SET007 Axioms: SET007+487.ax


%------------------------------------------------------------------------------
% File     : SET007+487 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Definitions and Properties of the Join and Meet of Subsets
% 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_4 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   94 (   0 unit)
%            Number of atoms       :  696 (  43 equality)
%            Maximal formula depth :   16 (   9 average)
%            Number of connectives :  658 (  56 ~  ;   0  |; 316  &)
%                                         (  10 <=>; 276 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   27 (   0 propositional; 1-3 arity)
%            Number of functors    :   32 (   1 constant; 0-3 arity)
%            Number of variables   :  324 (   0 singleton; 314 !;  10 ?)
%            Maximal term depth    :    4 (   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_yellow_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ~ v1_xboole_0(k1_yellow_4(A,B,C)) ) )).

fof(fc2_yellow_4,axiom,(
    ! [A,B,C] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & v1_waybel_0(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & v1_waybel_0(C,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => v1_waybel_0(k1_yellow_4(A,B,C),A) ) )).

fof(fc3_yellow_4,axiom,(
    ! [A,B,C] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & v2_waybel_0(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & v2_waybel_0(C,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => v2_waybel_0(k1_yellow_4(A,B,C),A) ) )).

fof(fc4_yellow_4,axiom,(
    ! [A,B,C] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & v13_waybel_0(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & v13_waybel_0(C,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => v13_waybel_0(k1_yellow_4(A,B,C),A) ) )).

fof(fc5_yellow_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ~ v1_xboole_0(k3_yellow_4(A,B,C)) ) )).

fof(fc6_yellow_4,axiom,(
    ! [A,B,C] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & v1_waybel_0(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & v1_waybel_0(C,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => v1_waybel_0(k3_yellow_4(A,B,C),A) ) )).

fof(fc7_yellow_4,axiom,(
    ! [A,B,C] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & v2_waybel_0(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & v2_waybel_0(C,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => v2_waybel_0(k3_yellow_4(A,B,C),A) ) )).

fof(fc8_yellow_4,axiom,(
    ! [A,B,C] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & v12_waybel_0(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & v12_waybel_0(C,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => v12_waybel_0(k3_yellow_4(A,B,C),A) ) )).

fof(t1_yellow_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B,C] :
          ( m1_subset_1(C,u1_struct_0(A))
         => ( ( r2_hidden(C,B)
              & r1_yellow_0(A,B) )
           => r1_orders_2(A,C,k1_yellow_0(A,B)) ) ) ) )).

fof(t2_yellow_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B,C] :
          ( m1_subset_1(C,u1_struct_0(A))
         => ( ( r2_hidden(C,B)
              & r2_yellow_0(A,B) )
           => r1_orders_2(A,k2_yellow_0(A,B),C) ) ) ) )).

fof(d1_yellow_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_yellow_4(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( r2_hidden(D,B)
                        & ! [E] :
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ~ ( r2_hidden(E,C)
                                & r1_orders_2(A,D,E) ) ) ) ) ) ) ) ) )).

fof(d2_yellow_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_yellow_4(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( r2_hidden(D,C)
                        & ! [E] :
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ~ ( r2_hidden(E,B)
                                & r1_orders_2(A,E,D) ) ) ) ) ) ) ) ) )).

fof(t3_yellow_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r1_yellow_4(A,k1_pre_topc(A),B) ) ) )).

fof(t4_yellow_4,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( r1_yellow_4(A,B,C)
                      & r1_yellow_4(A,C,D) )
                   => r1_yellow_4(A,B,D) ) ) ) ) ) )).

fof(t5_yellow_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( r1_yellow_4(A,C,B)
                  & v12_waybel_0(B,A) )
               => r1_tarski(C,B) ) ) ) ) )).

fof(t6_yellow_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r2_yellow_4(A,B,k1_pre_topc(A)) ) ) )).

fof(t7_yellow_4,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( r2_yellow_4(A,C,D)
                      & r2_yellow_4(A,B,C) )
                   => r2_yellow_4(A,B,D) ) ) ) ) ) )).

