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( ( r1_orders_2(A,F,C)
                                & r2_hidden(k4_tarski(C,D),B)
                                & r1_orders_2(A,D,E) )
                             => r2_hidden(k4_tarski(F,E),B) ) ) ) ) ) ) ) ) )).

fof(d6_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v3_waybel_4(B,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(A))
                       => ( ( r2_hidden(k4_tarski(C,E),B)
                            & r2_hidden(k4_tarski(D,E),B) )
                         => r2_hidden(k4_tarski(k10_lattice3(A,C,D),E),B) ) ) ) ) ) ) ) )).

fof(d7_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v4_waybel_4(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => r2_hidden(k4_tarski(k3_yellow_0(A),C),B) ) ) ) ) )).

fof(d8_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v5_waybel_4(B,A)
          <=> ( v1_waybel_4(B,A)
              & v2_waybel_4(B,A)
              & v3_waybel_4(B,A)
              & v4_waybel_4(B,A) ) ) ) ) )).

fof(t1_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_waybel_4(B,A)
            & v3_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_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(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r2_hidden(k4_tarski(C,E),B)
                              & r2_hidden(k4_tarski(D,F),B) )
                           => r2_hidden(k4_tarski(k13_lattice3(A,C,D),k13_lattice3(A,E,F)),B) ) ) ) ) ) ) ) )).

fof(d9_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( B = k3_waybel_4(A)
        <=> ! [C] :
              ( r2_hidden(C,B)
            <=> ( v5_waybel_4(C,A)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) ) ) ) ) )).

fof(t2_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => r1_tarski(B,k2_waybel_4(A)) ) ) )).

fof(t3_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => k4_yellow_0(k2_yellow_1(k3_waybel_4(A))) = k2_waybel_4(A) ) )).

fof(d10_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( B = k4_waybel_4(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(k4_tarski(C,D),B)
                    <=> C = k3_yellow_0(A) ) ) ) ) ) ) )).

fof(t4_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v4_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => r1_tarski(k4_waybel_4(A),B) ) ) )).

fof(t5_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => k3_yellow_0(k2_yellow_1(k3_waybel_4(A))) = k4_waybel_4(A) ) )).

fof(t6_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_waybel_4(C,A)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( v1_waybel_4(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),A)
                & m2_relset_1(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(A),u1_struct_0(A)) ) ) ) ) )).

fof(t7_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( v2_waybel_4(C,A)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( v2_waybel_4(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),A)
                & m2_relset_1(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(A),u1_struct_0(A)) ) ) ) ) )).

fof(t8_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v3_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( v3_waybel_4(C,A)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( v3_waybel_4(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),A)
                & m2_relset_1(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(A),u1_struct_0(A)) ) ) ) ) )).

fof(t9_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v4_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( v4_waybel_4(C,A)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( v4_waybel_4(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),A)
                & m2_relset_1(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(A),u1_struct_0(A)) ) ) ) ) )).

fof(t10_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v5_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( v5_waybel_4(C,A)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( v5_waybel_4(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),A)
                & m2_relset_1(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(A),u1_struct_0(A)) ) ) ) ) )).

fof(t11_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k3_waybel_4(A))))) )
         => ( v5_waybel_4(k1_setfam_1(B),A)
            & m2_relset_1(k1_setfam_1(B),u1_struct_0(A),u1_struct_0(A)) ) ) ) )).

fof(t12_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v1_waybel_4(C,A)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => r1_tarski(k5_waybel_4(A,B,C),k6_waybel_0(A,B)) ) ) ) )).

fof(d13_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_waybel_4(B,A)
            & v3_waybel_4(B,A)
            & v4_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) )
             => ( C = k7_waybel_4(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),C,D) = k5_waybel_4(A,D,B) ) ) ) ) ) )).

fof(t13_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ! [C,D] :
              ( m1_subset_1(D,u1_struct_0(A))
             => ( r2_hidden(C,k5_waybel_4(A,D,B))
              <=> r2_hidden(k4_tarski(C,D),B) ) ) ) ) )).

fof(t14_waybel_4,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & l1_orders_2(B) )
     => ! [C] :
          ( m2_relset_1(C,u1_struct_0(B),u1_struct_0(B))
         => ! [D] :
              ( m1_subset_1(D,u1_struct_0(B))
             => ( r2_hidden(A,k6_waybel_4(B,D,C))
              <=> r2_hidden(k4_tarski(D,A),C) ) ) ) ) )).

