SET007 Axioms: SET007+500.ax


%------------------------------------------------------------------------------
% File     : SET007+500 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On the Topological Properties of 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_9 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  104 (   1 unit)
%            Number of atoms       :  950 (  51 equality)
%            Maximal formula depth :   36 (   9 average)
%            Number of connectives :  987 ( 141 ~  ;   0  |; 586  &)
%                                         (  10 <=>; 250 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   81 (   0 propositional; 1-3 arity)
%            Number of functors    :   52 (   0 constant; 1-5 arity)
%            Number of variables   :  294 (   0 singleton; 286 !;   8 ?)
%            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_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ~ v1_xboole_0(k7_grcat_1(A))
        & v1_relat_1(k7_grcat_1(A))
        & v1_funct_1(k7_grcat_1(A))
        & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
        & v5_orders_3(k7_grcat_1(A),A,A)
        & v1_partfun1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(fc2_waybel_9,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B)
        & v1_waybel_0(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(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(g1_waybel_0(A,B,k1_toler_1(u1_orders_2(A),B),C))
        & v6_waybel_0(g1_waybel_0(A,B,k1_toler_1(u1_orders_2(A),B),C),A)
        & v7_waybel_0(g1_waybel_0(A,B,k1_toler_1(u1_orders_2(A),B),C)) ) ) )).

fof(fc3_waybel_9,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B)
        & v1_waybel_0(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(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(g1_waybel_0(A,B,k1_toler_1(u1_orders_2(A),B),C))
        & v3_orders_2(g1_waybel_0(A,B,k1_toler_1(u1_orders_2(A),B),C))
        & v6_waybel_0(g1_waybel_0(A,B,k1_toler_1(u1_orders_2(A),B),C),A)
        & v7_waybel_0(g1_waybel_0(A,B,k1_toler_1(u1_orders_2(A),B),C)) ) ) )).

fof(fc4_waybel_9,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & ~ v3_struct_0(C)
        & v2_orders_2(C)
        & l1_waybel_0(C,A) )
     => ( ~ v3_struct_0(k3_waybel_2(A,B,C))
        & v2_orders_2(k3_waybel_2(A,B,C))
        & v6_waybel_0(k3_waybel_2(A,B,C),A) ) ) )).

fof(fc5_waybel_9,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & ~ v3_struct_0(C)
        & v4_orders_2(C)
        & l1_waybel_0(C,A) )
     => ( ~ v3_struct_0(k3_waybel_2(A,B,C))
        & v4_orders_2(k3_waybel_2(A,B,C))
        & v6_waybel_0(k3_waybel_2(A,B,C),A) ) ) )).

fof(fc6_waybel_9,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & ~ v3_struct_0(C)
        & v3_orders_2(C)
        & l1_waybel_0(C,A) )
     => ( ~ v3_struct_0(k3_waybel_2(A,B,C))
        & v3_orders_2(k3_waybel_2(A,B,C))
        & v6_waybel_0(k3_waybel_2(A,B,C),A) ) ) )).

fof(fc7_waybel_9,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))
        & v3_orders_2(k2_waybel_2(A,B,C))
        & v7_waybel_0(k2_waybel_2(A,B,C)) ) ) )).

fof(fc8_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k3_waybel_9(A))
        & v6_waybel_0(k3_waybel_9(A),A) ) ) )).

fof(fc9_waybel_9,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & l1_orders_2(A) )
     => ( v2_orders_2(k3_waybel_9(A))
        & v6_waybel_0(k3_waybel_9(A),A) ) ) )).

fof(fc10_waybel_9,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v4_orders_2(k3_waybel_9(A))
        & v6_waybel_0(k3_waybel_9(A),A) ) ) )).

fof(fc11_waybel_9,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & l1_orders_2(A) )
     => ( v3_orders_2(k3_waybel_9(A))
        & v6_waybel_0(k3_waybel_9(A),A) ) ) )).

fof(fc12_waybel_9,axiom,(
    ! [A] :
      ( ( v1_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k3_waybel_9(A))
        & v6_waybel_0(k3_waybel_9(A),A)
        & v7_waybel_0(k3_waybel_9(A)) ) ) )).

fof(fc13_waybel_9,axiom,(
    ! [A] :
      ( ( v7_waybel_0(A)
        & l1_orders_2(A) )
     => ( v6_waybel_0(k3_waybel_9(A),A)
        & v7_waybel_0(k3_waybel_9(A)) ) ) )).

