SET007 Axioms: SET007+486.ax


%------------------------------------------------------------------------------
% File     : SET007+486 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Cartesian Products of Relations and Relational Structures
% 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_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  110 (   4 unit)
%            Number of atoms       :  867 (  43 equality)
%            Maximal formula depth :   19 (   9 average)
%            Number of connectives :  909 ( 152 ~  ;   2  |; 426  &)
%                                         (  26 <=>; 303 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   40 (   0 propositional; 1-4 arity)
%            Number of functors    :   53 (  19 constant; 0-6 arity)
%            Number of variables   :  372 (   0 singleton; 350 !;  22 ?)
%            Maximal term depth    :    4 (   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_3,axiom,(
    ! [A] :
      ( v1_xboole_0(A)
     => v1_xboole_0(k1_funct_5(A)) ) )).

fof(fc2_yellow_3,axiom,(
    ! [A] :
      ( v1_xboole_0(A)
     => v1_xboole_0(k2_funct_5(A)) ) )).

fof(fc3_yellow_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) )
     => ~ v1_xboole_0(k1_funct_5(C)) ) )).

fof(fc4_yellow_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) )
     => ~ v1_xboole_0(k2_funct_5(C)) ) )).

fof(fc5_yellow_3,axiom,(
    ! [A,B] :
      ( ( l1_orders_2(A)
        & v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v1_xboole_0(k4_waybel_0(A,B)) ) )).

fof(fc6_yellow_3,axiom,(
    ! [A,B] :
      ( ( l1_orders_2(A)
        & v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v1_xboole_0(k5_waybel_0(A,B)) ) )).

fof(fc7_yellow_3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & l1_orders_2(B) )
     => ( ~ v3_struct_0(k3_yellow_3(A,B))
        & v1_orders_2(k3_yellow_3(A,B)) ) ) )).

fof(fc8_yellow_3,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & l1_orders_2(A)
        & v2_orders_2(B)
        & l1_orders_2(B) )
     => ( v1_orders_2(k3_yellow_3(A,B))
        & v2_orders_2(k3_yellow_3(A,B)) ) ) )).

fof(fc9_yellow_3,axiom,(
    ! [A,B] :
      ( ( v4_orders_2(A)
        & l1_orders_2(A)
        & v4_orders_2(B)
        & l1_orders_2(B) )
     => ( v1_orders_2(k3_yellow_3(A,B))
        & v4_orders_2(k3_yellow_3(A,B)) ) ) )).

fof(fc10_yellow_3,axiom,(
    ! [A,B] :
      ( ( v3_orders_2(A)
        & l1_orders_2(A)
        & v3_orders_2(B)
        & l1_orders_2(B) )
     => ( v1_orders_2(k3_yellow_3(A,B))
        & v3_orders_2(k3_yellow_3(A,B)) ) ) )).

fof(fc11_yellow_3,axiom,(
    ! [A,B] :
      ( ( v1_lattice3(A)
        & l1_orders_2(A)
        & v1_lattice3(B)
        & l1_orders_2(B) )
     => ( ~ v3_struct_0(k3_yellow_3(A,B))
        & v1_orders_2(k3_yellow_3(A,B))
        & v1_lattice3(k3_yellow_3(A,B)) ) ) )).

fof(fc12_yellow_3,axiom,(
    ! [A,B] :
      ( ( v2_lattice3(A)
        & l1_orders_2(A)
        & v2_lattice3(B)
        & l1_orders_2(B) )
     => ( ~ v3_struct_0(k3_yellow_3(A,B))
        & v1_orders_2(k3_yellow_3(A,B))
        & v2_lattice3(k3_yellow_3(A,B)) ) ) )).

fof(cc1_yellow_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v3_struct_0(A)
       => v1_yellow_3(A) ) ) )).

fof(rc1_yellow_3,axiom,(
    ? [A] :
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v1_orders_2(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & ~ v1_yellow_3(A) ) )).