fof(t15_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( B = u1_orders_2(A)
               => k5_waybel_4(A,C,B) = k6_waybel_0(A,C) ) ) ) ) )).

fof(d14_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_orders_2(B)
            & l1_orders_2(B) )
         => ( B = k8_waybel_4(A)
          <=> ! [C] :
                ( ~ ( r2_hidden(C,u1_struct_0(B))
                    & ! [D] :
                        ( ( v1_funct_1(D)
                          & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
                          & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) )
                       => ~ ( C = D
                            & v5_orders_3(D,A,k2_yellow_1(k8_waybel_0(A)))
                            & ! [E] :
                                ( m1_subset_1(E,u1_struct_0(A))
                               => r1_tarski(k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),D,E),k6_waybel_0(A,E)) ) ) ) )
                & ( ? [D] :
                      ( v1_funct_1(D)
                      & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
                      & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
                      & C = D
                      & v5_orders_3(D,A,k2_yellow_1(k8_waybel_0(A)))
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => r1_tarski(k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),D,E),k6_waybel_0(A,E)) ) )
                 => r2_hidden(C,u1_struct_0(B)) )
                & ! [D,E] :
                    ( r2_hidden(k4_tarski(D,E),u1_orders_2(B))
                  <=> ? [F] :
                        ( v1_funct_1(F)
                        & v1_funct_2(F,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
                        & m2_relset_1(F,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
                        & ? [G] :
                            ( v1_funct_1(G)
                            & v1_funct_2(G,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
                            & m2_relset_1(G,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
                            & D = F
                            & E = G
                            & r2_hidden(D,u1_struct_0(B))
                            & r2_hidden(E,u1_struct_0(B))
                            & r1_yellow_2(u1_struct_0(A),k2_yellow_1(k8_waybel_0(A)),F,G) ) ) ) ) ) ) ) )).

fof(t16_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( v4_yellow_0(k8_waybel_4(A),k6_yellow_1(u1_struct_0(A),k2_yellow_1(k8_waybel_0(A))))
        & m1_yellow_0(k8_waybel_4(A),k6_yellow_1(u1_struct_0(A),k2_yellow_1(k8_waybel_0(A)))) ) ) )).

fof(t17_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),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,C,D)
                   => r1_tarski(k5_waybel_4(A,C,B),k5_waybel_4(A,D,B)) ) ) ) ) ) )).

fof(t18_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v5_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => r2_hidden(k7_waybel_4(A,B),u1_struct_0(k8_waybel_4(A))) ) ) )).

fof(t19_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => r2_hidden(k4_yellow_2(A),u1_struct_0(k8_waybel_4(A))) ) )).

fof(t20_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v5_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => r1_yellow_2(u1_struct_0(A),k2_yellow_1(k8_waybel_0(A)),k7_waybel_4(A,B),k4_yellow_2(A)) ) ) )).

fof(t21_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(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))) )
         => r2_hidden(k3_yellow_0(A),B) ) ) )).

fof(t22_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v2_waybel_0(B,A)
            & v13_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => r2_hidden(k4_yellow_0(A),B) ) ) )).

fof(t23_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => k6_waybel_0(A,k3_yellow_0(A)) = k1_struct_0(A,k3_yellow_0(A)) ) )).

fof(t24_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_yellow_0(A)
        & l1_orders_2(A) )
     => k7_waybel_0(A,k4_yellow_0(A)) = k1_struct_0(A,k4_yellow_0(A)) ) )).

fof(t25_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( v1_funct_1(k2_pre_circ(u1_struct_0(A),k1_struct_0(A,k3_yellow_0(A))))
        & v1_funct_2(k2_pre_circ(u1_struct_0(A),k1_struct_0(A,k3_yellow_0(A))),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
        & m2_relset_1(k2_pre_circ(u1_struct_0(A),k1_struct_0(A,k3_yellow_0(A))),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) ) ) )).

fof(t26_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => r2_hidden(k2_pre_circ(u1_struct_0(A),k1_struct_0(A,k3_yellow_0(A))),u1_struct_0(k8_waybel_4(A))) ) )).

fof(t27_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v5_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => r2_hidden(k4_tarski(k2_pre_circ(u1_struct_0(A),k1_struct_0(A,k3_yellow_0(A))),k7_waybel_4(A,B)),u1_orders_2(k8_waybel_4(A))) ) ) )).

