SET007 Axioms: SET007+484.ax


%------------------------------------------------------------------------------
% File     : SET007+484 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Properties of Relational Structures, Posets, Lattices and Maps
% 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    : yellow_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   86 (   1 unit)
%            Number of atoms       :  835 (  35 equality)
%            Maximal formula depth :   20 (   9 average)
%            Number of connectives :  844 (  95 ~  ;   1  |; 510  &)
%                                         (  12 <=>; 226 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   48 (   1 propositional; 0-4 arity)
%            Number of functors    :   42 (   1 constant; 0-5 arity)
%            Number of variables   :  236 (   0 singleton; 231 !;   5 ?)
%            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_yellow_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v3_struct_0(k5_yellow_0(A,B))
        & v1_orders_2(k5_yellow_0(A,B))
        & v4_yellow_0(k5_yellow_0(A,B),A) ) ) )).

fof(fc2_yellow_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & l1_orders_2(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(k2_yellow_2(A,B,C))
        & v1_orders_2(k2_yellow_2(A,B,C))
        & v4_yellow_0(k2_yellow_2(A,B,C),B) ) ) )).

fof(cc1_yellow_2,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v2_yellow_0(A)
          & v24_waybel_0(A)
          & v25_waybel_0(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_yellow_0(A)
          & v2_yellow_0(A)
          & v3_yellow_0(A)
          & v24_waybel_0(A)
          & v25_waybel_0(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v3_lattice3(A) ) ) ) )).

fof(fc3_yellow_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ~ v1_xboole_0(k8_waybel_0(A)) ) )).

fof(fc4_yellow_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k2_yellow_1(k8_waybel_0(A)))
        & v1_orders_2(k2_yellow_1(k8_waybel_0(A)))
        & v2_orders_2(k2_yellow_1(k8_waybel_0(A)))
        & v3_orders_2(k2_yellow_1(k8_waybel_0(A)))
        & v4_orders_2(k2_yellow_1(k8_waybel_0(A)))
        & v2_lattice3(k2_yellow_1(k8_waybel_0(A))) ) ) )).

fof(fc5_yellow_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k2_yellow_1(k8_waybel_0(A)))
        & v1_orders_2(k2_yellow_1(k8_waybel_0(A)))
        & v2_orders_2(k2_yellow_1(k8_waybel_0(A)))
        & v3_orders_2(k2_yellow_1(k8_waybel_0(A)))
        & v4_orders_2(k2_yellow_1(k8_waybel_0(A)))
        & v1_lattice3(k2_yellow_1(k8_waybel_0(A))) ) ) )).

fof(fc6_yellow_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k2_yellow_1(k8_waybel_0(A)))
        & v1_orders_2(k2_yellow_1(k8_waybel_0(A)))
        & v2_orders_2(k2_yellow_1(k8_waybel_0(A)))
        & v3_orders_2(k2_yellow_1(k8_waybel_0(A)))
        & v4_orders_2(k2_yellow_1(k8_waybel_0(A)))
        & v1_yellow_0(k2_yellow_1(k8_waybel_0(A)))
        & v2_yellow_0(k2_yellow_1(k8_waybel_0(A)))
        & v3_yellow_0(k2_yellow_1(k8_waybel_0(A)))
        & v24_waybel_0(k2_yellow_1(k8_waybel_0(A)))
        & v25_waybel_0(k2_yellow_1(k8_waybel_0(A)))
        & v1_lattice3(k2_yellow_1(k8_waybel_0(A)))
        & v2_lattice3(k2_yellow_1(k8_waybel_0(A)))
        & v3_lattice3(k2_yellow_1(k8_waybel_0(A))) ) ) )).

fof(fc7_yellow_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(k3_yellow_2(A))
        & v1_funct_1(k3_yellow_2(A))
        & v1_funct_2(k3_yellow_2(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A))
        & v5_orders_3(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A) ) ) )).

