SET007 Axioms: SET007+503.ax


%------------------------------------------------------------------------------
% File     : SET007+503 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Closure Operators and Subalgebras
% 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    : waybel10 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   73 (   1 unit)
%            Number of atoms       :  799 (  30 equality)
%            Maximal formula depth :   21 (  10 average)
%            Number of connectives :  789 (  63 ~  ;   0  |; 521  &)
%                                         (  34 <=>; 171 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   64 (   1 propositional; 0-4 arity)
%            Number of functors    :   40 (   9 constant; 0-4 arity)
%            Number of variables   :  174 (   0 singleton; 170 !;   4 ?)
%            Maximal term depth    :    6 (   2 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_waybel10,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l1_orders_2(B) )
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B))
        & v1_yellow_1(k2_funcop_1(A,B))
        & v4_waybel_3(k2_funcop_1(A,B))
        & v2_pralg_1(k2_funcop_1(A,B)) ) ) )).

fof(rc1_waybel10,axiom,(
    ! [A,B] :
      ( ( l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v2_orders_2(B)
        & l1_orders_2(B) )
     => ? [C] :
          ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
          & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B))
          & v5_orders_3(C,A,B) ) ) )).

fof(cc1_waybel10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
              & v6_waybel_1(B,A) )
           => ( v1_funct_1(B)
              & ~ v1_xboole_0(B)
              & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
              & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
              & v11_quantal1(B)
              & v5_orders_3(B,A,A) ) ) ) ) )).

fof(fc2_waybel10,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v2_orders_2(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & v5_orders_3(C,A,B)
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => ( v1_relat_1(k2_waybel_1(A,B,C))
        & v1_funct_1(k2_waybel_1(A,B,C))
        & ~ v1_xboole_0(k2_waybel_1(A,B,C))
        & v1_funct_2(k2_waybel_1(A,B,C),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,B,C)))
        & v2_funct_2(k2_waybel_1(A,B,C),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,B,C)))
        & v1_partfun1(k2_waybel_1(A,B,C),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,B,C)))
        & v5_orders_3(k2_waybel_1(A,B,C),A,k2_yellow_2(A,B,C)) ) ) )).

fof(fc3_waybel10,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ( v1_relat_1(k7_grcat_1(A))
        & v1_funct_1(k7_grcat_1(A))
        & v2_funct_1(k7_grcat_1(A))
        & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(fc4_waybel10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(k7_grcat_1(A))
        & v1_funct_1(k7_grcat_1(A))
        & v2_funct_1(k7_grcat_1(A))
        & ~ v1_xboole_0(k7_grcat_1(A))
        & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
        & v1_partfun1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
        & v11_quantal1(k7_grcat_1(A))
        & v5_orders_3(k7_grcat_1(A),A,A)
        & v17_waybel_0(k7_grcat_1(A),A,A)
        & v18_waybel_0(k7_grcat_1(A),A,A)
        & v19_waybel_0(k7_grcat_1(A),A,A)
        & v20_waybel_0(k7_grcat_1(A),A,A)
        & v21_waybel_0(k7_grcat_1(A),A,A)
        & v22_waybel_0(k7_grcat_1(A),A,A)
        & v23_waybel_0(k7_grcat_1(A),A,A)
        & v6_waybel_1(k7_grcat_1(A),A)
        & v7_waybel_1(k7_grcat_1(A),A)
        & v8_waybel_1(k7_grcat_1(A),A) ) ) )).

fof(rc2_waybel10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v2_funct_1(B)
          & ~ v1_xboole_0(B)
          & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
          & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
          & v11_quantal1(B)
          & v5_orders_3(B,A,A)
          & v17_waybel_0(B,A,A)
          & v18_waybel_0(B,A,A)
          & v19_waybel_0(B,A,A)
          & v20_waybel_0(B,A,A)
          & v21_waybel_0(B,A,A)
          & v22_waybel_0(B,A,A)
          & v6_waybel_1(B,A)
          & v7_waybel_1(B,A)
          & v8_waybel_1(B,A) ) ) )).