fof(d15_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k2_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A)))
            & m2_relset_1(B,u1_struct_0(k2_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A))) )
         => ( B = k9_waybel_4(A)
          <=> ! [C] :
                ( ( v5_waybel_4(C,A)
                  & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
               => k1_funct_1(B,C) = k7_waybel_4(A,C) ) ) ) ) )).

fof(t28_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v5_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( v5_waybel_4(C,A)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( r1_tarski(B,C)
               => r1_yellow_2(u1_struct_0(A),k2_yellow_1(k8_waybel_0(A)),k7_waybel_4(A,B),k7_waybel_4(A,C)) ) ) ) ) )).

fof(t29_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
             => ! [D] :
                  ( m2_relset_1(D,u1_struct_0(A),u1_struct_0(A))
                 => ( r1_tarski(C,D)
                   => r1_tarski(k5_waybel_4(A,B,C),k5_waybel_4(A,B,D)) ) ) ) ) ) )).

fof(d16_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k8_waybel_4(A)),u1_struct_0(k2_yellow_1(k3_waybel_4(A))))
            & m2_relset_1(B,u1_struct_0(k8_waybel_4(A)),u1_struct_0(k2_yellow_1(k3_waybel_4(A)))) )
         => ( B = k10_waybel_4(A)
          <=> ! [C] :
                ~ ( r2_hidden(C,u1_struct_0(k8_waybel_4(A)))
                  & ! [D] :
                      ( ( v5_waybel_4(D,A)
                        & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                     => ~ ( D = k1_funct_1(B,C)
                          & ! [E,F] :
                              ( r2_hidden(k4_tarski(E,F),D)
                            <=> ? [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                  & ? [H] :
                                      ( m1_subset_1(H,u1_struct_0(A))
                                      & ? [I] :
                                          ( v1_funct_1(I)
                                          & v1_funct_2(I,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
                                          & m2_relset_1(I,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
                                          & G = E
                                          & H = F
                                          & I = C
                                          & r2_hidden(G,k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),I,H)) ) ) ) ) ) ) ) ) ) ) )).

fof(t30_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => k7_funct_2(u1_struct_0(k2_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A)),u1_struct_0(k2_yellow_1(k3_waybel_4(A))),k9_waybel_4(A),k10_waybel_4(A)) = k6_partfun1(k4_relset_1(u1_struct_0(k2_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A)),k9_waybel_4(A))) ) )).

fof(t31_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => k7_funct_2(u1_struct_0(k8_waybel_4(A)),u1_struct_0(k2_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A)),k10_waybel_4(A),k9_waybel_4(A)) = k6_partfun1(u1_struct_0(k8_waybel_4(A))) ) )).

fof(t32_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => k2_funct_1(k9_waybel_4(A)) = k10_waybel_4(A) ) )).

fof(t33_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => v23_waybel_0(k9_waybel_4(A),k2_yellow_1(k3_waybel_4(A)),k8_waybel_4(A)) ) )).

fof(d17_waybel_4,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,A)
            & v12_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) )
             => ( C = k11_waybel_4(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r3_orders_2(A,D,k1_yellow_0(A,B))
                       => k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),C,D) = k5_subset_1(u1_struct_0(A),k6_waybel_0(A,D),B) )
                      & ( ~ r3_orders_2(A,D,k1_yellow_0(A,B))
                       => k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),C,D) = k6_waybel_0(A,D) ) ) ) ) ) ) ) )).

fof(t35_waybel_4,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,A)
            & v12_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => r2_hidden(k11_waybel_4(A,B),u1_struct_0(k8_waybel_4(A))) ) ) )).

fof(t36_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v12_waybel_0(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => k4_yellow_4(A,k1_struct_0(A,B),C) = k5_subset_1(u1_struct_0(A),k6_waybel_0(A,B),C) ) ) ) )).

fof(d18_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v6_waybel_4(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => C = k1_yellow_0(A,k5_waybel_4(A,C,B)) ) ) ) ) )).

fof(d19_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(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(A))))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) )
         => ( v7_waybel_4(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ? [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                    & D = k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),B,C)
                    & C = k1_yellow_0(A,D) ) ) ) ) ) )).

fof(t37_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v2_waybel_2(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))) )
         => v7_waybel_4(k11_waybel_4(A,B),A) ) ) )).

fof(t38_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => v2_waybel_2(A) ) )).

fof(t39_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & v1_lattice3(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))) )
         => v7_waybel_4(k11_waybel_4(A,B),A) ) ) )).