fof(fc14_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k3_waybel_9(A))
        & v6_waybel_0(k3_waybel_9(A),A)
        & v8_waybel_0(k3_waybel_9(A),A)
        & v10_waybel_0(k3_waybel_9(A),A) ) ) )).

fof(fc15_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k4_waybel_9(A))
        & v6_waybel_0(k4_waybel_9(A),A) ) ) )).

fof(fc16_waybel_9,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & l1_orders_2(A) )
     => ( v2_orders_2(k4_waybel_9(A))
        & v6_waybel_0(k4_waybel_9(A),A) ) ) )).

fof(fc17_waybel_9,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v4_orders_2(k4_waybel_9(A))
        & v6_waybel_0(k4_waybel_9(A),A) ) ) )).

fof(fc18_waybel_9,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & l1_orders_2(A) )
     => ( v3_orders_2(k4_waybel_9(A))
        & v6_waybel_0(k4_waybel_9(A),A) ) ) )).

fof(fc19_waybel_9,axiom,(
    ! [A] :
      ( ( v2_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k4_waybel_9(A))
        & v6_waybel_0(k4_waybel_9(A),A)
        & v7_waybel_0(k4_waybel_9(A)) ) ) )).

fof(fc20_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k4_waybel_9(A))
        & v6_waybel_0(k4_waybel_9(A),A)
        & v9_waybel_0(k4_waybel_9(A),A)
        & v11_waybel_0(k4_waybel_9(A),A) ) ) )).

fof(fc21_waybel_9,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v2_orders_2(B)
        & l1_waybel_0(B,A)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( ~ v3_struct_0(k5_waybel_9(A,B,C))
        & v2_orders_2(k5_waybel_9(A,B,C))
        & v6_waybel_0(k5_waybel_9(A,B,C),A) ) ) )).

fof(fc22_waybel_9,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( ~ v3_struct_0(k5_waybel_9(A,B,C))
        & v6_waybel_0(k5_waybel_9(A,B,C),A) ) ) )).

fof(fc23_waybel_9,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v4_orders_2(B)
        & l1_waybel_0(B,A)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( ~ v3_struct_0(k5_waybel_9(A,B,C))
        & v2_orders_2(k5_waybel_9(A,B,C))
        & v4_orders_2(k5_waybel_9(A,B,C))
        & v6_waybel_0(k5_waybel_9(A,B,C),A) ) ) )).

fof(fc24_waybel_9,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v4_orders_2(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( ~ v3_struct_0(k5_waybel_9(A,B,C))
        & v4_orders_2(k5_waybel_9(A,B,C))
        & v6_waybel_0(k5_waybel_9(A,B,C),A) ) ) )).

fof(fc25_waybel_9,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & l1_waybel_0(B,A)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( ~ v3_struct_0(k5_waybel_9(A,B,C))
        & v2_orders_2(k5_waybel_9(A,B,C))
        & v3_orders_2(k5_waybel_9(A,B,C))
        & v6_waybel_0(k5_waybel_9(A,B,C),A) ) ) )).

fof(fc26_waybel_9,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v3_orders_2(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( ~ v3_struct_0(k5_waybel_9(A,B,C))
        & v3_orders_2(k5_waybel_9(A,B,C))
        & v6_waybel_0(k5_waybel_9(A,B,C),A)
        & v7_waybel_0(k5_waybel_9(A,B,C)) ) ) )).

fof(rc1_waybel_9,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v3_orders_2(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A) )
     => ? [C] :
          ( m2_yellow_6(C,A,B)
          & ~ v3_struct_0(C)
          & v3_orders_2(C)
          & v6_waybel_0(C,A)
          & v7_waybel_0(C) ) ) )).

fof(fc27_waybel_9,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
        & ~ v3_struct_0(D)
        & l1_waybel_0(D,A) )
     => ( ~ v3_struct_0(k7_waybel_9(A,B,C,D))
        & v6_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) )).

fof(fc28_waybel_9,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
        & v2_orders_2(D)
        & l1_waybel_0(D,A) )
     => ( v2_orders_2(k7_waybel_9(A,B,C,D))
        & v6_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) )).