fof(t8_yellow_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( r2_yellow_4(A,C,B)
                  & v13_waybel_0(C,A) )
               => r1_tarski(B,C) ) ) ) ) )).

fof(t9_yellow_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k1_yellow_4(A,B,k1_pre_topc(A)) = k1_xboole_0 ) ) )).

fof(t10_yellow_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r2_hidden(D,B)
                          & r2_hidden(E,C) )
                       => r2_hidden(k10_lattice3(A,D,E),k1_yellow_4(A,B,C)) ) ) ) ) ) ) )).

fof(t11_yellow_4,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => r1_yellow_4(A,B,k2_yellow_4(A,B,C)) ) ) ) )).

fof(t12_yellow_4,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => r2_yellow_4(A,B,k2_yellow_4(A,B,C)) ) ) ) )).

fof(t13_yellow_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r1_tarski(B,k2_yellow_4(A,B,B)) ) ) )).

fof(t14_yellow_4,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => k2_yellow_4(A,k2_yellow_4(A,B,C),D) = k2_yellow_4(A,B,k2_yellow_4(A,C,D)) ) ) ) ) )).

fof(t16_yellow_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => k1_yellow_4(A,B,k4_subset_1(u1_struct_0(A),C,D)) = k4_subset_1(u1_struct_0(A),k1_yellow_4(A,B,C),k1_yellow_4(A,B,D)) ) ) ) ) )).

fof(t17_yellow_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => r1_tarski(k4_subset_1(u1_struct_0(A),B,k2_yellow_4(A,C,D)),k2_yellow_4(A,k4_subset_1(u1_struct_0(A),B,C),k4_subset_1(u1_struct_0(A),B,D))) ) ) ) ) )).

fof(t18_yellow_4,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v13_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => r1_tarski(k2_yellow_4(A,k4_subset_1(u1_struct_0(A),B,C),k4_subset_1(u1_struct_0(A),B,D)),k4_subset_1(u1_struct_0(A),B,k2_yellow_4(A,C,D))) ) ) ) ) )).

fof(t19_yellow_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_yellow_4(A,k1_struct_0(A,B),k1_struct_0(A,C)) = k1_struct_0(A,k10_lattice3(A,B,C)) ) ) ) )).

fof(t20_yellow_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k1_yellow_4(A,k1_struct_0(A,B),k2_struct_0(A,C,D)) = k2_struct_0(A,k10_lattice3(A,B,C),k10_lattice3(A,B,D)) ) ) ) ) )).

fof(t21_yellow_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r1_tarski(B,D)
                          & r1_tarski(C,E) )
                       => r1_tarski(k1_yellow_4(A,B,C),k1_yellow_4(A,D,E)) ) ) ) ) ) ) )).

fof(t22_yellow_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_lattice3(A,B,C)
               => k2_yellow_4(A,k1_struct_0(A,C),B) = B ) ) ) ) )).

fof(t23_yellow_4,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_lattice3(A,k2_yellow_4(A,k1_struct_0(A,C),B),C) ) ) ) )).

fof(t24_yellow_4,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,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( r2_yellow_0(A,k2_yellow_4(A,k1_struct_0(A,C),B))
                  & r2_yellow_0(A,B) )
               => r3_orders_2(A,k13_lattice3(A,C,k2_yellow_0(A,B)),k2_yellow_0(A,k2_yellow_4(A,k1_struct_0(A,C),B))) ) ) ) ) )).

fof(t25_yellow_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => r2_lattice3(A,B,k1_yellow_0(A,k2_yellow_4(A,B,C))) ) ) ) )).

fof(t26_yellow_4,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r1_lattice3(A,D,B)
                          & r1_lattice3(A,E,C) )
                       => r1_lattice3(A,k2_yellow_4(A,D,E),k13_lattice3(A,B,C)) ) ) ) ) ) ) )).

fof(t27_yellow_4,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r2_lattice3(A,D,B)
                          & r2_lattice3(A,E,C) )
                       => r2_lattice3(A,k2_yellow_4(A,D,E),k13_lattice3(A,B,C)) ) ) ) ) ) ) )).