fof(t40_waybel_4,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))
         => k5_waybel_4(A,B,k1_waybel_4(A)) = k1_waybel_3(A,B) ) ) )).

fof(t41_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => v6_waybel_4(k2_waybel_4(A),A) ) )).

fof(d20_waybel_4,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] :
          ( B = k12_waybel_4(A)
        <=> ! [C] :
              ( r2_hidden(C,B)
            <=> ( v5_waybel_4(C,A)
                & v6_waybel_4(C,A)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) ) ) ) ) )).

fof(t42_waybel_4,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) )
         => ~ ( v7_waybel_4(B,A)
              & r2_hidden(B,u1_struct_0(k8_waybel_4(A)))
              & ! [C] :
                  ( ( v5_waybel_4(C,A)
                    & v6_waybel_4(C,A)
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
                 => C != k1_funct_1(k10_waybel_4(A),B) ) ) ) ) )).

fof(t45_waybel_4,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) )
     => ( v3_waybel_3(A)
      <=> ! [B] :
            ( ( v5_waybel_4(B,A)
              & v6_waybel_4(B,A)
              & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
           => ( r1_tarski(k1_waybel_4(A),B)
              & v6_waybel_4(k1_waybel_4(A),A) ) ) ) ) )).

fof(t46_waybel_4,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) )
     => ( v3_waybel_3(A)
      <=> ( v2_waybel_2(A)
          & ? [B] :
              ( v5_waybel_4(B,A)
              & v6_waybel_4(B,A)
              & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
              & ! [C] :
                  ( ( v5_waybel_4(C,A)
                    & v6_waybel_4(C,A)
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
                 => r1_tarski(B,C) ) ) ) ) ) )).

fof(d21_waybel_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v8_waybel_4(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( r2_hidden(k4_tarski(C,D),B)
                        & C != D
                        & ! [E] :
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ~ ( r2_hidden(k4_tarski(C,E),B)
                                & r2_hidden(k4_tarski(E,D),B)
                                & C != E ) ) ) ) ) ) ) ) )).

fof(d22_waybel_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v9_waybel_4(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( r2_hidden(k4_tarski(C,D),B)
                        & ! [E] :
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ~ ( r2_hidden(k4_tarski(C,E),B)
                                & r2_hidden(k4_tarski(E,D),B) ) ) ) ) ) ) ) ) )).

fof(t47_waybel_4,axiom,(
    $true )).

fof(t48_waybel_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v8_waybel_4(B,A)
           => v9_waybel_4(B,A) ) ) ) )).

fof(t49_waybel_4,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] :
                  ( ( v6_waybel_4(D,A)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => ~ ( ~ r3_orders_2(A,B,C)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r2_hidden(k4_tarski(E,B),D)
                              & ~ r3_orders_2(A,E,C) ) ) ) ) ) ) ) )).

fof(t50_waybel_4,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] :
                  ( ( v1_waybel_4(D,A)
                    & v3_waybel_4(D,A)
                    & v6_waybel_4(D,A)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => ~ ( r2_hidden(k4_tarski(B,C),D)
                      & B != C
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r3_orders_2(A,B,E)
                              & r2_hidden(k4_tarski(E,C),D)
                              & B != E ) ) ) ) ) ) ) )).

fof(t51_waybel_4,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] :
                  ( ( v5_waybel_4(D,A)
                    & v6_waybel_4(D,A)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => ~ ( r1_waybel_3(A,B,C)
                      & B != C
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r2_hidden(k4_tarski(B,E),D)
                              & r2_hidden(k4_tarski(E,C),D)
                              & B != E ) ) ) ) ) ) ) )).

fof(t52_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => v8_waybel_4(k1_waybel_4(A),A) ) )).

fof(t53_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(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))
                     => ~ ( r1_waybel_3(A,B,D)
                          & r1_waybel_3(A,D,C) ) ) ) ) ) ) )).

fof(t54_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(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] :
                    ( ( ~ v1_xboole_0(D)
                      & v1_waybel_0(D,A)
                      & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                   => ~ ( r3_orders_2(A,C,k1_yellow_0(A,D))
                        & ! [E] :
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ~ ( r2_hidden(E,D)
                                & r1_waybel_3(A,B,E) ) ) ) ) ) ) ) ) )).