fof(fc29_waybel_9,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
        & v4_orders_2(D)
        & l1_waybel_0(D,A) )
     => ( v4_orders_2(k7_waybel_9(A,B,C,D))
        & v6_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) )).

fof(fc30_waybel_9,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
        & v3_orders_2(D)
        & l1_waybel_0(D,A) )
     => ( v3_orders_2(k7_waybel_9(A,B,C,D))
        & v6_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) )).

fof(fc31_waybel_9,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
        & v7_waybel_0(D)
        & l1_waybel_0(D,A) )
     => ( v6_waybel_0(k7_waybel_9(A,B,C,D),B)
        & v7_waybel_0(k7_waybel_9(A,B,C,D)) ) ) )).

fof(rc2_waybel_9,axiom,(
    ? [A] :
      ( l1_waybel_9(A)
      & v1_waybel_9(A) ) )).

fof(fc32_waybel_9,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_relset_1(B,A,A)
        & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ( ~ v3_struct_0(g1_waybel_9(A,B,C))
        & v1_waybel_9(g1_waybel_9(A,B,C)) ) ) )).

fof(fc33_waybel_9,axiom,(
    ! [A,B,C] :
      ( ( m1_relset_1(B,k1_tarski(A),k1_tarski(A))
        & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(k1_tarski(A)))) )
     => ( ~ v3_struct_0(g1_waybel_9(k1_tarski(A),B,C))
        & v3_realset2(g1_waybel_9(k1_tarski(A),B,C))
        & v1_waybel_9(g1_waybel_9(k1_tarski(A),B,C)) ) ) )).

fof(fc34_waybel_9,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_2(B)
        & v4_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A)
        & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ( v2_orders_2(g1_waybel_9(A,B,C))
        & v3_orders_2(g1_waybel_9(A,B,C))
        & v4_orders_2(g1_waybel_9(A,B,C))
        & v1_waybel_9(g1_waybel_9(A,B,C)) ) ) )).

fof(rc3_waybel_9,axiom,(
    ? [A] :
      ( l1_waybel_9(A)
      & ~ v3_struct_0(A)
      & v2_pre_topc(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_waybel_2(A)
      & v2_waybel_2(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v2_waybel_1(A)
      & v9_waybel_1(A)
      & v10_waybel_1(A)
      & v1_tdlat_3(A)
      & v3_tdlat_3(A)
      & v4_tdlat_3(A)
      & v5_tdlat_3(A)
      & v2_waybel_3(A)
      & v3_waybel_3(A)
      & v6_group_1(A)
      & v3_realset2(A)
      & v1_waybel_9(A) ) )).

fof(rc4_waybel_9,axiom,(
    ? [A] :
      ( l1_waybel_9(A)
      & ~ v3_struct_0(A)
      & v2_pre_topc(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_waybel_2(A)
      & v2_waybel_2(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v2_waybel_1(A)
      & v9_waybel_1(A)
      & v10_waybel_1(A)
      & v2_compts_1(A)
      & v3_compts_1(A)
      & v4_compts_1(A)
      & v5_compts_1(A)
      & v1_tdlat_3(A)
      & v3_tdlat_3(A)
      & v4_tdlat_3(A)
      & v5_tdlat_3(A)
      & v2_waybel_3(A)
      & v3_waybel_3(A)
      & v6_waybel_3(A)
      & v6_group_1(A)
      & v3_realset2(A)
      & v1_waybel_9(A) ) )).

fof(cc1_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_compts_1(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ~ v3_struct_0(B)
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v3_compts_1(B) ) ) ) ) )).

fof(d1_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v5_waybel_0(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( r1_orders_2(A,D,E)
                         => r1_orders_2(B,k3_yellow_6(u1_struct_0(A),B,C,E),k3_yellow_6(u1_struct_0(A),B,C,D)) ) ) ) ) ) ) ) )).

fof(t1_waybel_9,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l1_orders_2(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
                            & m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
                         => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(C),u1_orders_2(C))
                              & g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
                              & E = F
                              & v5_orders_3(E,A,B) )
                           => v5_orders_3(F,C,D) ) ) ) ) ) ) ) )).

fof(t2_waybel_9,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l1_orders_2(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
                            & m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
                         => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(C),u1_orders_2(C))
                              & g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
                              & E = F
                              & v5_waybel_0(E,A,B) )
                           => v5_waybel_0(F,C,D) ) ) ) ) ) ) ) )).

