SET007 Axioms: SET007+617.ax


%------------------------------------------------------------------------------
% File     : SET007+617 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Injective Spaces. Part II
% 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    : waybel25 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   77 (   0 unit)
%            Number of atoms       :  868 (  24 equality)
%            Maximal formula depth :   21 (  10 average)
%            Number of connectives :  915 ( 124 ~  ;   0  |; 598  &)
%                                         (   5 <=>; 188 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   71 (   0 propositional; 1-6 arity)
%            Number of functors    :   32 (   3 constant; 0-5 arity)
%            Number of variables   :  176 (   0 singleton; 170 !;   6 ?)
%            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(fc1_waybel25,axiom,
    ( ~ v3_struct_0(k9_waybel18)
    & v1_pre_topc(k9_waybel18)
    & v2_pre_topc(k9_waybel18)
    & v2_t_0topsp(k9_waybel18)
    & ~ v1_urysohn1(k9_waybel18)
    & v2_waybel18(k9_waybel18) )).

fof(cc1_waybel25,axiom,(
    ! [A] :
      ( l1_waybel_9(A)
     => ( ( v2_pre_topc(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v3_lattice3(A)
          & v4_waybel11(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v2_t_0topsp(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A) ) ) ) )).

fof(rc1_waybel25,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v2_t_0topsp(A)
      & v2_waybel18(A) ) )).

fof(rc2_waybel25,axiom,(
    ? [A] :
      ( l1_waybel_9(A)
      & ~ v3_struct_0(A)
      & v2_pre_topc(A)
      & v2_t_0topsp(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v1_yellow_0(A)
      & v2_yellow_0(A)
      & v3_yellow_0(A)
      & v24_waybel_0(A)
      & v25_waybel_0(A)
      & v1_waybel_9(A)
      & v4_waybel11(A) ) )).

fof(cc2_waybel25,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_yellow_9(B,A)
         => ( v4_waybel11(B)
           => ( ~ v3_struct_0(B)
              & v2_orders_2(B)
              & v3_orders_2(B)
              & v4_orders_2(B)
              & v1_lattice3(B)
              & v2_lattice3(B)
              & v3_lattice3(B)
              & v1_yellow_0(B)
              & v2_yellow_0(B)
              & v3_yellow_0(B)
              & v24_waybel_0(B)
              & v25_waybel_0(B)
              & ~ v1_yellow_3(B)
              & v2_waybel_3(B)
              & v3_waybel_3(B)
              & v2_waybel18(B) ) ) ) ) )).

fof(fc2_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_waybel18(A)
        & l1_pre_topc(A) )
     => ( ~ v3_struct_0(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)))
        & v1_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)))
        & v2_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)))
        & v2_waybel18(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) ) ) )).

fof(fc3_waybel25,axiom,(
    ! [A] :
      ( ( v3_struct_0(A)
        & l1_pre_topc(A) )
     => ( v3_struct_0(k1_waybel25(A))
        & v1_yellow_0(k1_waybel25(A))
        & v2_yellow_0(k1_waybel25(A))
        & v3_yellow_0(k1_waybel25(A))
        & v1_waybel_9(k1_waybel25(A)) ) ) )).

fof(fc4_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ( ~ v3_struct_0(k1_waybel25(A))
        & v1_waybel_9(k1_waybel25(A)) ) ) )).

fof(fc5_waybel25,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v2_pre_topc(k1_waybel25(A))
        & v1_waybel_9(k1_waybel25(A)) ) ) )).

fof(fc6_waybel25,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( v2_orders_2(k1_waybel25(A))
        & v1_waybel_9(k1_waybel25(A)) ) ) )).

fof(fc7_waybel25,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( v2_orders_2(k1_waybel25(A))
        & v3_orders_2(k1_waybel25(A))
        & v1_waybel_9(k1_waybel25(A)) ) ) )).

fof(fc8_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_t_0topsp(A)
        & l1_pre_topc(A) )
     => ( ~ v3_struct_0(k1_waybel25(A))
        & v2_pre_topc(k1_waybel25(A))
        & v2_orders_2(k1_waybel25(A))
        & v3_orders_2(k1_waybel25(A))
        & v4_orders_2(k1_waybel25(A))
        & v1_waybel_9(k1_waybel25(A)) ) ) )).