fof(d23_waybel_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
             => ( r1_waybel_4(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ~ ( r2_hidden(D,B)
                            & r2_hidden(E,B)
                            & ! [F] :
                                ( m1_subset_1(F,u1_struct_0(A))
                               => ~ ( r2_hidden(F,B)
                                    & r2_hidden(k4_tarski(D,F),C)
                                    & r2_hidden(k4_tarski(E,F),C) ) ) ) ) ) ) ) ) ) )).

fof(t55_waybel_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( r1_waybel_4(A,B,u1_orders_2(A))
           => v1_waybel_0(B,A) ) ) ) )).

fof(d24_waybel_4,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( r2_waybel_4(A,B,C)
      <=> ( r2_hidden(B,A)
          & ! [D] :
              ~ ( r2_hidden(D,A)
                & D != B
                & r2_hidden(k4_tarski(B,D),C) ) ) ) ) )).

fof(d25_waybel_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B,C] :
          ( m1_subset_1(C,u1_struct_0(A))
         => ( r3_waybel_4(A,B,C)
          <=> r2_waybel_4(B,C,u1_orders_2(A)) ) ) ) )).

fof(t56_waybel_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B,C] :
          ( m1_subset_1(C,u1_struct_0(A))
         => ( r3_waybel_4(A,B,C)
          <=> ( r2_hidden(C,B)
              & ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ~ ( r2_hidden(D,B)
                      & r2_orders_2(A,C,D) ) ) ) ) ) ) )).

fof(d26_waybel_4,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( r4_waybel_4(A,B,C)
      <=> ( r2_hidden(B,A)
          & ! [D] :
              ~ ( r2_hidden(D,A)
                & D != B
                & r2_hidden(k4_tarski(D,B),C) ) ) ) ) )).

fof(d27_waybel_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B,C] :
          ( m1_subset_1(C,u1_struct_0(A))
         => ( r5_waybel_4(A,B,C)
          <=> r4_waybel_4(B,C,u1_orders_2(A)) ) ) ) )).

fof(t57_waybel_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B,C] :
          ( m1_subset_1(C,u1_struct_0(A))
         => ( r5_waybel_4(A,B,C)
          <=> ( r2_hidden(C,B)
              & ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ~ ( r2_hidden(D,B)
                      & r2_orders_2(A,D,C) ) ) ) ) ) ) )).

fof(t58_waybel_4,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] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v8_waybel_4(B,A)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( ? [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                      & r2_waybel_4(k5_waybel_4(A,C,B),D,B) )
                 => r2_hidden(k4_tarski(C,C),B) ) ) ) ) ) )).

fof(t59_waybel_4,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] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( ? [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                      & r2_waybel_4(k5_waybel_4(A,C,B),D,B) )
                 => r2_hidden(k4_tarski(C,C),B) ) )
           => v8_waybel_4(B,A) ) ) ) )).

fof(t60_waybel_4,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] :
          ( ( v2_waybel_4(B,A)
            & v3_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v9_waybel_4(B,A)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => r1_waybel_4(A,k5_waybel_4(A,C,B),B) ) ) ) ) )).

fof(t61_waybel_4,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] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => r1_waybel_4(A,k5_waybel_4(A,C,B),B) )
           => v9_waybel_4(B,A) ) ) ) )).

fof(t62_waybel_4,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] :
          ( ( v1_waybel_4(B,A)
            & v2_waybel_4(B,A)
            & v3_waybel_4(B,A)
            & v6_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v9_waybel_4(B,A)
           => v8_waybel_4(B,A) ) ) ) )).

fof(s1_waybel_4,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = f1_s1_waybel_4
      & ! [B] :
          ( m1_subset_1(B,f1_s1_waybel_4)
         => ( ( p1_s1_waybel_4(B)
             => k1_funct_1(A,B) = f2_s1_waybel_4(B) )
            & ( ~ p1_s1_waybel_4(B)
             => k1_funct_1(A,B) = f3_s1_waybel_4(B) ) ) ) ) )).

fof(dt_k1_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => m2_relset_1(k1_waybel_4(A),u1_struct_0(A),u1_struct_0(A)) ) )).

fof(dt_k2_waybel_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => m2_relset_1(k2_waybel_4(A),u1_struct_0(A),u1_struct_0(A)) ) )).

fof(dt_k3_waybel_4,axiom,(
    $true )).

fof(dt_k4_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => m2_relset_1(k4_waybel_4(A),u1_struct_0(A),u1_struct_0(A)) ) )).