fof(t3_waybel_9,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( l1_struct_0(B)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B))))
                 => ( ( u1_struct_0(A) = u1_struct_0(B)
                      & C = D
                      & r1_pre_topc(A,C) )
                   => r1_pre_topc(B,D) ) ) ) ) ) )).

fof(t4_waybel_9,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k7_waybel_0(A,B) = k2_yellow_4(A,k1_struct_0(A,B),k2_pre_topc(A)) ) ) )).

fof(t5_waybel_9,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))
         => k6_waybel_0(A,B) = k4_yellow_4(A,k1_struct_0(A,B),k2_pre_topc(A)) ) ) )).

fof(t6_waybel_9,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))
         => k4_pre_topc(A,A,k4_waybel_1(A,B),k7_waybel_0(A,B)) = k1_struct_0(A,B) ) ) )).

fof(t7_waybel_9,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))
         => k5_pre_topc(A,A,k4_waybel_1(A,B),k1_struct_0(A,B)) = k7_waybel_0(A,B) ) ) )).

fof(t8_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => r1_waybel_0(A,B,k8_yellow_2(u1_struct_0(B),A,u1_waybel_0(A,B))) ) ) )).

fof(t9_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( ( ~ v3_struct_0(C)
                  & v3_orders_2(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(t10_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_orders_2(C)
                & v7_waybel_0(C)
                & l1_waybel_0(C,A) )
             => ( ~ v3_struct_0(k3_waybel_2(A,B,C))
                & v3_orders_2(k3_waybel_2(A,B,C))
                & v7_waybel_0(k3_waybel_2(A,B,C))
                & l1_waybel_0(k3_waybel_2(A,B,C),A) ) ) ) ) )).

fof(d2_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( l1_waybel_0(B,A)
         => k2_waybel_9(A,B) = k6_yellow_2(A,u1_waybel_0(A,B)) ) ) )).

fof(d3_waybel_9,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_waybel_0(B,A)
         => ( r1_waybel_9(A,B)
          <=> r1_yellow_0(A,k1_yellow_2(B,A,u1_waybel_0(A,B))) ) ) ) )).

fof(d4_waybel_9,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_waybel_0(B,A)
         => ( r2_waybel_9(A,B)
          <=> r2_yellow_0(A,k1_yellow_2(B,A,u1_waybel_0(A,B))) ) ) ) )).

fof(d5_waybel_9,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( ( v6_waybel_0(B,A)
            & l1_waybel_0(B,A) )
         => ( B = k3_waybel_9(A)
          <=> ( g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(A),u1_orders_2(A))
              & u1_waybel_0(A,B) = k7_grcat_1(A) ) ) ) ) )).

fof(d6_waybel_9,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( ( v6_waybel_0(B,A)
            & l1_waybel_0(B,A) )
         => ( B = k4_waybel_9(A)
          <=> ( u1_struct_0(B) = u1_struct_0(A)
              & u1_orders_2(B) = k6_relset_1(u1_struct_0(A),u1_struct_0(A),u1_orders_2(A))
              & u1_waybel_0(A,B) = k7_grcat_1(A) ) ) ) ) )).

fof(t11_waybel_9,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => g1_orders_2(u1_struct_0(k7_lattice3(A)),u1_orders_2(k7_lattice3(A))) = g1_orders_2(u1_struct_0(k4_waybel_9(A)),u1_orders_2(k4_waybel_9(A))) ) )).

fof(d7_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( ( v6_waybel_0(D,A)
                    & l1_waybel_0(D,A) )
                 => ( D = k5_waybel_9(A,B,C)
                  <=> ( ! [E] :
                          ( r2_hidden(E,u1_struct_0(D))
                        <=> ? [F] :
                              ( m1_subset_1(F,u1_struct_0(B))
                              & F = E
                              & r1_orders_2(B,C,F) ) )
                      & u1_orders_2(D) = k1_toler_1(u1_orders_2(B),u1_struct_0(D))
                      & u1_waybel_0(A,D) = k2_partfun1(u1_struct_0(B),u1_struct_0(A),u1_waybel_0(A,B),u1_struct_0(D)) ) ) ) ) ) ) )).

fof(t13_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => r1_tarski(u1_struct_0(k5_waybel_9(A,B,C)),u1_struct_0(B)) ) ) ) )).