fof(fc5_waybel10,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v2_orders_2(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & v5_orders_3(C,A,B)
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
        & m1_yellow_0(D,A) )
     => ( v1_relat_1(k2_waybel10(A,B,C,D))
        & v1_funct_1(k2_waybel10(A,B,C,D))
        & v1_funct_2(k2_waybel10(A,B,C,D),u1_struct_0(D),u1_struct_0(B))
        & v1_partfun1(k2_waybel10(A,B,C,D),u1_struct_0(D),u1_struct_0(B))
        & v5_orders_3(k2_waybel10(A,B,C,D),D,B) ) ) )).

fof(fc6_waybel10,axiom,(
    ! [A,B] :
      ( ( l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v2_orders_2(B)
        & l1_orders_2(B) )
     => ( ~ v3_struct_0(k7_yellow_1(A,B))
        & v1_orders_2(k7_yellow_1(A,B))
        & v2_orders_2(k7_yellow_1(A,B))
        & v4_yellow_0(k7_yellow_1(A,B),k6_yellow_1(u1_struct_0(A),B)) ) ) )).

fof(fc7_waybel10,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ~ v3_struct_0(k4_waybel10(A))
        & v1_orders_2(k4_waybel10(A))
        & v2_orders_2(k4_waybel10(A))
        & v3_orders_2(k4_waybel10(A))
        & v4_orders_2(k4_waybel10(A)) ) ) )).

fof(fc8_waybel10,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ~ v3_struct_0(k4_waybel10(A))
        & v1_orders_2(k4_waybel10(A))
        & v2_orders_2(k4_waybel10(A))
        & v3_orders_2(k4_waybel10(A))
        & v4_orders_2(k4_waybel10(A))
        & v1_lattice3(k4_waybel10(A))
        & v2_lattice3(k4_waybel10(A))
        & v3_lattice3(k4_waybel10(A))
        & v1_yellow_0(k4_waybel10(A))
        & v2_yellow_0(k4_waybel10(A))
        & v3_yellow_0(k4_waybel10(A))
        & v24_waybel_0(k4_waybel10(A))
        & v25_waybel_0(k4_waybel10(A)) ) ) )).

fof(cc2_waybel10,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_0(B,A)
         => ( v7_yellow_0(B,A)
           => ~ v3_struct_0(B) ) ) ) )).

fof(cc3_waybel10,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_0(B,A)
         => ( v8_yellow_0(B,A)
           => ~ v3_struct_0(B) ) ) ) )).

fof(fc9_waybel10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k5_yellow_0(A,k2_pre_topc(A)))
        & v1_orders_2(k5_yellow_0(A,k2_pre_topc(A)))
        & v4_yellow_0(k5_yellow_0(A,k2_pre_topc(A)),A)
        & v5_yellow_0(k5_yellow_0(A,k2_pre_topc(A)),A)
        & v6_yellow_0(k5_yellow_0(A,k2_pre_topc(A)),A)
        & v7_yellow_0(k5_yellow_0(A,k2_pre_topc(A)),A)
        & v8_yellow_0(k5_yellow_0(A,k2_pre_topc(A)),A)
        & v3_waybel_0(k5_yellow_0(A,k2_pre_topc(A)),A)
        & v4_waybel_0(k5_yellow_0(A,k2_pre_topc(A)),A) ) ) )).

fof(fc10_waybel10,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
        & v7_waybel_1(B,A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
     => ( ~ v3_struct_0(k2_yellow_2(A,A,B))
        & v1_orders_2(k2_yellow_2(A,A,B))
        & v2_orders_2(k2_yellow_2(A,A,B))
        & v3_orders_2(k2_yellow_2(A,A,B))
        & v4_orders_2(k2_yellow_2(A,A,B))
        & v4_yellow_0(k2_yellow_2(A,A,B),A)
        & v5_yellow_0(k2_yellow_2(A,A,B),A)
        & v7_yellow_0(k2_yellow_2(A,A,B),A)
        & v3_waybel_0(k2_yellow_2(A,A,B),A) ) ) )).