fof(fc9_waybel25,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_lattice3(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ( ~ v3_struct_0(k1_waybel25(A))
        & v2_pre_topc(k1_waybel25(A))
        & v2_orders_2(k1_waybel25(A))
        & v3_orders_2(k1_waybel25(A))
        & v4_orders_2(k1_waybel25(A))
        & v1_lattice3(k1_waybel25(A))
        & v2_lattice3(k1_waybel25(A))
        & v3_lattice3(k1_waybel25(A))
        & v1_yellow_0(k1_waybel25(A))
        & v2_yellow_0(k1_waybel25(A))
        & v3_yellow_0(k1_waybel25(A))
        & v24_waybel_0(k1_waybel25(A))
        & v25_waybel_0(k1_waybel25(A))
        & v1_waybel_9(k1_waybel25(A)) ) ) )).

fof(fc10_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_t_0topsp(A)
        & v2_waybel18(A)
        & l1_pre_topc(A) )
     => ( ~ v3_struct_0(k1_waybel25(A))
        & v2_pre_topc(k1_waybel25(A))
        & v2_orders_2(k1_waybel25(A))
        & v3_orders_2(k1_waybel25(A))
        & v4_orders_2(k1_waybel25(A))
        & v1_lattice3(k1_waybel25(A))
        & v2_lattice3(k1_waybel25(A))
        & v3_lattice3(k1_waybel25(A))
        & v1_yellow_0(k1_waybel25(A))
        & v2_yellow_0(k1_waybel25(A))
        & v3_yellow_0(k1_waybel25(A))
        & v24_waybel_0(k1_waybel25(A))
        & v25_waybel_0(k1_waybel25(A))
        & v1_waybel_9(k1_waybel25(A))
        & v3_waybel_3(k1_waybel25(A)) ) ) )).

fof(cc3_waybel25,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B) )
     => ! [C] :
          ( m1_relset_1(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B)))
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B)))
              & v5_pre_topc(C,k1_waybel25(A),k1_waybel25(B)) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_funct_2(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B)))
              & v1_partfun1(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B)))
              & v5_orders_3(C,k1_waybel25(A),k1_waybel25(B)) ) ) ) ) )).

fof(fc11_waybel25,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(k1_waybel25(A))) )
     => ( ~ v1_xboole_0(k6_pre_topc(k1_waybel25(A),k1_struct_0(k1_waybel25(A),B)))
        & v4_pre_topc(k6_pre_topc(k1_waybel25(A),k1_struct_0(k1_waybel25(A),B)),k1_waybel25(A))
        & v1_waybel_0(k6_pre_topc(k1_waybel25(A),k1_struct_0(k1_waybel25(A),B)),k1_waybel25(A))
        & v12_waybel_0(k6_pre_topc(k1_waybel25(A),k1_struct_0(k1_waybel25(A),B)),k1_waybel25(A)) ) ) )).

fof(fc12_waybel25,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(k1_waybel25(A))) )
     => ( ~ v1_xboole_0(k6_waybel_0(k1_waybel25(A),B))
        & v4_pre_topc(k6_waybel_0(k1_waybel25(A),B),k1_waybel25(A))
        & v1_waybel_0(k6_waybel_0(k1_waybel25(A),B),k1_waybel25(A))
        & v12_waybel_0(k6_waybel_0(k1_waybel25(A),B),k1_waybel25(A)) ) ) )).

fof(cc4_waybel25,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_waybel25(A))))
         => ( v3_pre_topc(B,k1_waybel25(A))
           => v13_waybel_0(B,k1_waybel25(A)) ) ) ) )).

fof(fc13_waybel25,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & ~ v3_struct_0(C)
        & v3_orders_2(C)
        & v7_waybel_0(C)
        & v10_waybel_0(C,k3_waybel24(A,k1_waybel25(B)))
        & l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B)))
        & m1_subset_1(D,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D))
        & v3_orders_2(k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D))
        & v6_waybel_0(k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D),k1_waybel25(B))
        & v7_waybel_0(k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D))
        & v10_waybel_0(k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D),k1_waybel25(B)) ) ) )).

fof(cc5_waybel25,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B) )
     => ! [C] :
          ( l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B)))
         => ( ( ~ v3_struct_0(C)
              & v3_orders_2(C)
              & v7_waybel_0(C) )
           => ( ~ v3_struct_0(C)
              & v3_orders_2(C)
              & v7_waybel_0(C)
              & v1_yellow14(C,k3_waybel24(A,k1_waybel25(B))) ) ) ) ) )).