fof(t14_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ( v2_yellow_6(k5_waybel_9(A,B,C),A,B)
                & m1_yellow_6(k5_waybel_9(A,B,C),A,B) ) ) ) ) )).

fof(t15_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k5_waybel_9(A,B,C)))
                     => ( D = E
                       => k3_waybel_0(A,B,D) = k3_waybel_0(A,k5_waybel_9(A,B,C),E) ) ) ) ) ) ) )).

fof(t16_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k5_waybel_9(A,B,C)))
                     => ( D = E
                       => k3_waybel_0(A,B,D) = k3_waybel_0(A,k5_waybel_9(A,B,C),E) ) ) ) ) ) ) )).

fof(t17_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => m2_yellow_6(k5_waybel_9(A,B,C),A,B) ) ) ) )).

fof(d8_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( l1_struct_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( l1_waybel_0(D,A)
                 => ! [E] :
                      ( ( v6_waybel_0(E,B)
                        & l1_waybel_0(E,B) )
                     => ( E = k7_waybel_9(A,B,C,D)
                      <=> ( g1_orders_2(u1_struct_0(E),u1_orders_2(E)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
                          & u1_waybel_0(B,E) = k7_funct_2(u1_struct_0(D),u1_struct_0(A),u1_struct_0(B),u1_waybel_0(A,D),C) ) ) ) ) ) ) ) )).

fof(t18_waybel_9,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))
             => k7_waybel_9(A,A,k4_waybel_1(A,C),B) = k3_waybel_2(A,C,B) ) ) ) )).

fof(t19_waybel_9,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( l1_pre_topc(B)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B))))
                 => ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
                      & C = D
                      & v1_tops_2(C,A) )
                   => v1_tops_2(D,B) ) ) ) ) ) )).

fof(t20_waybel_9,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( l1_pre_topc(B)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B))))
                 => ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
                      & C = D
                      & v2_tops_2(C,A) )
                   => v2_tops_2(D,B) ) ) ) ) ) )).

fof(t21_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k10_yellow_6(A,B)))
             => m1_connsp_2(C,A,B) ) ) ) )).

fof(t22_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k10_yellow_6(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k10_yellow_6(A,B)))
                 => m1_subset_1(k3_xboole_0(C,D),u1_struct_0(k10_yellow_6(A,B))) ) ) ) ) )).

fof(t23_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k10_yellow_6(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k10_yellow_6(A,B)))
                 => m1_subset_1(k2_xboole_0(C,D),u1_struct_0(k10_yellow_6(A,B))) ) ) ) ) )).

fof(t24_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_orders_2(C)
                & v7_waybel_0(C)
                & l1_waybel_0(C,A) )
             => ( r2_hidden(B,k11_yellow_6(A,C))
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( D = k8_yellow_2(u1_struct_0(C),A,u1_waybel_0(A,C))
                     => r2_hidden(B,k6_pre_topc(A,D)) ) ) ) ) ) ) )).

fof(t25_waybel_9,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_compts_1(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & v3_yellow_6(B,A)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( v5_pre_topc(C,A,A)
               => r2_hidden(k3_yellow_6(u1_struct_0(A),A,C,k12_yellow_6(A,B)),k11_yellow_6(A,k7_waybel_9(A,A,C,B))) ) ) ) ) )).

fof(t26_waybel_9,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_compts_1(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & v3_yellow_6(B,A)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( v5_pre_topc(k4_waybel_1(A,C),A,A)
               => r2_hidden(k12_lattice3(A,C,k12_yellow_6(A,B)),k11_yellow_6(A,k1_waybel_9(A,C,B))) ) ) ) ) )).

fof(t27_waybel_9,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_compts_1(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => v5_pre_topc(k4_waybel_1(A,C),A,A) )
           => v4_pre_topc(k7_waybel_0(A,B),A) ) ) ) )).

fof(t28_waybel_9,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v2_compts_1(A)
        & v3_compts_1(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => v5_pre_topc(k4_waybel_1(A,C),A,A) )
           => v4_pre_topc(k6_waybel_0(A,B),A) ) ) ) )).

fof(d9_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_waybel_9(A,B,C)
              <=> ! [D] :
                    ( m1_connsp_2(D,A,C)
                   => r2_waybel_0(A,B,D) ) ) ) ) ) )).