fof(fc8_yellow_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(k4_yellow_2(A))
        & v1_funct_1(k4_yellow_2(A))
        & v1_funct_2(k4_yellow_2(A),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
        & v5_orders_3(k4_yellow_2(A),A,k2_yellow_1(k8_waybel_0(A))) ) ) )).

fof(t1_yellow_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_tarski(C,k6_waybel_0(A,B))
              <=> r2_lattice3(A,C,B) ) ) ) ) )).

fof(t2_yellow_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_tarski(C,k7_waybel_0(A,B))
              <=> r1_lattice3(A,C,B) ) ) ) ) )).

fof(t3_yellow_2,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B,C] :
          ( ( r1_yellow_0(A,B)
            & r1_yellow_0(A,C) )
         => ( r1_yellow_0(A,k2_xboole_0(B,C))
            & k1_yellow_0(A,k2_xboole_0(B,C)) = k13_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) ) ) ) )).

fof(t4_yellow_2,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B,C] :
          ( ( r2_yellow_0(A,B)
            & r2_yellow_0(A,C) )
         => ( r2_yellow_0(A,k2_xboole_0(B,C))
            & k2_yellow_0(A,k2_xboole_0(B,C)) = k12_lattice3(A,k2_yellow_0(A,B),k2_yellow_0(A,C)) ) ) ) )).

fof(t5_yellow_2,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B,C] :
          ( r1_tarski(B,C)
         => r1_tarski(k2_wellord1(A,B),k2_wellord1(A,C)) ) ) )).

fof(t6_yellow_2,axiom,(
    ! [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))
               => r1_tarski(u1_orders_2(B),u1_orders_2(C)) ) ) ) ) )).

fof(t7_yellow_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l1_orders_2(B) )
     => ! [C] :
          ( ( ~ v3_struct_0(C)
            & m1_yellow_0(C,B) )
         => ( ( ( v1_waybel_0(A,C)
                & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(C))) )
             => ( v1_waybel_0(A,B)
                & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(B))) ) )
            & ( ( v2_waybel_0(A,C)
                & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(C))) )
             => ( v2_waybel_0(A,B)
                & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(B))) ) ) ) ) ) )).

fof(t8_yellow_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v4_yellow_0(C,A)
                & m1_yellow_0(C,A) )
             => ( r1_tarski(u1_struct_0(B),u1_struct_0(C))
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                   => ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C)))
                      & ! [E] :
                          ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C)))
                         => ( D = E
                           => ( ( v2_waybel_0(D,B)
                               => v2_waybel_0(E,C) )
                              & ( v1_waybel_0(D,B)
                               => v1_waybel_0(E,C) ) ) ) ) ) ) ) ) ) ) )).

fof(d1_yellow_2,axiom,(
    ! [A,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)) )
             => ( r1_yellow_2(A,B,C,D)
              <=> ! [E] :
                    ~ ( r2_hidden(E,A)
                      & ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(B))
                             => ~ ( F = k1_funct_1(C,E)
                                  & G = k1_funct_1(D,E)
                                  & r1_orders_2(B,F,G) ) ) ) ) ) ) ) ) )).

fof(t9_yellow_2,axiom,(
    $true )).

fof(t10_yellow_2,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)) )
             => ! [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)) )
                 => ( r1_yellow_2(u1_struct_0(A),B,C,D)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => r1_orders_2(B,k1_waybel_0(A,B,C,E),k1_waybel_0(A,B,D,E)) ) ) ) ) ) ) )).

fof(d2_yellow_2,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)) )
             => k2_yellow_2(A,B,C) = k5_yellow_0(B,k1_yellow_2(A,B,C)) ) ) ) )).

fof(t11_yellow_2,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)) )
             => k1_yellow_2(A,B,C) = u1_struct_0(k2_yellow_2(A,B,C)) ) ) ) )).

fof(t12_yellow_2,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)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k2_yellow_2(A,B,C)))
                 => ? [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                      & k1_waybel_0(A,B,C,E) = D ) ) ) ) ) )).