fof(cc6_waybel25,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v2_t_0topsp(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v2_t_0topsp(A)
          & v1_waybel25(A) ) ) ) )).

fof(rc3_waybel25,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v2_t_0topsp(A)
      & v3_realset2(A)
      & v1_waybel25(A) ) )).

fof(cc7_waybel25,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_yellow_9(B,A)
         => ( v4_waybel11(B)
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v2_t_0topsp(B)
              & v2_orders_2(B)
              & v3_orders_2(B)
              & v4_orders_2(B)
              & v1_lattice3(B)
              & v2_lattice3(B)
              & v3_lattice3(B)
              & v1_yellow_0(B)
              & v2_yellow_0(B)
              & v3_yellow_0(B)
              & v24_waybel_0(B)
              & v25_waybel_0(B)
              & v4_waybel11(B)
              & v1_waybel25(B) ) ) ) ) )).

fof(fc14_waybel25,axiom,(
    ! [A,B] :
      ( ( 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)
        & v4_waybel11(B)
        & m1_yellow_9(B,A) )
     => ( ~ v3_struct_0(g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)))
        & v1_pre_topc(g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)))
        & v2_pre_topc(g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)))
        & v1_waybel25(g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))) ) ) )).

fof(fc15_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_t_0topsp(A)
        & v1_waybel25(A)
        & l1_pre_topc(A) )
     => ( ~ v3_struct_0(k1_waybel25(A))
        & v2_pre_topc(k1_waybel25(A))
        & v2_orders_2(k1_waybel25(A))
        & v3_orders_2(k1_waybel25(A))
        & v4_orders_2(k1_waybel25(A))
        & v24_waybel_0(k1_waybel25(A))
        & v1_waybel_9(k1_waybel25(A)) ) ) )).

fof(cc8_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_waybel25(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( l1_waybel_0(B,k1_waybel25(A))
         => ( ( ~ v3_struct_0(B)
              & v3_orders_2(B)
              & v7_waybel_0(B)
              & v10_waybel_0(B,k1_waybel25(A)) )
           => ( ~ v3_struct_0(B)
              & v3_orders_2(B)
              & v7_waybel_0(B)
              & v10_waybel_0(B,k1_waybel25(A))
              & v3_yellow_6(B,k1_waybel25(A)) ) ) ) ) )).

fof(cc9_waybel25,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_waybel25(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & v2_t_0topsp(B)
        & l1_pre_topc(B) )
     => ! [C] :
          ( m1_relset_1(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B)))
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B)))
              & v5_pre_topc(C,k1_waybel25(A),k1_waybel25(B)) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_funct_2(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B)))
              & v1_partfun1(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B)))
              & v22_waybel_0(C,k1_waybel25(A),k1_waybel25(B)) ) ) ) ) )).

fof(cc10_waybel25,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v2_t_0topsp(A)
          & v2_waybel18(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v2_t_0topsp(A)
          & v1_waybel25(A) ) ) ) )).

fof(t1_waybel25,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k9_waybel18))
     => ( A = np__0
       => v4_pre_topc(k1_struct_0(k9_waybel18,A),k9_waybel18) ) ) )).

fof(t2_waybel25,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k9_waybel18))
     => ~ ( A = np__1
          & v4_pre_topc(k1_struct_0(k9_waybel18,A),k9_waybel18) ) ) )).

fof(t3_waybel25,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(B,k5_yellow_1(A,k2_pre_circ(A,k3_yellow_1(np__1)))) )
         => u1_struct_0(B) = u1_struct_0(k3_waybel18(A,k2_pre_circ(A,k9_waybel18))) ) ) )).

fof(t4_waybel25,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_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v4_waybel11(C)
                & m1_yellow_9(C,A) )
             => ! [D] :
                  ( ( v4_waybel11(D)
                    & m1_yellow_9(D,B) )
                 => ! [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)) )
                         => ( ( r4_nattra_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),u1_struct_0(D),E,F)
                              & v23_waybel_0(E,A,B) )
                           => v3_tops_2(F,C,D) ) ) ) ) ) ) ) )).

fof(t5_waybel25,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_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v4_waybel11(C)
                & m1_yellow_9(C,A) )
             => ! [D] :
                  ( ( v4_waybel11(D)
                    & m1_yellow_9(D,B) )
                 => ( r5_waybel_1(A,B)
                   => r1_borsuk_3(C,D) ) ) ) ) ) )).