fof(cc2_yellow_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ~ v1_yellow_3(A)
       => ~ v3_struct_0(A) ) ) )).

fof(cc3_yellow_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A) )
       => ( ~ v3_struct_0(A)
          & ~ v1_yellow_3(A) ) ) ) )).

fof(fc13_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v1_yellow_3(A)
        & l1_orders_2(A) )
     => ( ~ v1_xboole_0(u1_orders_2(A))
        & v1_relat_1(u1_orders_2(A)) ) ) )).

fof(fc14_yellow_3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v4_orders_2(B)
        & v3_lattice3(B)
        & l1_orders_2(B) )
     => ( ~ v3_struct_0(k3_yellow_3(A,B))
        & v1_orders_2(k3_yellow_3(A,B))
        & v4_orders_2(k3_yellow_3(A,B))
        & v1_lattice3(k3_yellow_3(A,B))
        & v2_lattice3(k3_yellow_3(A,B))
        & v3_lattice3(k3_yellow_3(A,B))
        & v1_yellow_0(k3_yellow_3(A,B))
        & v2_yellow_0(k3_yellow_3(A,B))
        & v3_yellow_0(k3_yellow_3(A,B)) ) ) )).

fof(t1_yellow_3,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => r1_tarski(C,k2_zfmisc_1(k1_funct_5(C),k2_funct_5(C))) ) )).

fof(t2_yellow_3,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,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r1_orders_2(A,B,D)
                          & r1_orders_2(A,C,E) )
                       => r1_orders_2(A,k12_lattice3(A,B,C),k12_lattice3(A,D,E)) ) ) ) ) ) ) )).

fof(t3_yellow_3,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,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r1_orders_2(A,B,D)
                          & r1_orders_2(A,C,E) )
                       => r1_orders_2(A,k13_lattice3(A,B,C),k13_lattice3(A,D,E)) ) ) ) ) ) ) )).

fof(t4_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_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] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,B)
               => k12_lattice3(A,k1_yellow_0(A,B),C) = C ) ) ) ) )).

fof(t5_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_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] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,B)
               => k13_lattice3(A,k2_yellow_0(A,B),C) = C ) ) ) ) )).

fof(t6_yellow_3,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_tarski(B,C)
               => r1_tarski(k4_waybel_0(A,B),k4_waybel_0(A,C)) ) ) ) ) )).

fof(t7_yellow_3,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_tarski(B,C)
               => r1_tarski(k5_waybel_0(A,B),k5_waybel_0(A,C)) ) ) ) ) )).

fof(t8_yellow_3,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v2_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)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r3_waybel_0(A,B,C,k2_struct_0(A,D,E))
                      <=> k1_waybel_0(A,B,C,k12_lattice3(A,D,E)) = k12_lattice3(B,k1_waybel_0(A,B,C,D),k1_waybel_0(A,B,C,E)) ) ) ) ) ) ) )).

fof(t9_yellow_3,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_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)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r4_waybel_0(A,B,C,k2_struct_0(A,D,E))
                      <=> k1_waybel_0(A,B,C,k13_lattice3(A,D,E)) = k13_lattice3(B,k1_waybel_0(A,B,C,D),k1_waybel_0(A,B,C,E)) ) ) ) ) ) ) )).

fof(d1_yellow_3,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ! [C] :
              ( v1_relat_1(C)
             => ( C = k1_yellow_3(A,B)
              <=> ! [D,E] :
                    ( r2_hidden(k4_tarski(D,E),C)
                  <=> ? [F,G,H,I] :
                        ( D = k4_tarski(F,G)
                        & E = k4_tarski(H,I)
                        & r2_hidden(k4_tarski(F,H),A)
                        & r2_hidden(k4_tarski(G,I),B) ) ) ) ) ) ) )).