fof(t13_yellow_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => v5_orders_3(k7_grcat_1(A),A,A) ) )).

fof(t14_yellow_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_orders_2(C) )
             => ! [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(C))
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                     => ( ( v5_orders_3(D,A,B)
                          & v5_orders_3(E,B,C) )
                       => v5_orders_3(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C) ) ) ) ) ) ) )).

fof(t15_yellow_2,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)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( v5_orders_3(C,A,B)
                          & r1_lattice3(A,D,E) )
                       => r1_lattice3(B,k4_pre_topc(A,B,C,D),k1_waybel_0(A,B,C,E)) ) ) ) ) ) ) )).

fof(t16_yellow_2,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)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( v5_orders_3(C,A,B)
                          & r2_lattice3(A,D,E) )
                       => r2_lattice3(B,k4_pre_topc(A,B,C,D),k1_waybel_0(A,B,C,E)) ) ) ) ) ) ) )).

fof(t17_yellow_2,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)) )
             => ! [D] :
                  ( ( v1_waybel_0(D,A)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                 => ( v5_orders_3(C,A,B)
                   => v1_waybel_0(k4_pre_topc(A,B,C,D),B) ) ) ) ) ) )).

fof(t18_yellow_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_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)) )
         => ( v22_waybel_0(B,A,A)
           => v5_orders_3(B,A,A) ) ) ) )).

fof(t19_yellow_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_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)) )
         => ( v21_waybel_0(B,A,A)
           => v5_orders_3(B,A,A) ) ) ) )).

fof(t20_yellow_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(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)) )
         => ( v11_quantal1(B)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k1_waybel_0(A,A,B,k1_waybel_0(A,A,B,C)) = k1_waybel_0(A,A,B,C) ) ) ) ) )).

fof(t22_yellow_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l1_struct_0(B) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
            & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
         => ( ( v11_quantal1(C)
              & r1_tarski(A,k1_yellow_2(B,B,C)) )
           => k4_pre_topc(B,B,C,A) = A ) ) ) )).

fof(t23_yellow_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => v11_quantal1(k7_grcat_1(A)) ) )).

fof(t24_yellow_2,axiom,(
    ! [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] :
          ( m1_subset_1(C,u1_struct_0(B))
         => ( r2_hidden(C,A)
           => ( r3_orders_2(B,C,k1_yellow_0(B,A))
              & r3_orders_2(B,k2_yellow_0(B,A),C) ) ) ) ) )).

fof(t25_yellow_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ! [B] : r1_yellow_0(A,B)
      <=> ! [B] : r2_yellow_0(A,B) ) ) )).

fof(t26_yellow_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ! [B] : r1_yellow_0(A,B)
       => v3_lattice3(A) ) ) )).

fof(t27_yellow_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ! [B] : r2_yellow_0(A,B)
       => v3_lattice3(A) ) ) )).

fof(t28_yellow_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => r2_yellow_0(A,B) )
       => ! [B] :
            ( r2_yellow_0(A,B)
            & k2_yellow_0(A,B) = k2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) ) ) ) )).

fof(t29_yellow_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => r1_yellow_0(A,B) )
       => ! [B] :
            ( r1_yellow_0(A,B)
            & k1_yellow_0(A,B) = k1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) ) ) ) )).

fof(t30_yellow_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => r2_yellow_0(A,B) )
       => v3_lattice3(A) ) ) )).

fof(t32_yellow_2,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] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & v7_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ( 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) ) ) ) )).

fof(t33_yellow_2,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] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & v8_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ( 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) ) ) ) )).

fof(t34_yellow_2,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] :
          ( ( ~ 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)) )
             => ( v18_waybel_0(C,A,B)
               => v8_yellow_0(k2_yellow_2(A,B,C),B) ) ) ) ) )).

fof(t35_yellow_2,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] :
          ( ( ~ 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)) )
             => ( v17_waybel_0(C,A,B)
               => v7_yellow_0(k2_yellow_2(A,B,C),B) ) ) ) ) )).