fof(t6_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ( ( v2_waybel18(A)
              & r1_borsuk_3(A,B) )
           => v2_waybel18(B) ) ) ) )).

fof(t7_waybel25,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_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v4_waybel11(C)
                & m1_yellow_9(C,A) )
             => ! [D] :
                  ( ( v4_waybel11(D)
                    & m1_yellow_9(D,B) )
                 => ( ( r5_waybel_1(A,B)
                      & v2_waybel18(C) )
                   => v2_waybel18(D) ) ) ) ) ) )).

fof(d1_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ( r1_waybel18(A,B)
          <=> ? [C] :
                ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v5_pre_topc(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
                & ? [D] :
                    ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
                    & v5_pre_topc(D,B,A)
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A))
                    & r4_nattra_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k4_borsuk_1(A,B,A,C,D),k7_grcat_1(A)) ) ) ) ) ) )).

fof(t8_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_pre_topc(C)
                & l1_pre_topc(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v2_pre_topc(D)
                    & l1_pre_topc(D) )
                 => ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
                      & g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = g1_pre_topc(u1_struct_0(D),u1_pre_topc(D))
                      & r1_waybel18(A,C) )
                   => r1_waybel18(B,D) ) ) ) ) ) )).

fof(t9_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_pre_topc(C) )
             => ( ( r1_borsuk_3(B,C)
                  & r1_waybel18(B,A) )
               => r1_waybel18(C,A) ) ) ) ) )).

fof(t10_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ( ( v2_waybel18(B)
              & r1_waybel18(A,B) )
           => v2_waybel18(A) ) ) ) )).

fof(t11_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_waybel18(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ( m1_pre_topc(A,B)
           => r1_waybel18(A,B) ) ) ) )).

fof(t12_waybel25,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(B,A) )
         => v2_waybel18(B) ) ) )).

fof(d2_waybel25,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( ( v1_waybel_9(B)
            & l1_waybel_9(B) )
         => ( B = k1_waybel25(A)
          <=> ( g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(B))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(B))
                     => ( r1_orders_2(B,C,D)
                      <=> ? [E] :
                            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                            & E = k1_tarski(D)
                            & r2_hidden(C,k6_pre_topc(A,E)) ) ) ) ) ) ) ) ) )).

fof(t13_waybel25,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
           => k1_waybel25(A) = k1_waybel25(B) ) ) ) )).

fof(t14_waybel25,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => g1_orders_2(u1_struct_0(k1_waybel25(k3_waybel18(A,k2_pre_circ(A,B)))),u1_orders_2(k1_waybel25(k3_waybel18(A,k2_pre_circ(A,B))))) = g1_orders_2(u1_struct_0(k5_yellow_1(A,k2_pre_circ(A,k1_waybel25(B)))),u1_orders_2(k5_yellow_1(A,k2_pre_circ(A,k1_waybel25(B))))) ) ) )).

fof(t15_waybel25,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_lattice3(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => k1_waybel25(A) = g1_waybel_9(u1_struct_0(A),u1_orders_2(A),u1_pre_topc(A)) ) )).

fof(t16_waybel25,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] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(B,A) )
         => g1_orders_2(u1_struct_0(k1_waybel25(B)),u1_orders_2(k1_waybel25(B))) = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) )).

fof(t17_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => ( v4_yellow_0(k1_waybel25(B),k1_waybel25(A))
            & m1_yellow_0(k1_waybel25(B),k1_waybel25(A)) ) ) ) )).

fof(t18_waybel25,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(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] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B)))
                    & m2_relset_1(D,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B))) )
                 => ( ( C = D
                      & v3_tops_2(C,A,B) )
                   => v23_waybel_0(D,k1_waybel25(A),k1_waybel25(B)) ) ) ) ) ) )).

fof(t19_waybel25,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ( r1_t_0topsp(A,B)
           => r5_waybel_1(k1_waybel25(A),k1_waybel25(B)) ) ) ) )).

fof(t20_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_t_0topsp(A)
        & v2_waybel18(A)
        & l1_pre_topc(A) )
     => ( v2_orders_2(k1_waybel25(A))
        & v3_orders_2(k1_waybel25(A))
        & v4_orders_2(k1_waybel25(A))
        & v1_lattice3(k1_waybel25(A))
        & v2_lattice3(k1_waybel25(A))
        & v3_lattice3(k1_waybel25(A))
        & v3_waybel_3(k1_waybel25(A))
        & l1_orders_2(k1_waybel25(A)) ) ) )).