fof(fc11_waybel10,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_yellow_0(B,A)
        & v7_yellow_0(B,A)
        & m1_yellow_0(B,A) )
     => ( v1_relat_1(k7_waybel10(A,B))
        & v1_funct_1(k7_waybel10(A,B))
        & ~ v1_xboole_0(k7_waybel10(A,B))
        & v1_funct_2(k7_waybel10(A,B),u1_struct_0(A),u1_struct_0(A))
        & v1_partfun1(k7_waybel10(A,B),u1_struct_0(A),u1_struct_0(A))
        & v11_quantal1(k7_waybel10(A,B))
        & v5_orders_3(k7_waybel10(A,B),A,A)
        & v6_waybel_1(k7_waybel10(A,B),A)
        & v7_waybel_1(k7_waybel10(A,B),A) ) ) )).

fof(fc12_waybel10,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_relat_1(k6_waybel10(A))
        & v1_funct_1(k6_waybel10(A))
        & v2_funct_1(k6_waybel10(A))
        & ~ v1_xboole_0(k6_waybel10(A))
        & v1_funct_2(k6_waybel10(A),u1_struct_0(k3_waybel10(A)),u1_struct_0(k1_waybel10(k4_waybel10(A),k5_waybel10(A))))
        & v1_partfun1(k6_waybel10(A),u1_struct_0(k3_waybel10(A)),u1_struct_0(k1_waybel10(k4_waybel10(A),k5_waybel10(A)))) ) ) )).

fof(fc13_waybel10,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_relat_1(k6_waybel10(A))
        & v1_funct_1(k6_waybel10(A))
        & v2_funct_1(k6_waybel10(A))
        & ~ v1_xboole_0(k6_waybel10(A))
        & v1_funct_2(k6_waybel10(A),u1_struct_0(k3_waybel10(A)),u1_struct_0(k1_waybel10(k4_waybel10(A),k5_waybel10(A))))
        & v1_partfun1(k6_waybel10(A),u1_struct_0(k3_waybel10(A)),u1_struct_0(k1_waybel10(k4_waybel10(A),k5_waybel10(A))))
        & v5_orders_3(k6_waybel10(A),k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)))
        & v23_waybel_0(k6_waybel10(A),k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A))) ) ) )).

fof(fc14_waybel10,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_yellow_0(B,A)
        & v7_yellow_0(B,A)
        & v4_waybel_0(B,A)
        & m1_yellow_0(B,A) )
     => ( v1_relat_1(k7_waybel10(A,B))
        & v1_funct_1(k7_waybel10(A,B))
        & ~ v1_xboole_0(k7_waybel10(A,B))
        & v1_funct_2(k7_waybel10(A,B),u1_struct_0(A),u1_struct_0(A))
        & v1_partfun1(k7_waybel10(A,B),u1_struct_0(A),u1_struct_0(A))
        & v11_quantal1(k7_waybel10(A,B))
        & v5_orders_3(k7_waybel10(A,B),A,A)
        & v22_waybel_0(k7_waybel10(A,B),A,A)
        & v6_waybel_1(k7_waybel10(A,B),A)
        & v7_waybel_1(k7_waybel10(A,B),A) ) ) )).

fof(fc15_waybel10,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)
        & v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
        & v22_waybel_0(B,A,A)
        & v7_waybel_1(B,A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
     => ( ~ v3_struct_0(k2_yellow_2(A,A,B))
        & v1_orders_2(k2_yellow_2(A,A,B))
        & v2_orders_2(k2_yellow_2(A,A,B))
        & v3_orders_2(k2_yellow_2(A,A,B))
        & v4_orders_2(k2_yellow_2(A,A,B))
        & v2_lattice3(k2_yellow_2(A,A,B))
        & v4_yellow_0(k2_yellow_2(A,A,B),A)
        & v5_yellow_0(k2_yellow_2(A,A,B),A)
        & v7_yellow_0(k2_yellow_2(A,A,B),A)
        & v3_waybel_0(k2_yellow_2(A,A,B),A)
        & v4_waybel_0(k2_yellow_2(A,A,B),A) ) ) )).