fof(t10_yellow_3,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ! [C] :
              ( r2_hidden(C,k1_yellow_3(A,B))
            <=> ( r2_hidden(k4_tarski(k1_mcart_1(k1_mcart_1(C)),k1_mcart_1(k2_mcart_1(C))),A)
                & r2_hidden(k4_tarski(k2_mcart_1(k1_mcart_1(C)),k2_mcart_1(k2_mcart_1(C))),B)
                & ? [D,E] : C = k4_tarski(D,E)
                & ? [D,E] : k1_mcart_1(C) = k4_tarski(D,E)
                & ? [D,E] : k2_mcart_1(C) = k4_tarski(D,E) ) ) ) ) )).

fof(d2_yellow_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ! [C] :
              ( ( v1_orders_2(C)
                & l1_orders_2(C) )
             => ( C = k3_yellow_3(A,B)
              <=> ( u1_struct_0(C) = k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))
                  & u1_orders_2(C) = k2_yellow_3(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_orders_2(A),u1_orders_2(B)) ) ) ) ) ) )).

fof(t11_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( r1_orders_2(A,C,D)
                              & r1_orders_2(B,E,F) )
                          <=> r1_orders_2(k3_yellow_3(A,B),k7_yellow_3(A,B,C,E),k7_yellow_3(A,B,D,F)) ) ) ) ) ) ) ) )).

fof(t12_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k3_yellow_3(A,B)))
                 => ( r1_orders_2(k3_yellow_3(A,B),C,D)
                  <=> ( r1_orders_2(A,k8_yellow_3(A,B,C),k8_yellow_3(A,B,D))
                      & r1_orders_2(B,k9_yellow_3(A,B,C),k9_yellow_3(A,B,D)) ) ) ) ) ) ) )).

fof(t13_yellow_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [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(k3_yellow_3(A,B)),u1_struct_0(C))
                    & m2_relset_1(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C)) )
                     => ( ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(B))
                               => k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)) ) )
                       => D = E ) ) ) ) ) ) )).

fof(t14_yellow_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ( ~ v3_struct_0(k3_yellow_3(A,B))
           => ( ~ v3_struct_0(A)
              & ~ v3_struct_0(B) ) ) ) ) )).

fof(t15_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ( v2_orders_2(k3_yellow_3(A,B))
           => ( v2_orders_2(A)
              & v2_orders_2(B) ) ) ) ) )).

fof(t16_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & l1_orders_2(B) )
         => ( v4_orders_2(k3_yellow_3(A,B))
           => ( v4_orders_2(A)
              & v4_orders_2(B) ) ) ) ) )).

fof(t17_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & l1_orders_2(B) )
         => ( v3_orders_2(k3_yellow_3(A,B))
           => ( v3_orders_2(A)
              & v3_orders_2(B) ) ) ) ) )).

fof(t18_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & l1_orders_2(B) )
         => ( v1_lattice3(k3_yellow_3(A,B))
           => ( v1_lattice3(A)
              & v1_lattice3(B) ) ) ) ) )).

fof(t19_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & l1_orders_2(B) )
         => ( v2_lattice3(k3_yellow_3(A,B))
           => ( v2_lattice3(A)
              & v2_lattice3(B) ) ) ) ) )).

fof(t20_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
                 => ( v1_waybel_0(k6_yellow_3(A,B,C,D),k3_yellow_3(A,B))
                   => ( v1_waybel_0(C,A)
                      & v1_waybel_0(D,B) ) ) ) ) ) ) )).

fof(t21_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
             => ( ~ v1_xboole_0(k4_yellow_3(A,B,C))
                & ~ v1_xboole_0(k5_yellow_3(A,B,C)) ) ) ) ) )).

fof(t22_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_waybel_0(C,k3_yellow_3(A,B))
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
             => ( v1_waybel_0(k4_yellow_3(A,B,C),A)
                & v1_waybel_0(k5_yellow_3(A,B,C),B) ) ) ) ) )).