fof(t21_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B)))
                & v5_pre_topc(C,k1_waybel25(A),k1_waybel25(B))
                & m2_relset_1(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B))) )
             => v5_orders_3(C,k1_waybel25(A),k1_waybel25(B)) ) ) ) )).

fof(t22_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k1_waybel25(A)))
         => k6_pre_topc(k1_waybel25(A),k1_struct_0(k1_waybel25(A),B)) = k6_waybel_0(k1_waybel25(A),B) ) ) )).

fof(t23_waybel25,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v3_pre_topc(B,k1_waybel25(A))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_waybel25(A)))) )
         => v13_waybel_0(B,k1_waybel25(A)) ) ) )).

fof(d3_waybel25,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v3_orders_2(D)
                    & v7_waybel_0(D)
                    & l1_waybel_0(D,C) )
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ( r1_tarski(u1_struct_0(C),u1_struct_0(k6_yellow_1(A,B)))
                       => ! [F] :
                            ( ( ~ v3_struct_0(F)
                              & v3_orders_2(F)
                              & v6_waybel_0(F,B)
                              & v7_waybel_0(F)
                              & l1_waybel_0(F,B) )
                           => ( F = k2_waybel25(A,B,C,D,E)
                            <=> ( g1_orders_2(u1_struct_0(F),u1_orders_2(F)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
                                & u1_waybel_0(B,F) = k1_funct_1(k10_funct_6(u1_waybel_0(C,D)),E) ) ) ) ) ) ) ) ) ) )).

fof(t24_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_orders_2(C)
                & v7_waybel_0(C)
                & l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => k1_funct_1(u1_waybel_0(k1_waybel25(B),k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,E)),D) = k1_funct_1(k3_yellow_6(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C),D),E) ) ) ) ) ) )).

fof(t25_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_orders_2(C)
                & v7_waybel_0(C)
                & v10_waybel_0(C,k3_waybel24(A,k1_waybel25(B)))
                & l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => v10_waybel_0(k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D),k1_waybel25(B)) ) ) ) ) )).

fof(t26_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & v2_t_0topsp(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_orders_2(C)
                & v7_waybel_0(C)
                & l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) )
             => ( ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => r1_waybel_9(k1_waybel25(B),k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D)) )
               => r1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C))) ) ) ) ) )).

fof(d4_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_waybel25(A)
      <=> ! [B] :
            ( ( ~ v1_xboole_0(B)
              & v1_waybel_0(B,k1_waybel25(A))
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_waybel25(A)))) )
           => ( r1_yellow_0(k1_waybel25(A),B)
              & ! [C] :
                  ( ( v3_pre_topc(C,A)
                    & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
                 => ~ ( r2_hidden(k1_yellow_0(k1_waybel25(A),B),C)
                      & r1_xboole_0(B,C) ) ) ) ) ) ) )).

fof(t27_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
              & v1_waybel25(A) )
           => v1_waybel25(B) ) ) ) )).

fof(t28_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_t_0topsp(A)
        & v1_waybel25(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & v2_t_0topsp(B)
            & l1_pre_topc(B) )
         => ( r1_borsuk_3(A,B)
           => v1_waybel25(B) ) ) ) )).

fof(t29_waybel25,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_lattice3(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => v1_waybel25(A) ) )).

fof(t30_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_t_0topsp(A)
        & v1_waybel25(A)
        & l1_pre_topc(A) )
     => v24_waybel_0(k1_waybel25(A)) ) )).

fof(t31_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_waybel25(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v7_waybel_0(B)
            & v10_waybel_0(B,k1_waybel25(A))
            & l1_waybel_0(B,k1_waybel25(A)) )
         => r1_waybel_9(k1_waybel25(A),B) ) ) )).

fof(t32_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_waybel25(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & v10_waybel_0(B,k1_waybel25(A))
            & l1_waybel_0(B,k1_waybel25(A)) )
         => r2_hidden(k1_waybel_2(k1_waybel25(A),B),k11_yellow_6(k1_waybel25(A),B)) ) ) )).

fof(t33_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_waybel25(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & v10_waybel_0(B,k1_waybel25(A))
            & l1_waybel_0(B,k1_waybel25(A)) )
         => v3_yellow_6(B,k1_waybel25(A)) ) ) )).