fof(fc16_waybel10,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_relat_1(k2_waybel_1(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))))
        & v1_funct_1(k2_waybel_1(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))))
        & v2_funct_1(k2_waybel_1(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))))
        & ~ v1_xboole_0(k2_waybel_1(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))))
        & v1_funct_2(k2_waybel_1(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))),u1_struct_0(k8_waybel10(A)),u1_struct_0(k2_yellow_2(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A)))))
        & v2_funct_2(k2_waybel_1(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))),u1_struct_0(k8_waybel10(A)),u1_struct_0(k2_yellow_2(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A)))))
        & v3_funct_2(k2_waybel_1(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))),u1_struct_0(k8_waybel10(A)),u1_struct_0(k2_yellow_2(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A)))))
        & v1_partfun1(k2_waybel_1(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))),u1_struct_0(k8_waybel10(A)),u1_struct_0(k2_yellow_2(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A)))))
        & v5_orders_3(k2_waybel_1(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))),k8_waybel10(A),k2_yellow_2(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))))
        & v23_waybel_0(k2_waybel_1(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))),k8_waybel10(A),k2_yellow_2(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A)))) ) ) )).

fof(t1_waybel10,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ( ( r1_tarski(A,B)
             => r1_tarski(k4_relat_1(A),k4_relat_1(B)) )
            & ( r1_tarski(k4_relat_1(A),k4_relat_1(B))
             => r1_tarski(A,B) )
            & ( r1_tarski(k4_relat_1(A),B)
             => r1_tarski(A,k4_relat_1(B)) )
            & ( r1_tarski(A,k4_relat_1(B))
             => r1_tarski(k4_relat_1(A),B) ) ) ) ) )).

fof(t2_waybel10,axiom,(
    $true )).

fof(t3_waybel10,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ( ( m1_yellow_0(B,A)
             => m1_yellow_0(k7_lattice3(B),k7_lattice3(A)) )
            & ( m1_yellow_0(k7_lattice3(B),k7_lattice3(A))
             => m1_yellow_0(B,A) )
            & ( m1_yellow_0(k7_lattice3(B),A)
             => m1_yellow_0(B,k7_lattice3(A)) )
            & ( m1_yellow_0(B,k7_lattice3(A))
             => m1_yellow_0(k7_lattice3(B),A) ) ) ) ) )).

fof(t4_waybel10,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ( ( ( v4_yellow_0(B,A)
                & m1_yellow_0(B,A) )
             => ( v4_yellow_0(k7_lattice3(B),k7_lattice3(A))
                & m1_yellow_0(k7_lattice3(B),k7_lattice3(A)) ) )
            & ( ( v4_yellow_0(k7_lattice3(B),k7_lattice3(A))
                & m1_yellow_0(k7_lattice3(B),k7_lattice3(A)) )
             => ( v4_yellow_0(B,A)
                & m1_yellow_0(B,A) ) )
            & ( ( v4_yellow_0(k7_lattice3(B),A)
                & m1_yellow_0(k7_lattice3(B),A) )
             => ( v4_yellow_0(B,k7_lattice3(A))
                & m1_yellow_0(B,k7_lattice3(A)) ) )
            & ( ( v4_yellow_0(B,k7_lattice3(A))
                & m1_yellow_0(B,k7_lattice3(A)) )
             => ( v4_yellow_0(k7_lattice3(B),A)
                & m1_yellow_0(k7_lattice3(B),A) ) ) ) ) ) )).

fof(t5_waybel10,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_funct_1(k6_partfun1(B))
            & v1_funct_2(k6_partfun1(B),u1_struct_0(k5_yellow_0(A,B)),u1_struct_0(A))
            & m2_relset_1(k6_partfun1(B),u1_struct_0(k5_yellow_0(A,B)),u1_struct_0(A))
            & ! [C] :
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(k5_yellow_0(A,B)),u1_struct_0(A))
                  & m2_relset_1(C,u1_struct_0(k5_yellow_0(A,B)),u1_struct_0(A)) )
               => ( C = k6_partfun1(B)
                 => v5_orders_3(C,k5_yellow_0(A,B),A) ) ) ) ) ) )).

fof(t6_waybel10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v7_waybel_1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_orders_2(A,C,k7_yellow_2(u1_struct_0(A),A,B,C)) ) ) ) )).