fof(t29_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,k11_yellow_6(A,B))
               => r3_waybel_9(A,B,C) ) ) ) ) )).

fof(t30_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_compts_1(A)
        & v3_compts_1(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ? [C] :
              ( m1_subset_1(C,u1_struct_0(A))
              & r3_waybel_9(A,B,C) ) ) ) )).

fof(t31_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m2_yellow_6(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r3_waybel_9(A,C,D)
                   => r3_waybel_9(A,B,D) ) ) ) ) ) )).

fof(t32_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( r3_waybel_9(A,B,C)
                  & ! [D] :
                      ( m2_yellow_6(D,A,B)
                     => ~ r2_hidden(C,k11_yellow_6(A,D)) ) ) ) ) ) )).

fof(t33_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_compts_1(A)
        & v3_compts_1(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r3_waybel_9(A,B,C)
                        & r3_waybel_9(A,B,D) )
                     => C = D ) ) )
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r3_waybel_9(A,B,C)
                 => r2_hidden(C,k11_yellow_6(A,B)) ) ) ) ) ) )).

fof(t34_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_orders_2(C)
                & v7_waybel_0(C)
                & l1_waybel_0(C,A) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( r3_waybel_9(A,C,B)
                      & v4_pre_topc(D,A)
                      & r1_tarski(k8_yellow_2(u1_struct_0(C),A,u1_waybel_0(A,C)),D) )
                   => r2_hidden(B,D) ) ) ) ) ) )).

fof(t35_waybel_9,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v2_compts_1(A)
        & v3_compts_1(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_orders_2(C)
                & v7_waybel_0(C)
                & l1_waybel_0(C,A) )
             => ( ( ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => v5_pre_topc(k4_waybel_1(A,D),A,A) )
                  & v10_waybel_0(C,A)
                  & r3_waybel_9(A,C,B) )
               => B = k1_waybel_2(A,C) ) ) ) ) )).

fof(t36_waybel_9,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v2_compts_1(A)
        & v3_compts_1(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_orders_2(C)
                & v7_waybel_0(C)
                & l1_waybel_0(C,A) )
             => ( ( ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => v5_pre_topc(k4_waybel_1(A,D),A,A) )
                  & v11_waybel_0(C,A)
                  & r3_waybel_9(A,C,B) )
               => B = k2_waybel_9(A,C) ) ) ) ) )).

fof(t37_waybel_9,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_compts_1(A)
        & l1_waybel_9(A) )
     => ( ( ! [B] :
              ( ( ~ v3_struct_0(B)
                & v3_orders_2(B)
                & v7_waybel_0(B)
                & l1_waybel_0(B,A) )
             => ( v10_waybel_0(B,A)
               => ( r1_waybel_9(A,B)
                  & r2_hidden(k1_waybel_2(A,B),k11_yellow_6(A,B)) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => v5_pre_topc(k4_waybel_1(A,B),A,A) ) )
       => v2_waybel_2(A) ) ) )).

fof(t38_waybel_9,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v2_compts_1(A)
        & v3_compts_1(A)
        & l1_waybel_9(A) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => v5_pre_topc(k4_waybel_1(A,B),A,A) )
       => ! [B] :
            ( ( ~ v3_struct_0(B)
              & v3_orders_2(B)
              & v7_waybel_0(B)
              & l1_waybel_0(B,A) )
           => ( v10_waybel_0(B,A)
             => ( r1_waybel_9(A,B)
                & r2_hidden(k1_waybel_2(A,B),k11_yellow_6(A,B)) ) ) ) ) ) )).

fof(t39_waybel_9,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v2_compts_1(A)
        & v3_compts_1(A)
        & l1_waybel_9(A) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => v5_pre_topc(k4_waybel_1(A,B),A,A) )
       => ! [B] :
            ( ( ~ v3_struct_0(B)
              & v3_orders_2(B)
              & v7_waybel_0(B)
              & l1_waybel_0(B,A) )
           => ( v11_waybel_0(B,A)
             => ( r2_waybel_9(A,B)
                & r2_hidden(k2_waybel_9(A,B),k11_yellow_6(A,B)) ) ) ) ) ) )).

fof(t40_waybel_9,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v2_compts_1(A)
        & v3_compts_1(A)
        & l1_waybel_9(A) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => v5_pre_topc(k4_waybel_1(A,B),A,A) )
       => v3_yellow_0(A) ) ) )).