fof(t28_yellow_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => k1_yellow_0(A,k2_yellow_4(A,B,C)) = k13_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) ) ) ) )).

fof(t29_yellow_4,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => r1_tarski(B,k4_waybel_0(A,k2_yellow_4(A,B,C))) ) ) ) )).

fof(t30_yellow_4,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)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( B = D
                          & C = E )
                       => k13_lattice3(k2_yellow_1(k8_waybel_0(A)),B,C) = k4_waybel_0(A,k2_yellow_4(A,D,E)) ) ) ) ) ) ) )).

fof(t32_yellow_4,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => r1_tarski(k4_waybel_0(A,k2_yellow_4(A,k4_waybel_0(A,B),k4_waybel_0(A,C))),k4_waybel_0(A,k2_yellow_4(A,B,C))) ) ) ) )).

fof(t33_yellow_4,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,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k4_waybel_0(A,k2_yellow_4(A,k4_waybel_0(A,B),k4_waybel_0(A,C))) = k4_waybel_0(A,k2_yellow_4(A,B,C)) ) ) ) )).

fof(t34_yellow_4,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => r1_tarski(k5_waybel_0(A,k2_yellow_4(A,k5_waybel_0(A,B),k5_waybel_0(A,C))),k5_waybel_0(A,k2_yellow_4(A,B,C))) ) ) ) )).

fof(t35_yellow_4,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,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k5_waybel_0(A,k2_yellow_4(A,k5_waybel_0(A,B),k5_waybel_0(A,C))) = k5_waybel_0(A,k2_yellow_4(A,B,C)) ) ) ) )).

fof(t36_yellow_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k3_yellow_4(A,B,k1_pre_topc(A)) = k1_xboole_0 ) ) )).

fof(t37_yellow_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r2_hidden(D,B)
                          & r2_hidden(E,C) )
                       => r2_hidden(k11_lattice3(A,D,E),k3_yellow_4(A,B,C)) ) ) ) ) ) ) )).

fof(t38_yellow_4,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => r2_yellow_4(A,k4_yellow_4(A,B,C),B) ) ) ) )).

fof(t39_yellow_4,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => r1_yellow_4(A,k4_yellow_4(A,B,C),B) ) ) ) )).

fof(t40_yellow_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r1_tarski(B,k4_yellow_4(A,B,B)) ) ) )).

fof(t41_yellow_4,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => k4_yellow_4(A,k4_yellow_4(A,B,C),D) = k4_yellow_4(A,B,k4_yellow_4(A,C,D)) ) ) ) ) )).

fof(t43_yellow_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => k3_yellow_4(A,B,k4_subset_1(u1_struct_0(A),C,D)) = k4_subset_1(u1_struct_0(A),k3_yellow_4(A,B,C),k3_yellow_4(A,B,D)) ) ) ) ) )).

fof(t44_yellow_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => r1_tarski(k4_subset_1(u1_struct_0(A),B,k4_yellow_4(A,C,D)),k4_yellow_4(A,k4_subset_1(u1_struct_0(A),B,C),k4_subset_1(u1_struct_0(A),B,D))) ) ) ) ) )).

fof(t45_yellow_4,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v12_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => r1_tarski(k4_yellow_4(A,k4_subset_1(u1_struct_0(A),B,C),k4_subset_1(u1_struct_0(A),B,D)),k4_subset_1(u1_struct_0(A),B,k4_yellow_4(A,C,D))) ) ) ) ) )).

fof(t46_yellow_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k3_yellow_4(A,k1_struct_0(A,B),k1_struct_0(A,C)) = k1_struct_0(A,k11_lattice3(A,B,C)) ) ) ) )).

fof(t47_yellow_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k3_yellow_4(A,k1_struct_0(A,B),k2_struct_0(A,C,D)) = k2_struct_0(A,k11_lattice3(A,B,C),k11_lattice3(A,B,D)) ) ) ) ) )).