fof(t23_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
                 => ( v2_waybel_0(k6_yellow_3(A,B,C,D),k3_yellow_3(A,B))
                   => ( v2_waybel_0(C,A)
                      & v2_waybel_0(D,B) ) ) ) ) ) ) )).

fof(t24_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v2_waybel_0(C,k3_yellow_3(A,B))
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
             => ( v2_waybel_0(k4_yellow_3(A,B,C),A)
                & v2_waybel_0(k5_yellow_3(A,B,C),B) ) ) ) ) )).

fof(t25_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
                 => ( v13_waybel_0(k6_yellow_3(A,B,C,D),k3_yellow_3(A,B))
                   => ( v13_waybel_0(C,A)
                      & v13_waybel_0(D,B) ) ) ) ) ) ) )).

fof(t26_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v13_waybel_0(C,k3_yellow_3(A,B))
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
             => ( v13_waybel_0(k4_yellow_3(A,B,C),A)
                & v13_waybel_0(k5_yellow_3(A,B,C),B) ) ) ) ) )).

fof(t27_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
                 => ( v12_waybel_0(k6_yellow_3(A,B,C,D),k3_yellow_3(A,B))
                   => ( v12_waybel_0(C,A)
                      & v12_waybel_0(D,B) ) ) ) ) ) ) )).

fof(t28_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v12_waybel_0(C,k3_yellow_3(A,B))
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
             => ( v12_waybel_0(k4_yellow_3(A,B,C),A)
                & v12_waybel_0(k5_yellow_3(A,B,C),B) ) ) ) ) )).

fof(d3_yellow_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v1_yellow_3(A)
      <=> v1_xboole_0(u1_orders_2(A)) ) ) )).

fof(t29_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( r2_lattice3(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D),k7_yellow_3(A,B,E,F))
                           => ( r2_lattice3(A,C,E)
                              & r2_lattice3(B,D,F) ) ) ) ) ) ) ) ) )).

fof(t30_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( r2_lattice3(A,C,E)
                              & r2_lattice3(B,D,F) )
                           => r2_lattice3(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D),k7_yellow_3(A,B,E,F)) ) ) ) ) ) ) ) )).

fof(t31_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ( r2_lattice3(k3_yellow_3(A,B),C,k7_yellow_3(A,B,D,E))
                      <=> ( r2_lattice3(A,k4_yellow_3(A,B,C),D)
                          & r2_lattice3(B,k5_yellow_3(A,B,C),E) ) ) ) ) ) ) ) )).

fof(t32_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( r1_lattice3(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D),k7_yellow_3(A,B,E,F))
                           => ( r1_lattice3(A,C,E)
                              & r1_lattice3(B,D,F) ) ) ) ) ) ) ) ) )).

fof(t33_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( r1_lattice3(A,C,E)
                              & r1_lattice3(B,D,F) )
                           => r1_lattice3(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D),k7_yellow_3(A,B,E,F)) ) ) ) ) ) ) ) )).

fof(t34_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ( r1_lattice3(k3_yellow_3(A,B),C,k7_yellow_3(A,B,D,E))
                      <=> ( r1_lattice3(A,k4_yellow_3(A,B,C),D)
                          & r1_lattice3(B,k5_yellow_3(A,B,C),E) ) ) ) ) ) ) ) )).

fof(t35_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( r1_yellow_0(A,C)
                              & r1_yellow_0(B,D)
                              & ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(k3_yellow_3(A,B)))
                                 => ( r2_lattice3(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D),G)
                                   => r1_orders_2(k3_yellow_3(A,B),k7_yellow_3(A,B,E,F),G) ) ) )
                           => ( ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( r2_lattice3(A,C,G)
                                   => r1_orders_2(A,E,G) ) )
                              & ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(B))
                                 => ( r2_lattice3(B,D,G)
                                   => r1_orders_2(B,F,G) ) ) ) ) ) ) ) ) ) ) )).