fof(d1_waybel10,axiom,(
    ! [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_struct_0(D)
                 => ( r1_tarski(u1_struct_0(D),u1_struct_0(A))
                   => k2_waybel10(A,B,C,D) = k2_partfun1(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(D)) ) ) ) ) ) )).

fof(t7_waybel10,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ! [C] :
              ( m1_yellow_0(C,A)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ( k2_waybel10(A,B,D,C) = k2_partfun1(u1_struct_0(A),u1_struct_0(B),D,u1_struct_0(C))
                    & ! [E] :
                        ( r2_hidden(E,u1_struct_0(C))
                       => k1_funct_1(k2_waybel10(A,B,D,C),E) = k1_funct_1(D,E) ) ) ) ) ) ) )).

fof(t8_waybel10,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [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)) )
             => ( v2_funct_1(C)
               => ! [D] :
                    ( m1_yellow_0(D,A)
                   => v2_funct_1(k2_waybel10(A,B,C,D)) ) ) ) ) ) )).

fof(t9_waybel10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & m1_yellow_0(C,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) )
                     => ( ( v2_funct_1(D)
                          & E = k2_funct_1(D) )
                       => ( v1_funct_1(k2_waybel10(B,A,E,k2_yellow_2(C,B,k2_waybel10(A,B,D,C))))
                          & v1_funct_2(k2_waybel10(B,A,E,k2_yellow_2(C,B,k2_waybel10(A,B,D,C))),u1_struct_0(k2_yellow_2(C,B,k2_waybel10(A,B,D,C))),u1_struct_0(C))
                          & m2_relset_1(k2_waybel10(B,A,E,k2_yellow_2(C,B,k2_waybel10(A,B,D,C))),u1_struct_0(k2_yellow_2(C,B,k2_waybel10(A,B,D,C))),u1_struct_0(C))
                          & k2_waybel10(B,A,E,k2_yellow_2(C,B,k2_waybel10(A,B,D,C))) = k2_funct_1(k2_waybel10(A,B,D,C)) ) ) ) ) ) ) ) )).

fof(t10_waybel10,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k7_yellow_1(A,B)))
            <=> ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v5_orders_3(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) )).

fof(d2_waybel10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_orders_2(B)
            & v4_yellow_0(B,k7_yellow_1(A,A))
            & m1_yellow_0(B,k7_yellow_1(A,A)) )
         => ( B = k3_waybel10(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)) )
               => ( m1_subset_1(C,u1_struct_0(B))
                <=> v7_waybel_1(C,A) ) ) ) ) ) )).

fof(t11_waybel10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k3_waybel10(A)))
        <=> ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v7_waybel_1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) ) ) ) )).

fof(t12_waybel10,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l1_orders_2(B) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,u1_struct_0(B))
            & m2_relset_1(C,A,u1_struct_0(B)) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,u1_struct_0(B))
                & m2_relset_1(D,A,u1_struct_0(B)) )
             => ! [E] :
                  ( m1_subset_1(E,u1_struct_0(k6_yellow_1(A,B)))
                 => ! [F] :
                      ( m1_subset_1(F,u1_struct_0(k6_yellow_1(A,B)))
                     => ( ( E = C
                          & F = D )
                       => ( r1_orders_2(k6_yellow_1(A,B),E,F)
                        <=> r1_yellow_2(A,B,C,D) ) ) ) ) ) ) ) )).

fof(t13_waybel10,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(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(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k3_waybel10(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k3_waybel10(A)))
                     => ( ( D = B
                          & E = C )
                       => ( r3_orders_2(k3_waybel10(A),D,E)
                        <=> r1_yellow_2(u1_struct_0(A),A,B,C) ) ) ) ) ) ) ) )).

fof(t14_waybel10,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( ( v4_yellow_0(C,A)
                & m1_yellow_0(C,A) )
             => ( r1_tarski(u1_struct_0(B),u1_struct_0(C))
               => m1_yellow_0(B,C) ) ) ) ) )).

fof(t15_waybel10,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(A))
            & v7_waybel_1(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(A))
                & v7_waybel_1(C,A)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( r1_yellow_2(u1_struct_0(A),A,B,C)
              <=> m1_yellow_0(k2_yellow_2(A,A,C),k2_yellow_2(A,A,B)) ) ) ) ) )).