fof(t36_yellow_2,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] :
              ( ( 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)) )
             => ( ( v18_waybel_0(C,A,B)
                  | v17_waybel_0(C,A,B) )
               => ( v2_orders_2(k2_yellow_2(A,B,C))
                  & v3_orders_2(k2_yellow_2(A,B,C))
                  & v4_orders_2(k2_yellow_2(A,B,C))
                  & v1_lattice3(k2_yellow_2(A,B,C))
                  & v2_lattice3(k2_yellow_2(A,B,C))
                  & v3_lattice3(k2_yellow_2(A,B,C))
                  & l1_orders_2(k2_yellow_2(A,B,C)) ) ) ) ) ) )).

fof(t37_yellow_2,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)) )
         => ( ( v11_quantal1(B)
              & v22_waybel_0(B,A,A) )
           => ( v4_waybel_0(k2_yellow_2(A,A,B),A)
              & 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))
              & v1_lattice3(k2_yellow_2(A,A,B))
              & v2_lattice3(k2_yellow_2(A,A,B))
              & v3_lattice3(k2_yellow_2(A,A,B))
              & l1_orders_2(k2_yellow_2(A,A,B)) ) ) ) ) )).

fof(t38_yellow_2,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                 => v12_waybel_0(C,A) ) )
           => ( v12_waybel_0(k6_setfam_1(u1_struct_0(A),B),A)
              & m1_subset_1(k6_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) )).

fof(t39_yellow_2,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                 => v13_waybel_0(C,A) ) )
           => ( v13_waybel_0(k6_setfam_1(u1_struct_0(A),B),A)
              & m1_subset_1(k6_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) )).

fof(t40_yellow_2,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                 => ( v12_waybel_0(C,A)
                    & v1_waybel_0(C,A) ) ) )
           => ( v1_waybel_0(k6_setfam_1(u1_struct_0(A),B),A)
              & m1_subset_1(k6_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) )).

fof(t41_yellow_2,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                 => ( v13_waybel_0(C,A)
                    & v2_waybel_0(C,A) ) ) )
           => ( v2_waybel_0(k6_setfam_1(u1_struct_0(A),B),A)
              & m1_subset_1(k6_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) )).

fof(t42_yellow_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,A)
            & v12_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_waybel_0(C,A)
                & v12_waybel_0(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( ~ v1_xboole_0(k5_subset_1(u1_struct_0(A),B,C))
                & v1_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A)
                & v12_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A)
                & m1_subset_1(k5_subset_1(u1_struct_0(A),B,C),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) )).

fof(t43_yellow_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & l1_orders_2(B) )
     => ( m1_subset_1(A,u1_struct_0(k2_yellow_1(k8_waybel_0(B))))
      <=> ( ~ v1_xboole_0(A)
          & v1_waybel_0(A,B)
          & v12_waybel_0(A,B)
          & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(B))) ) ) ) )).

fof(t44_yellow_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & l1_orders_2(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(B))))
         => ( r2_hidden(A,C)
           => m1_subset_1(A,u1_struct_0(B)) ) ) ) )).

fof(t45_yellow_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
             => k11_lattice3(k2_yellow_1(k8_waybel_0(A)),B,C) = k3_xboole_0(B,C) ) ) ) )).

fof(t47_yellow_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k8_waybel_0(A))) )
         => ( ~ v1_xboole_0(k1_setfam_1(B))
            & v1_waybel_0(k1_setfam_1(B),A)
            & v12_waybel_0(k1_setfam_1(B),A)
            & m1_subset_1(k1_setfam_1(B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).

fof(t48_yellow_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))) )
         => ( r2_yellow_0(k2_yellow_1(k8_waybel_0(A)),B)
            & k2_yellow_0(k2_yellow_1(k8_waybel_0(A)),B) = k1_setfam_1(B) ) ) ) )).