fof(t48_yellow_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r1_tarski(B,D)
                          & r1_tarski(C,E) )
                       => r1_tarski(k3_yellow_4(A,B,C),k3_yellow_4(A,D,E)) ) ) ) ) ) ) )).

fof(t49_yellow_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => r1_tarski(k5_subset_1(u1_struct_0(A),B,C),k4_yellow_4(A,B,C)) ) ) ) )).

fof(t50_yellow_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v12_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( v12_waybel_0(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => k4_yellow_4(A,B,C) = k5_subset_1(u1_struct_0(A),B,C) ) ) ) )).

fof(t51_yellow_4,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_lattice3(A,B,C)
               => k4_yellow_4(A,k1_struct_0(A,C),B) = B ) ) ) ) )).

fof(t52_yellow_4,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r2_lattice3(A,k4_yellow_4(A,k1_struct_0(A,C),B),C) ) ) ) )).

fof(t53_yellow_4,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,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( r1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,C),B))
                  & r1_yellow_0(A,B) )
               => r3_orders_2(A,k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,C),B)),k12_lattice3(A,C,k1_yellow_0(A,B))) ) ) ) ) )).

fof(t54_yellow_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => r1_lattice3(A,B,k2_yellow_0(A,k4_yellow_4(A,B,C))) ) ) ) )).

fof(t55_yellow_4,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r1_lattice3(A,D,B)
                          & r1_lattice3(A,E,C) )
                       => r1_lattice3(A,k4_yellow_4(A,D,E),k12_lattice3(A,B,C)) ) ) ) ) ) ) )).

fof(t56_yellow_4,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r2_lattice3(A,D,B)
                          & r2_lattice3(A,E,C) )
                       => r2_lattice3(A,k4_yellow_4(A,D,E),k12_lattice3(A,B,C)) ) ) ) ) ) ) )).

fof(t57_yellow_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => k2_yellow_0(A,k4_yellow_4(A,B,C)) = k12_lattice3(A,k2_yellow_0(A,B),k2_yellow_0(A,C)) ) ) ) )).

fof(t58_yellow_4,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))))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( B = D
                          & C = E )
                       => k12_lattice3(k2_yellow_1(k8_waybel_0(A)),B,C) = k4_yellow_4(A,D,E) ) ) ) ) ) ) )).

fof(t59_yellow_4,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => r1_tarski(B,k5_waybel_0(A,k4_yellow_4(A,B,C))) ) ) ) )).

fof(t61_yellow_4,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => r1_tarski(k4_waybel_0(A,k4_yellow_4(A,k4_waybel_0(A,B),k4_waybel_0(A,C))),k4_waybel_0(A,k4_yellow_4(A,B,C))) ) ) ) )).

fof(t62_yellow_4,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,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k4_waybel_0(A,k4_yellow_4(A,k4_waybel_0(A,B),k4_waybel_0(A,C))) = k4_waybel_0(A,k4_yellow_4(A,B,C)) ) ) ) )).

fof(t63_yellow_4,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => r1_tarski(k5_waybel_0(A,k4_yellow_4(A,k5_waybel_0(A,B),k5_waybel_0(A,C))),k5_waybel_0(A,k4_yellow_4(A,B,C))) ) ) ) )).

fof(t64_yellow_4,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,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k5_waybel_0(A,k4_yellow_4(A,k5_waybel_0(A,B),k5_waybel_0(A,C))) = k5_waybel_0(A,k4_yellow_4(A,B,C)) ) ) ) )).

fof(reflexivity_r3_yellow_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => r3_yellow_4(A,B,B) ) )).

fof(redefinition_r3_yellow_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( r3_yellow_4(A,B,C)
      <=> r1_yellow_4(A,B,C) ) ) )).

fof(reflexivity_r4_yellow_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => r4_yellow_4(A,C,C) ) )).

fof(redefinition_r4_yellow_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( r4_yellow_4(A,B,C)
      <=> r2_yellow_4(A,B,C) ) ) )).

fof(dt_k1_yellow_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k1_yellow_4(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k2_yellow_4,axiom,(
    ! [A,B,C] :
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k2_yellow_4(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(commutativity_k2_yellow_4,axiom,(
    ! [A,B,C] :
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => k2_yellow_4(A,B,C) = k2_yellow_4(A,C,B) ) )).