fof(d3_waybel10,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_orders_2(B)
            & l1_orders_2(B) )
         => ( B = k4_waybel10(A)
          <=> ( ! [C] :
                  ( m1_subset_1(C,u1_struct_0(B))
                <=> ( v1_orders_2(C)
                    & m1_yellow_0(C,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] :
                            ( l1_orders_2(E)
                            & D = E
                            & m1_yellow_0(C,E) ) ) ) ) ) ) ) ) )).

fof(t16_waybel10,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k4_waybel10(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k4_waybel10(A)))
                 => ( D = B
                   => ( r1_orders_2(k4_waybel10(A),C,D)
                    <=> m1_yellow_0(C,B) ) ) ) ) ) ) )).

fof(d4_waybel10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_orders_2(B)
            & v4_yellow_0(B,k4_waybel10(A))
            & m1_yellow_0(B,k4_waybel10(A)) )
         => ( B = k5_waybel10(A)
          <=> ! [C] :
                ( ( v1_orders_2(C)
                  & m1_yellow_0(C,A) )
               => ( m1_subset_1(C,u1_struct_0(B))
                <=> ( v7_yellow_0(C,A)
                    & v4_yellow_0(C,A) ) ) ) ) ) ) )).

fof(t17_waybel10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k5_waybel10(A)))
        <=> ( v1_orders_2(B)
            & v4_yellow_0(B,A)
            & v7_yellow_0(B,A)
            & m1_yellow_0(B,A) ) ) ) )).

fof(t18_waybel10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( l1_orders_2(B)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k5_waybel10(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k5_waybel10(A)))
                 => ( D = B
                   => ( r3_orders_2(k5_waybel10(A),C,D)
                    <=> m1_yellow_0(C,B) ) ) ) ) ) ) )).

fof(d5_waybel10,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(k3_waybel10(A)),u1_struct_0(k1_waybel10(k4_waybel10(A),k5_waybel10(A))))
            & m2_relset_1(B,u1_struct_0(k3_waybel10(A)),u1_struct_0(k1_waybel10(k4_waybel10(A),k5_waybel10(A)))) )
         => ( B = k6_waybel10(A)
          <=> ! [C] :
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                  & v7_waybel_1(C,A)
                  & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
               => k1_funct_1(B,C) = k2_yellow_2(A,A,C) ) ) ) ) )).

fof(d6_waybel10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_yellow_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)) )
             => ( C = k7_waybel10(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k7_yellow_2(u1_struct_0(A),A,C,D) = k2_yellow_0(A,k3_xboole_0(k7_waybel_0(A,D),u1_struct_0(B))) ) ) ) ) ) )).

fof(t19_waybel10,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_yellow_0(B,A)
            & v7_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => k2_yellow_2(A,A,k7_waybel10(A,B)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) ) ) )).

fof(t20_waybel10,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(A))
            & v7_waybel_1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => k7_waybel10(A,k2_yellow_2(A,A,B)) = B ) ) )).

fof(t21_waybel10,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_funct_1(k2_funct_1(k6_waybel10(A)))
        & v1_funct_2(k2_funct_1(k6_waybel10(A)),u1_struct_0(k1_waybel10(k4_waybel10(A),k5_waybel10(A))),u1_struct_0(k3_waybel10(A)))
        & m2_relset_1(k2_funct_1(k6_waybel10(A)),u1_struct_0(k1_waybel10(k4_waybel10(A),k5_waybel10(A))),u1_struct_0(k3_waybel10(A))) ) ) )).

fof(t22_waybel10,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_orders_2(B)
            & v4_yellow_0(B,A)
            & v7_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => k1_funct_1(k2_funct_1(k6_waybel10(A)),B) = k7_waybel10(A,B) ) ) )).

fof(t23_waybel10,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) )
     => r5_waybel_1(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A))) ) )).

fof(t24_waybel10,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( ( v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ( ( ( v1_waybel_0(C,A)
                    & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
                 => v1_waybel_0(C,B) )
                & ( ( v2_waybel_0(C,A)
                    & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
                 => v2_waybel_0(C,B) ) ) ) ) ) )).