fof(t41_waybel_9,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v2_compts_1(A)
        & v3_compts_1(A)
        & l1_waybel_9(A) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => v5_pre_topc(k4_waybel_1(A,B),A,A) )
       => v2_waybel_2(A) ) ) )).

fof(dt_l1_waybel_9,axiom,(
    ! [A] :
      ( l1_waybel_9(A)
     => ( l1_pre_topc(A)
        & l1_orders_2(A) ) ) )).

fof(existence_l1_waybel_9,axiom,(
    ? [A] : l1_waybel_9(A) )).

fof(abstractness_v1_waybel_9,axiom,(
    ! [A] :
      ( l1_waybel_9(A)
     => ( v1_waybel_9(A)
       => A = g1_waybel_9(u1_struct_0(A),u1_orders_2(A),u1_pre_topc(A)) ) ) )).

fof(dt_k1_waybel_9,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & ~ v3_struct_0(C)
        & v3_orders_2(C)
        & v7_waybel_0(C)
        & l1_waybel_0(C,A) )
     => ( ~ v3_struct_0(k1_waybel_9(A,B,C))
        & v3_orders_2(k1_waybel_9(A,B,C))
        & v6_waybel_0(k1_waybel_9(A,B,C),A)
        & v7_waybel_0(k1_waybel_9(A,B,C))
        & l1_waybel_0(k1_waybel_9(A,B,C),A) ) ) )).

fof(redefinition_k1_waybel_9,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & ~ v3_struct_0(C)
        & v3_orders_2(C)
        & v7_waybel_0(C)
        & l1_waybel_0(C,A) )
     => k1_waybel_9(A,B,C) = k3_waybel_2(A,B,C) ) )).

fof(dt_k2_waybel_9,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & l1_waybel_0(B,A) )
     => m1_subset_1(k2_waybel_9(A,B),u1_struct_0(A)) ) )).

fof(dt_k3_waybel_9,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v6_waybel_0(k3_waybel_9(A),A)
        & l1_waybel_0(k3_waybel_9(A),A) ) ) )).

fof(dt_k4_waybel_9,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v6_waybel_0(k4_waybel_9(A),A)
        & l1_waybel_0(k4_waybel_9(A),A) ) ) )).

fof(dt_k5_waybel_9,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_waybel_0(B,A)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( v6_waybel_0(k5_waybel_9(A,B,C),A)
        & l1_waybel_0(k5_waybel_9(A,B,C),A) ) ) )).

fof(dt_k6_waybel_9,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v3_orders_2(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( v6_waybel_0(k6_waybel_9(A,B,C),A)
        & m2_yellow_6(k6_waybel_9(A,B,C),A,B) ) ) )).

fof(redefinition_k6_waybel_9,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v3_orders_2(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A)
        & m1_subset_1(C,u1_struct_0(B)) )
     => k6_waybel_9(A,B,C) = k5_waybel_9(A,B,C) ) )).

fof(dt_k7_waybel_9,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
        & l1_waybel_0(D,A) )
     => ( v6_waybel_0(k7_waybel_9(A,B,C,D),B)
        & l1_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) )).

fof(dt_g1_waybel_9,axiom,(
    ! [A,B,C] :
      ( ( m1_relset_1(B,A,A)
        & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ( v1_waybel_9(g1_waybel_9(A,B,C))
        & l1_waybel_9(g1_waybel_9(A,B,C)) ) ) )).

fof(free_g1_waybel_9,axiom,(
    ! [A,B,C] :
      ( ( m1_relset_1(B,A,A)
        & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [D,E,F] :
          ( g1_waybel_9(A,B,C) = g1_waybel_9(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) )).

fof(t12_waybel_9,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => u1_struct_0(k5_waybel_9(A,B,C)) = a_3_0_waybel_9(A,B,C) ) ) ) )).

fof(fraenkel_a_3_0_waybel_9,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & l1_struct_0(B)
        & ~ v3_struct_0(C)
        & l1_waybel_0(C,B)
        & m1_subset_1(D,u1_struct_0(C)) )
     => ( r2_hidden(A,a_3_0_waybel_9(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(C))
            & A = E
            & r1_orders_2(C,D,E) ) ) ) )).
%------------------------------------------------------------------------------