fof(t49_yellow_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( r2_yellow_0(k2_yellow_1(k8_waybel_0(A)),k1_xboole_0)
        & k2_yellow_0(k2_yellow_1(k8_waybel_0(A)),k1_xboole_0) = k2_pre_topc(A) ) ) )).

fof(t50_yellow_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => v3_lattice3(k2_yellow_1(k8_waybel_0(A))) ) )).

fof(d3_yellow_2,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(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A)) )
         => ( B = k3_yellow_2(A)
          <=> ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v1_waybel_0(C,A)
                  & v12_waybel_0(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => k1_funct_1(B,C) = k1_yellow_0(A,C) ) ) ) ) )).

fof(t51_yellow_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( k1_relat_1(k3_yellow_2(A)) = k8_waybel_0(A)
        & m1_subset_1(k1_yellow_2(k2_yellow_1(k8_waybel_0(A)),A,k3_yellow_2(A)),k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(t52_yellow_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & l1_orders_2(B) )
     => ( r2_hidden(A,k1_relat_1(k3_yellow_2(B)))
      <=> ( ~ v1_xboole_0(A)
          & v1_waybel_0(A,B)
          & v12_waybel_0(A,B)
          & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(B))) ) ) ) )).

fof(t53_yellow_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & l1_orders_2(A) )
     => v5_orders_3(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A) ) )).

fof(d4_yellow_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) )
         => ( B = k4_yellow_2(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),B,C) = k6_waybel_0(A,C) ) ) ) ) )).

fof(t54_yellow_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => v5_orders_3(k4_yellow_2(A),A,k2_yellow_1(k8_waybel_0(A))) ) )).

fof(d5_yellow_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( v1_relat_1(B)
         => k5_yellow_2(A,B) = k1_yellow_0(A,k2_relat_1(B)) ) ) )).

fof(d6_yellow_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( v1_relat_1(B)
         => k6_yellow_2(A,B) = k2_yellow_0(A,k2_relat_1(B)) ) ) )).

fof(t55_yellow_2,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_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,B)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,u1_struct_0(A))
                    & m2_relset_1(D,B,u1_struct_0(A)) )
                 => ( r3_orders_2(A,k7_yellow_2(B,A,D,C),k5_yellow_2(A,D))
                    & r3_orders_2(A,k6_yellow_2(A,D),k7_yellow_2(B,A,D,C)) ) ) ) ) ) )).

fof(t56_yellow_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,C,u1_struct_0(A))
                    & m2_relset_1(D,C,u1_struct_0(A)) )
                 => ( ! [E] :
                        ( m1_subset_1(E,C)
                       => r3_orders_2(A,k7_yellow_2(C,A,D,E),B) )
                   => r3_orders_2(A,k5_yellow_2(A,D),B) ) ) ) ) ) )).

fof(t57_yellow_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,C,u1_struct_0(A))
                    & m2_relset_1(D,C,u1_struct_0(A)) )
                 => ( ! [E] :
                        ( m1_subset_1(E,C)
                       => r3_orders_2(A,B,k7_yellow_2(C,A,D,E)) )
                   => r3_orders_2(A,B,k6_yellow_2(A,D)) ) ) ) ) ) )).

fof(dt_k1_yellow_2,axiom,(
    ! [A,B,C] :
      ( ( 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)) )
     => m1_subset_1(k1_yellow_2(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) )).

fof(redefinition_k1_yellow_2,axiom,(
    ! [A,B,C] :
      ( ( 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)) )
     => k1_yellow_2(A,B,C) = k2_relat_1(C) ) )).

fof(dt_k2_yellow_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & l1_orders_2(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)) )
     => ( v1_orders_2(k2_yellow_2(A,B,C))
        & v4_yellow_0(k2_yellow_2(A,B,C),B)
        & m1_yellow_0(k2_yellow_2(A,B,C),B) ) ) )).

fof(dt_k3_yellow_2,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(k3_yellow_2(A))
        & v1_funct_2(k3_yellow_2(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A))
        & m2_relset_1(k3_yellow_2(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A)) ) ) )).