fof(t36_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( r2_yellow_0(A,C)
                              & r2_yellow_0(B,D)
                              & ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(k3_yellow_3(A,B)))
                                 => ( r1_lattice3(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D),G)
                                   => r1_orders_2(k3_yellow_3(A,B),G,k7_yellow_3(A,B,E,F)) ) ) )
                           => ( ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( r1_lattice3(A,C,G)
                                   => r1_orders_2(A,G,E) ) )
                              & ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(B))
                                 => ( r1_lattice3(B,D,G)
                                   => r1_orders_2(B,G,F) ) ) ) ) ) ) ) ) ) ) )).

fof(t37_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( r2_lattice3(A,C,G)
                                   => r1_orders_2(A,E,G) ) )
                              & ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(B))
                                 => ( r2_lattice3(B,D,G)
                                   => r1_orders_2(B,F,G) ) ) )
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(k3_yellow_3(A,B)))
                               => ( r2_lattice3(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D),G)
                                 => r1_orders_2(k3_yellow_3(A,B),k7_yellow_3(A,B,E,F),G) ) ) ) ) ) ) ) ) ) )).

fof(t38_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( r2_lattice3(A,C,G)
                                   => r1_orders_2(A,G,E) ) )
                              & ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(B))
                                 => ( r2_lattice3(B,D,G)
                                   => r1_orders_2(B,G,F) ) ) )
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(k3_yellow_3(A,B)))
                               => ( r2_lattice3(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D),G)
                                 => r1_orders_2(k3_yellow_3(A,B),G,k7_yellow_3(A,B,E,F)) ) ) ) ) ) ) ) ) ) )).

fof(t39_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
                 => ( ( r1_yellow_0(A,C)
                      & r1_yellow_0(B,D) )
                  <=> r1_yellow_0(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D)) ) ) ) ) ) )).

fof(t40_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
                 => ( ( r2_yellow_0(A,C)
                      & r2_yellow_0(B,D) )
                  <=> r2_yellow_0(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D)) ) ) ) ) ) )).

fof(t41_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
             => ( ( r1_yellow_0(A,k4_yellow_3(A,B,C))
                  & r1_yellow_0(B,k5_yellow_3(A,B,C)) )
              <=> r1_yellow_0(k3_yellow_3(A,B),C) ) ) ) ) )).

fof(t42_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
             => ( ( r2_yellow_0(A,k4_yellow_3(A,B,C))
                  & r2_yellow_0(B,k5_yellow_3(A,B,C)) )
              <=> r2_yellow_0(k3_yellow_3(A,B),C) ) ) ) ) )).

fof(t43_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
                 => ( ( r1_yellow_0(A,C)
                      & r1_yellow_0(B,D) )
                   => k1_yellow_0(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D)) = k7_yellow_3(A,B,k1_yellow_0(A,C),k1_yellow_0(B,D)) ) ) ) ) ) )).

fof(t44_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
                 => ( ( r2_yellow_0(A,C)
                      & r2_yellow_0(B,D) )
                   => k2_yellow_0(k3_yellow_3(A,B),k6_yellow_3(A,B,C,D)) = k7_yellow_3(A,B,k2_yellow_0(A,C),k2_yellow_0(B,D)) ) ) ) ) ) )).

fof(t45_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & l1_orders_2(B) )
         => ( v3_lattice3(k3_yellow_3(A,B))
           => ( v3_lattice3(A)
              & v3_lattice3(B) ) ) ) ) )).

fof(t46_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
             => ( ( v3_lattice3(k3_yellow_3(A,B))
                  | r1_yellow_0(k3_yellow_3(A,B),C) )
               => k1_yellow_0(k3_yellow_3(A,B),C) = k7_yellow_3(A,B,k1_yellow_0(A,k4_yellow_3(A,B,C)),k1_yellow_0(B,k5_yellow_3(A,B,C))) ) ) ) ) )).