fof(t34_waybel25,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)
              & v10_waybel_0(B,k1_waybel25(A))
              & l1_waybel_0(B,k1_waybel25(A)) )
           => ( r1_waybel_9(k1_waybel25(A),B)
              & r2_hidden(k1_waybel_2(k1_waybel25(A),B),k11_yellow_6(k1_waybel25(A),B)) ) )
       => v1_waybel25(A) ) ) )).

fof(t35_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_waybel25(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & v2_t_0topsp(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B)))
                & v5_pre_topc(C,k1_waybel25(A),k1_waybel25(B))
                & m2_relset_1(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B))) )
             => v22_waybel_0(C,k1_waybel25(A),k1_waybel25(B)) ) ) ) )).

fof(t36_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_t_0topsp(A)
        & v1_waybel25(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & v2_t_0topsp(B)
            & l1_pre_topc(B) )
         => ( r1_waybel18(B,A)
           => v1_waybel25(B) ) ) ) )).

fof(t37_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_t_0topsp(A)
        & v2_waybel18(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(B,k1_waybel25(A)) )
         => g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) ) ) )).

fof(t38_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_t_0topsp(A)
        & v2_waybel18(A)
        & l1_pre_topc(A) )
     => ( v2_compts_1(A)
        & v6_waybel_3(A)
        & v3_yellow_8(A) ) ) )).

fof(t39_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_t_0topsp(A)
        & v2_waybel18(A)
        & l1_pre_topc(A) )
     => v1_waybel25(A) ) )).

fof(t40_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & v2_t_0topsp(B)
            & v1_waybel25(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_orders_2(C)
                & v7_waybel_0(C)
                & l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k1_waybel25(B)))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k1_waybel25(B))) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(k1_waybel25(B)))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(k1_waybel25(B))) )
                     => ( ( D = k1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C)))
                          & r1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C)))
                          & r2_hidden(E,k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C))) )
                       => r1_yellow_2(u1_struct_0(A),k1_waybel25(B),E,D) ) ) ) ) ) ) )).

fof(t41_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & v2_t_0topsp(B)
            & v1_waybel25(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_orders_2(C)
                & v7_waybel_0(C)
                & l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(k1_waybel25(B)))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(k1_waybel25(B))) )
                     => ( ( ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => v10_waybel_0(k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,F),k1_waybel25(B)) )
                          & E = k1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C))) )
                       => k3_yellow_6(u1_struct_0(A),k1_waybel25(B),E,D) = k1_waybel_2(k1_waybel25(B),k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D)) ) ) ) ) ) ) )).

fof(t42_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & v2_t_0topsp(B)
            & v1_waybel25(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_orders_2(C)
                & v7_waybel_0(C)
                & l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) )
             => ( ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => v10_waybel_0(k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D),k1_waybel25(B)) )
               => ( v1_funct_1(k1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C))))
                  & v1_funct_2(k1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C))),u1_struct_0(A),u1_struct_0(B))
                  & v5_pre_topc(k1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C))),A,B)
                  & m2_relset_1(k1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C))),u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ) )).

fof(t43_waybel25,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & v2_t_0topsp(B)
            & v1_waybel25(B)
            & l1_pre_topc(B) )
         => ( v4_waybel_0(k3_waybel24(A,k1_waybel25(B)),k6_yellow_1(u1_struct_0(A),k1_waybel25(B)))
            & m1_yellow_0(k3_waybel24(A,k1_waybel25(B)),k6_yellow_1(u1_struct_0(A),k1_waybel25(B))) ) ) ) )).

fof(dt_k1_waybel25,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( v1_waybel_9(k1_waybel25(A))
        & l1_waybel_9(k1_waybel25(A)) ) ) )).

fof(dt_k2_waybel25,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & l1_orders_2(B)
        & ~ v3_struct_0(C)
        & l1_orders_2(C)
        & ~ v3_struct_0(D)
        & v3_orders_2(D)
        & v7_waybel_0(D)
        & l1_waybel_0(D,C)
        & m1_subset_1(E,A) )
     => ( ~ v3_struct_0(k2_waybel25(A,B,C,D,E))
        & v3_orders_2(k2_waybel25(A,B,C,D,E))
        & v6_waybel_0(k2_waybel25(A,B,C,D,E),B)
        & v7_waybel_0(k2_waybel25(A,B,C,D,E))
        & l1_waybel_0(k2_waybel25(A,B,C,D,E),B) ) ) )).
%------------------------------------------------------------------------------