fof(t25_waybel10,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_yellow_0(B,A)
            & v7_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ( v22_waybel_0(k7_waybel10(A,B),A,A)
          <=> v4_waybel_0(B,A) ) ) ) )).

fof(t26_waybel10,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(A))
            & v7_waybel_1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v22_waybel_0(B,A,A)
          <=> v4_waybel_0(k2_yellow_2(A,A,B),A) ) ) ) )).

fof(d7_waybel10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_orders_2(B)
            & v4_yellow_0(B,k3_waybel10(A))
            & m1_yellow_0(B,k3_waybel10(A)) )
         => ( B = k8_waybel10(A)
          <=> ! [C] :
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                  & v7_waybel_1(C,A)
                  & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
               => ( m1_subset_1(C,u1_struct_0(B))
                <=> v22_waybel_0(C,A,A) ) ) ) ) ) )).

fof(t27_waybel10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k8_waybel10(A)))
        <=> ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v22_waybel_0(B,A,A)
            & v7_waybel_1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) ) ) ) )).

fof(d8_waybel10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_orders_2(B)
            & v4_yellow_0(B,k5_waybel10(A))
            & m1_yellow_0(B,k5_waybel10(A)) )
         => ( B = k9_waybel10(A)
          <=> ! [C] :
                ( ( v1_orders_2(C)
                  & v4_yellow_0(C,A)
                  & v7_yellow_0(C,A)
                  & m1_yellow_0(C,A) )
               => ( m1_subset_1(C,u1_struct_0(B))
                <=> v4_waybel_0(C,A) ) ) ) ) ) )).

fof(t28_waybel10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k9_waybel10(A)))
        <=> ( v1_orders_2(B)
            & v4_yellow_0(B,A)
            & v7_yellow_0(B,A)
            & v4_waybel_0(B,A)
            & m1_yellow_0(B,A) ) ) ) )).

fof(t29_waybel10,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) )
     => k2_yellow_2(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))) = k1_waybel10(k5_waybel10(A),k9_waybel10(A)) ) )).

fof(t30_waybel10,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) )
     => r5_waybel_1(k8_waybel10(A),k1_waybel10(k5_waybel10(A),k9_waybel10(A))) ) )).

fof(s1_waybel10,axiom,
    ( ( p1_s1_waybel10(f2_s1_waybel10)
      & r2_hidden(f2_s1_waybel10,u1_struct_0(f1_s1_waybel10)) )
   => ? [A] :
        ( ~ v3_struct_0(A)
        & v1_orders_2(A)
        & v4_yellow_0(A,f1_s1_waybel10)
        & m1_yellow_0(A,f1_s1_waybel10)
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(f1_s1_waybel10))
           => ( m1_subset_1(B,u1_struct_0(A))
            <=> p1_s1_waybel10(B) ) ) ) )).

fof(s2_waybel10,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s2_waybel10))
        <=> p1_s2_waybel10(A) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f2_s2_waybel10))
        <=> p1_s2_waybel10(A) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s2_waybel10))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f1_s2_waybel10))
             => ( r1_orders_2(f1_s2_waybel10,A,B)
              <=> p2_s2_waybel10(A,B) ) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f2_s2_waybel10))
         => ! [B] :
              ( m1_subset_1(B,u1_struct_0(f2_s2_waybel10))
             => ( r1_orders_2(f2_s2_waybel10,A,B)
              <=> p2_s2_waybel10(A,B) ) ) ) )
   => g1_orders_2(u1_struct_0(f1_s2_waybel10),u1_orders_2(f1_s2_waybel10)) = g1_orders_2(u1_struct_0(f2_s2_waybel10),u1_orders_2(f2_s2_waybel10)) )).

fof(s3_waybel10,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,u1_struct_0(f2_s3_waybel10))
        <=> p1_s3_waybel10(A) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f3_s3_waybel10))
        <=> p1_s3_waybel10(A) ) )
   => g1_orders_2(u1_struct_0(f2_s3_waybel10),u1_orders_2(f2_s3_waybel10)) = g1_orders_2(u1_struct_0(f3_s3_waybel10),u1_orders_2(f3_s3_waybel10)) )).