fof(t47_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
             => ( ( v3_lattice3(k3_yellow_3(A,B))
                  | r2_yellow_0(k3_yellow_3(A,B),C) )
               => k2_yellow_0(k3_yellow_3(A,B),C) = k7_yellow_3(A,B,k2_yellow_0(A,k4_yellow_3(A,B,C)),k2_yellow_0(B,k5_yellow_3(A,B,C))) ) ) ) ) )).

fof(t48_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_waybel_0(C,k3_yellow_3(A,B))
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
             => r1_tarski(k6_yellow_3(A,B,k4_yellow_3(A,B,C),k5_yellow_3(A,B,C)),k4_waybel_0(k3_yellow_3(A,B),C)) ) ) ) )).

fof(t49_yellow_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v2_waybel_0(C,k3_yellow_3(A,B))
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
             => r1_tarski(k6_yellow_3(A,B,k4_yellow_3(A,B,C),k5_yellow_3(A,B,C)),k5_waybel_0(k3_yellow_3(A,B),C)) ) ) ) )).

fof(s2_yellow_3,axiom,
    ( ( ! [A,B] :
          ( r2_hidden(k4_tarski(A,B),f1_s2_yellow_3)
        <=> p1_s2_yellow_3(A,B) )
      & ! [A,B] :
          ( r2_hidden(k4_tarski(A,B),f2_s2_yellow_3)
        <=> p1_s2_yellow_3(A,B) ) )
   => f1_s2_yellow_3 = f2_s2_yellow_3 )).

fof(s7_yellow_3,axiom,
    ( ! [A] :
        ( m1_subset_1(A,u1_struct_0(f1_s7_yellow_3))
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(f2_s7_yellow_3))
           => m1_subset_1(f4_s7_yellow_3(A,B),u1_struct_0(f3_s7_yellow_3)) ) )
   => ? [A] :
        ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k3_yellow_3(f1_s7_yellow_3,f2_s7_yellow_3)),u1_struct_0(f3_s7_yellow_3))
        & m2_relset_1(A,u1_struct_0(k3_yellow_3(f1_s7_yellow_3,f2_s7_yellow_3)),u1_struct_0(f3_s7_yellow_3))
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(f1_s7_yellow_3))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(f2_s7_yellow_3))
               => k1_waybel_0(k3_yellow_3(f1_s7_yellow_3,f2_s7_yellow_3),f3_s7_yellow_3,A,k7_yellow_3(f1_s7_yellow_3,f2_s7_yellow_3,B,C)) = f4_s7_yellow_3(B,C) ) ) ) )).

fof(dt_k1_yellow_3,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k1_yellow_3(A,B)) ) )).

fof(dt_k2_yellow_3,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( m1_relset_1(E,A,B)
        & m1_relset_1(F,C,D) )
     => m2_relset_1(k2_yellow_3(A,B,C,D,E,F),k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ) )).

fof(redefinition_k2_yellow_3,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( m1_relset_1(E,A,B)
        & m1_relset_1(F,C,D) )
     => k2_yellow_3(A,B,C,D,E,F) = k1_yellow_3(E,F) ) )).

fof(dt_k3_yellow_3,axiom,(
    ! [A,B] :
      ( ( l1_orders_2(A)
        & l1_orders_2(B) )
     => ( v1_orders_2(k3_yellow_3(A,B))
        & l1_orders_2(k3_yellow_3(A,B)) ) ) )).

fof(dt_k4_yellow_3,axiom,(
    ! [A,B,C] :
      ( ( l1_orders_2(A)
        & l1_orders_2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
     => m1_subset_1(k4_yellow_3(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(redefinition_k4_yellow_3,axiom,(
    ! [A,B,C] :
      ( ( l1_orders_2(A)
        & l1_orders_2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
     => k4_yellow_3(A,B,C) = k1_funct_5(C) ) )).