fof(redefinition_k2_yellow_4,axiom,(
    ! [A,B,C] :
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => k2_yellow_4(A,B,C) = k1_yellow_4(A,B,C) ) )).

fof(dt_k3_yellow_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k3_yellow_4(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k4_yellow_4,axiom,(
    ! [A,B,C] :
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k4_yellow_4(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(commutativity_k4_yellow_4,axiom,(
    ! [A,B,C] :
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => k4_yellow_4(A,B,C) = k4_yellow_4(A,C,B) ) )).

fof(redefinition_k4_yellow_4,axiom,(
    ! [A,B,C] :
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => k4_yellow_4(A,B,C) = k3_yellow_4(A,B,C) ) )).

fof(d3_yellow_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k1_yellow_4(A,B,C) = a_3_0_yellow_4(A,B,C) ) ) ) )).

fof(t15_yellow_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_yellow_4(A,k1_struct_0(A,C),B) = a_3_1_yellow_4(A,B,C) ) ) ) )).

fof(t31_yellow_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A))))
         => k3_tarski(a_2_0_yellow_4(A,B)) = k1_yellow_4(A,k4_yellow_3(A,A,B),k5_yellow_3(A,A,B)) ) ) )).

fof(d4_yellow_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k3_yellow_4(A,B,C) = a_3_2_yellow_4(A,B,C) ) ) ) )).

fof(t42_yellow_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k3_yellow_4(A,k1_struct_0(A,C),B) = a_3_3_yellow_4(A,B,C) ) ) ) )).

fof(t60_yellow_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A))))
         => k3_tarski(a_2_1_yellow_4(A,B)) = k3_yellow_4(A,k4_yellow_3(A,A,B),k5_yellow_3(A,A,B)) ) ) )).

fof(fraenkel_a_3_0_yellow_4,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & l1_orders_2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_3_0_yellow_4(B,C,D))
      <=> ? [E,F] :
            ( m1_subset_1(E,u1_struct_0(B))
            & m1_subset_1(F,u1_struct_0(B))
            & A = k10_lattice3(B,E,F)
            & r2_hidden(E,C)
            & r2_hidden(F,D) ) ) ) )).

fof(fraenkel_a_3_1_yellow_4,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & l1_orders_2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_1_yellow_4(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = k10_lattice3(B,D,E)
            & r2_hidden(E,C) ) ) ) )).

fof(fraenkel_a_2_0_yellow_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & l1_orders_2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) )
     => ( r2_hidden(A,a_2_0_yellow_4(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = D
            & ? [E] :
                ( m1_subset_1(E,u1_struct_0(B))
                & D = k1_yellow_4(B,k1_struct_0(B,E),k5_yellow_3(B,B,C))
                & r2_hidden(E,k4_yellow_3(B,B,C)) ) ) ) ) )).

fof(fraenkel_a_3_2_yellow_4,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & l1_orders_2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_3_2_yellow_4(B,C,D))
      <=> ? [E,F] :
            ( m1_subset_1(E,u1_struct_0(B))
            & m1_subset_1(F,u1_struct_0(B))
            & A = k11_lattice3(B,E,F)
            & r2_hidden(E,C)
            & r2_hidden(F,D) ) ) ) )).

fof(fraenkel_a_3_3_yellow_4,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & l1_orders_2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_3_yellow_4(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = k11_lattice3(B,D,E)
            & r2_hidden(E,C) ) ) ) )).

fof(fraenkel_a_2_1_yellow_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & l1_orders_2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) )
     => ( r2_hidden(A,a_2_1_yellow_4(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = D
            & ? [E] :
                ( m1_subset_1(E,u1_struct_0(B))
                & D = k3_yellow_4(B,k1_struct_0(B,E),k5_yellow_3(B,B,C))
                & r2_hidden(E,k4_yellow_3(B,B,C)) ) ) ) ) )).
%------------------------------------------------------------------------------