fof(s4_waybel10,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s4_waybel10))
         => ( m1_subset_1(A,u1_struct_0(f2_s4_waybel10))
          <=> p1_s4_waybel10(A) ) )
      & ! [A] :
          ( m1_subset_1(A,u1_struct_0(f1_s4_waybel10))
         => ( m1_subset_1(A,u1_struct_0(f3_s4_waybel10))
          <=> p1_s4_waybel10(A) ) ) )
   => g1_orders_2(u1_struct_0(f2_s4_waybel10),u1_orders_2(f2_s4_waybel10)) = g1_orders_2(u1_struct_0(f3_s4_waybel10),u1_orders_2(f3_s4_waybel10)) )).

fof(dt_k1_waybel10,axiom,(
    ! [A,B] :
      ( ( l1_orders_2(A)
        & v4_yellow_0(B,A)
        & m1_yellow_0(B,A) )
     => ( v1_orders_2(k1_waybel10(A,B))
        & v4_yellow_0(k1_waybel10(A,B),k7_lattice3(A))
        & m1_yellow_0(k1_waybel10(A,B),k7_lattice3(A)) ) ) )).

fof(redefinition_k1_waybel10,axiom,(
    ! [A,B] :
      ( ( l1_orders_2(A)
        & v4_yellow_0(B,A)
        & m1_yellow_0(B,A) )
     => k1_waybel10(A,B) = k7_lattice3(B) ) )).

fof(dt_k2_waybel10,axiom,(
    ! [A,B,C,D] :
      ( ( 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_struct_0(D) )
     => ( v1_funct_1(k2_waybel10(A,B,C,D))
        & v1_funct_2(k2_waybel10(A,B,C,D),u1_struct_0(D),u1_struct_0(B))
        & m2_relset_1(k2_waybel10(A,B,C,D),u1_struct_0(D),u1_struct_0(B)) ) ) )).

fof(dt_k3_waybel10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k3_waybel10(A))
        & v1_orders_2(k3_waybel10(A))
        & v4_yellow_0(k3_waybel10(A),k7_yellow_1(A,A))
        & m1_yellow_0(k3_waybel10(A),k7_yellow_1(A,A)) ) ) )).

fof(dt_k4_waybel10,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ~ v3_struct_0(k4_waybel10(A))
        & v1_orders_2(k4_waybel10(A))
        & l1_orders_2(k4_waybel10(A)) ) ) )).

fof(dt_k5_waybel10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k5_waybel10(A))
        & v1_orders_2(k5_waybel10(A))
        & v4_yellow_0(k5_waybel10(A),k4_waybel10(A))
        & m1_yellow_0(k5_waybel10(A),k4_waybel10(A)) ) ) )).

fof(dt_k6_waybel10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_funct_1(k6_waybel10(A))
        & v1_funct_2(k6_waybel10(A),u1_struct_0(k3_waybel10(A)),u1_struct_0(k1_waybel10(k4_waybel10(A),k5_waybel10(A))))
        & m2_relset_1(k6_waybel10(A),u1_struct_0(k3_waybel10(A)),u1_struct_0(k1_waybel10(k4_waybel10(A),k5_waybel10(A)))) ) ) )).

fof(dt_k7_waybel10,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & m1_yellow_0(B,A) )
     => ( v1_funct_1(k7_waybel10(A,B))
        & v1_funct_2(k7_waybel10(A,B),u1_struct_0(A),u1_struct_0(A))
        & m2_relset_1(k7_waybel10(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(dt_k8_waybel10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k8_waybel10(A))
        & v1_orders_2(k8_waybel10(A))
        & v4_yellow_0(k8_waybel10(A),k3_waybel10(A))
        & m1_yellow_0(k8_waybel10(A),k3_waybel10(A)) ) ) )).

fof(dt_k9_waybel10,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k9_waybel10(A))
        & v1_orders_2(k9_waybel10(A))
        & v4_yellow_0(k9_waybel10(A),k5_waybel10(A))
        & m1_yellow_0(k9_waybel10(A),k5_waybel10(A)) ) ) )).
%------------------------------------------------------------------------------