fof(dt_k5_yellow_3,axiom,(
    ! [A,B,C] :
      ( ( l1_orders_2(A)
        & l1_orders_2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
     => m1_subset_1(k5_yellow_3(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) )).

fof(redefinition_k5_yellow_3,axiom,(
    ! [A,B,C] :
      ( ( l1_orders_2(A)
        & l1_orders_2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
     => k5_yellow_3(A,B,C) = k2_funct_5(C) ) )).

fof(dt_k6_yellow_3,axiom,(
    ! [A,B,C,D] :
      ( ( l1_orders_2(A)
        & l1_orders_2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
     => m1_subset_1(k6_yellow_3(A,B,C,D),k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) ) )).

fof(redefinition_k6_yellow_3,axiom,(
    ! [A,B,C,D] :
      ( ( l1_orders_2(A)
        & l1_orders_2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
     => k6_yellow_3(A,B,C,D) = k2_zfmisc_1(C,D) ) )).

fof(dt_k7_yellow_3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & l1_orders_2(B)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B)) )
     => m1_subset_1(k7_yellow_3(A,B,C,D),u1_struct_0(k3_yellow_3(A,B))) ) )).

fof(redefinition_k7_yellow_3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & l1_orders_2(B)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B)) )
     => k7_yellow_3(A,B,C,D) = k4_tarski(C,D) ) )).

fof(dt_k8_yellow_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & l1_orders_2(B)
        & m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B))) )
     => m1_subset_1(k8_yellow_3(A,B,C),u1_struct_0(A)) ) )).

fof(redefinition_k8_yellow_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & l1_orders_2(B)
        & m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B))) )
     => k8_yellow_3(A,B,C) = k1_mcart_1(C) ) )).

fof(dt_k9_yellow_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & l1_orders_2(B)
        & m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B))) )
     => m1_subset_1(k9_yellow_3(A,B,C),u1_struct_0(B)) ) )).

fof(redefinition_k9_yellow_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & l1_orders_2(B)
        & m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B))) )
     => k9_yellow_3(A,B,C) = k2_mcart_1(C) ) )).

fof(dt_k10_yellow_3,axiom,(
    ! [A,B,C,D] :
      ( ( l1_orders_2(A)
        & l1_orders_2(B)
        & v1_waybel_0(C,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
        & v1_waybel_0(D,B)
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
     => ( v1_waybel_0(k10_yellow_3(A,B,C,D),k3_yellow_3(A,B))
        & m1_subset_1(k10_yellow_3(A,B,C,D),k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) ) ) )).

fof(redefinition_k10_yellow_3,axiom,(
    ! [A,B,C,D] :
      ( ( l1_orders_2(A)
        & l1_orders_2(B)
        & v1_waybel_0(C,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
        & v1_waybel_0(D,B)
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
     => k10_yellow_3(A,B,C,D) = k2_zfmisc_1(C,D) ) )).

fof(dt_k11_yellow_3,axiom,(
    ! [A,B,C,D] :
      ( ( l1_orders_2(A)
        & l1_orders_2(B)
        & v2_waybel_0(C,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
        & v2_waybel_0(D,B)
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
     => ( v2_waybel_0(k11_yellow_3(A,B,C,D),k3_yellow_3(A,B))
        & m1_subset_1(k11_yellow_3(A,B,C,D),k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) ) ) )).

fof(redefinition_k11_yellow_3,axiom,(
    ! [A,B,C,D] :
      ( ( l1_orders_2(A)
        & l1_orders_2(B)
        & v2_waybel_0(C,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
        & v2_waybel_0(D,B)
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
     => k11_yellow_3(A,B,C,D) = k2_zfmisc_1(C,D) ) )).