fof(dt_k5_waybel_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
     => m1_subset_1(k5_waybel_4(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k6_waybel_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
     => m1_subset_1(k6_waybel_4(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k7_waybel_4,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & v2_waybel_4(B,A)
        & v3_waybel_4(B,A)
        & v4_waybel_4(B,A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
     => ( v1_funct_1(k7_waybel_4(A,B))
        & v1_funct_2(k7_waybel_4(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
        & m2_relset_1(k7_waybel_4(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) ) ) )).

fof(dt_k8_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_orders_2(k8_waybel_4(A))
        & l1_orders_2(k8_waybel_4(A)) ) ) )).

fof(dt_k9_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( v1_funct_1(k9_waybel_4(A))
        & v1_funct_2(k9_waybel_4(A),u1_struct_0(k2_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A)))
        & m2_relset_1(k9_waybel_4(A),u1_struct_0(k2_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A))) ) ) )).

fof(dt_k10_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( v1_funct_1(k10_waybel_4(A))
        & v1_funct_2(k10_waybel_4(A),u1_struct_0(k8_waybel_4(A)),u1_struct_0(k2_yellow_1(k3_waybel_4(A))))
        & m2_relset_1(k10_waybel_4(A),u1_struct_0(k8_waybel_4(A)),u1_struct_0(k2_yellow_1(k3_waybel_4(A)))) ) ) )).

fof(dt_k11_waybel_4,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & ~ 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))) )
     => ( v1_funct_1(k11_waybel_4(A,B))
        & v1_funct_2(k11_waybel_4(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
        & m2_relset_1(k11_waybel_4(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) ) ) )).

fof(dt_k12_waybel_4,axiom,(
    $true )).

fof(d11_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
             => k5_waybel_4(A,B,C) = a_3_0_waybel_4(A,B,C) ) ) ) )).

fof(d12_waybel_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
             => k6_waybel_4(A,B,C) = a_3_1_waybel_4(A,B,C) ) ) ) )).

fof(t34_waybel_4,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))
         => k1_setfam_1(a_2_0_waybel_4(A,B)) = k1_waybel_3(A,B) ) ) )).

fof(t43_waybel_4,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))
         => k1_setfam_1(a_2_1_waybel_4(A,B)) = k1_waybel_3(A,B) ) ) )).

fof(t44_waybel_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v2_waybel_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_setfam_1(a_2_2_waybel_4(A,B)) = k1_waybel_3(A,B) ) ) )).

fof(fraenkel_a_3_0_waybel_4,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & l1_orders_2(B)
        & m1_subset_1(C,u1_struct_0(B))
        & m2_relset_1(D,u1_struct_0(B),u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_0_waybel_4(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = E
            & r2_hidden(k4_tarski(E,C),D) ) ) ) )).

fof(fraenkel_a_3_1_waybel_4,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & l1_orders_2(B)
        & m1_subset_1(C,u1_struct_0(B))
        & m2_relset_1(D,u1_struct_0(B),u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_1_waybel_4(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = E
            & r2_hidden(k4_tarski(C,E),D) ) ) ) )).

fof(fraenkel_a_2_0_waybel_4,axiom,(
    ! [A,B,C] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v3_lattice3(B)
        & l1_orders_2(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_0_waybel_4(B,C))
      <=> ? [D] :
            ( ~ v1_xboole_0(D)
            & v1_waybel_0(D,B)
            & v12_waybel_0(D,B)
            & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = D
            & r3_orders_2(B,C,k1_yellow_0(B,D)) ) ) ) )).

fof(fraenkel_a_2_1_waybel_4,axiom,(
    ! [A,B,C] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v3_lattice3(B)
        & l1_orders_2(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_1_waybel_4(B,C))
      <=> ? [D] :
            ( ~ v1_xboole_0(D)
            & v1_waybel_0(D,B)
            & v12_waybel_0(D,B)
            & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = k1_waybel_0(B,k2_yellow_1(k8_waybel_0(B)),k11_waybel_4(B,D),C) ) ) ) )).

fof(fraenkel_a_2_2_waybel_4,axiom,(
    ! [A,B,C] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v2_waybel_2(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_2_waybel_4(B,C))
      <=> ? [D] :
            ( v5_waybel_4(D,B)
            & m2_relset_1(D,u1_struct_0(B),u1_struct_0(B))
            & A = k5_waybel_4(B,C,D)
            & r2_hidden(D,k12_waybel_4(B)) ) ) ) )).
%------------------------------------------------------------------------------