fof(dt_k4_yellow_2,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(k4_yellow_2(A))
        & v1_funct_2(k4_yellow_2(A),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
        & m2_relset_1(k4_yellow_2(A),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) ) ) )).

fof(dt_k5_yellow_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & v1_relat_1(B) )
     => m1_subset_1(k5_yellow_2(A,B),u1_struct_0(A)) ) )).

fof(dt_k6_yellow_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & v1_relat_1(B) )
     => m1_subset_1(k6_yellow_2(A,B),u1_struct_0(A)) ) )).

fof(dt_k7_yellow_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,u1_struct_0(B))
        & m1_relset_1(C,A,u1_struct_0(B))
        & m1_subset_1(D,A) )
     => m1_subset_1(k7_yellow_2(A,B,C,D),u1_struct_0(B)) ) )).

fof(redefinition_k7_yellow_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,u1_struct_0(B))
        & m1_relset_1(C,A,u1_struct_0(B))
        & m1_subset_1(D,A) )
     => k7_yellow_2(A,B,C,D) = k1_funct_1(C,D) ) )).

fof(dt_k8_yellow_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,u1_struct_0(B))
        & m1_relset_1(C,A,u1_struct_0(B)) )
     => m1_subset_1(k8_yellow_2(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) )).

fof(redefinition_k8_yellow_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,u1_struct_0(B))
        & m1_relset_1(C,A,u1_struct_0(B)) )
     => k8_yellow_2(A,B,C) = k2_relat_1(C) ) )).

fof(t21_yellow_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(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)) )
         => ( v11_quantal1(B)
           => k1_yellow_2(A,A,B) = a_2_0_yellow_2(A,B) ) ) ) )).

fof(t31_yellow_2,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)) )
         => ( v5_orders_3(B,A,A)
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( C = a_2_1_yellow_2(A,B)
                 => ( v2_orders_2(k5_yellow_0(A,C))
                    & v3_orders_2(k5_yellow_0(A,C))
                    & v4_orders_2(k5_yellow_0(A,C))
                    & v1_lattice3(k5_yellow_0(A,C))
                    & v2_lattice3(k5_yellow_0(A,C))
                    & v3_lattice3(k5_yellow_0(A,C))
                    & l1_orders_2(k5_yellow_0(A,C)) ) ) ) ) ) ) )).

fof(t46_yellow_2,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
             => ? [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                  & D = a_3_0_yellow_2(A,B,C)
                  & r1_yellow_0(k2_yellow_1(k8_waybel_0(A)),k2_struct_0(k2_yellow_1(k8_waybel_0(A)),B,C))
                  & k10_lattice3(k2_yellow_1(k8_waybel_0(A)),B,C) = k4_waybel_0(A,D) ) ) ) ) )).

fof(fraenkel_a_2_0_yellow_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
        & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_0_yellow_2(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & D = k1_waybel_0(B,B,C,D) ) ) ) )).

fof(fraenkel_a_2_1_yellow_2,axiom,(
    ! [A,B,C] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v3_lattice3(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
        & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_1_yellow_2(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & D = k1_waybel_0(B,B,C,D) ) ) ) )).

fof(fraenkel_a_3_0_yellow_2,axiom,(
    ! [A,B,C,D] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & l1_orders_2(B)
        & m1_subset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(B))))
        & m1_subset_1(D,u1_struct_0(k2_yellow_1(k8_waybel_0(B)))) )
     => ( r2_hidden(A,a_3_0_yellow_2(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = E
            & ~ ( ~ r2_hidden(E,C)
                & ~ r2_hidden(E,D)
                & ! [F] :
                    ( m1_subset_1(F,u1_struct_0(B))
                   => ! [G] :
                        ( m1_subset_1(G,u1_struct_0(B))
                       => ~ ( r2_hidden(F,C)
                            & r2_hidden(G,D)
                            & E = k13_lattice3(B,F,G) ) ) ) ) ) ) ) )).
%------------------------------------------------------------------------------