fof(dt_k12_yellow_3,axiom,(
    ! [A,B,C,D] :
      ( ( l1_orders_2(A)
        & l1_orders_2(B)
        & v13_waybel_0(C,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
        & v13_waybel_0(D,B)
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
     => ( v13_waybel_0(k12_yellow_3(A,B,C,D),k3_yellow_3(A,B))
        & m1_subset_1(k12_yellow_3(A,B,C,D),k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) ) ) )).

fof(redefinition_k12_yellow_3,axiom,(
    ! [A,B,C,D] :
      ( ( l1_orders_2(A)
        & l1_orders_2(B)
        & v13_waybel_0(C,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
        & v13_waybel_0(D,B)
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
     => k12_yellow_3(A,B,C,D) = k2_zfmisc_1(C,D) ) )).

fof(dt_k13_yellow_3,axiom,(
    ! [A,B,C,D] :
      ( ( l1_orders_2(A)
        & l1_orders_2(B)
        & v12_waybel_0(C,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
        & v12_waybel_0(D,B)
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
     => ( v12_waybel_0(k13_yellow_3(A,B,C,D),k3_yellow_3(A,B))
        & m1_subset_1(k13_yellow_3(A,B,C,D),k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) ) ) )).

fof(redefinition_k13_yellow_3,axiom,(
    ! [A,B,C,D] :
      ( ( l1_orders_2(A)
        & l1_orders_2(B)
        & v12_waybel_0(C,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
        & v12_waybel_0(D,B)
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
     => k13_yellow_3(A,B,C,D) = k2_zfmisc_1(C,D) ) )).

fof(s1_yellow_3,axiom,
    ( ! [A] :
        ( m1_subset_1(A,f1_s1_yellow_3)
       => ! [B] :
            ( m1_subset_1(B,f1_s1_yellow_3)
           => r2_hidden(f2_s1_yellow_3(A,B),f1_s1_yellow_3) ) )
   => m1_subset_1(a_0_0_yellow_3,k1_zfmisc_1(f1_s1_yellow_3)) )).

fof(s3_yellow_3,axiom,(
    r1_orders_2(f1_s3_yellow_3,k2_yellow_0(f1_s3_yellow_3,k3_tarski(a_0_1_yellow_3)),k2_yellow_0(f1_s3_yellow_3,a_0_2_yellow_3)) )).

fof(s4_yellow_3,axiom,(
    k2_yellow_0(f1_s4_yellow_3,a_0_3_yellow_3) = k2_yellow_0(f1_s4_yellow_3,k3_tarski(a_0_4_yellow_3)) )).

fof(s5_yellow_3,axiom,(
    r1_orders_2(f1_s5_yellow_3,k1_yellow_0(f1_s5_yellow_3,a_0_5_yellow_3),k1_yellow_0(f1_s5_yellow_3,k3_tarski(a_0_6_yellow_3))) )).

fof(s6_yellow_3,axiom,(
    k1_yellow_0(f1_s6_yellow_3,a_0_7_yellow_3) = k1_yellow_0(f1_s6_yellow_3,k3_tarski(a_0_8_yellow_3)) )).

fof(fraenkel_a_0_0_yellow_3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_yellow_3)
    <=> ? [B,C] :
          ( m1_subset_1(B,f1_s1_yellow_3)
          & m1_subset_1(C,f1_s1_yellow_3)
          & A = f2_s1_yellow_3(B,C)
          & p1_s1_yellow_3(B,C) ) ) )).

fof(fraenkel_a_0_1_yellow_3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_1_yellow_3)
    <=> ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s3_yellow_3)))
          & A = B
          & p1_s3_yellow_3(B) ) ) )).

fof(fraenkel_a_0_2_yellow_3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_2_yellow_3)
    <=> ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s3_yellow_3)))
          & A = k2_yellow_0(f1_s3_yellow_3,B)
          & p1_s3_yellow_3(B) ) ) )).

fof(fraenkel_a_0_3_yellow_3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_3_yellow_3)
    <=> ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s4_yellow_3)))
          & A = k2_yellow_0(f1_s4_yellow_3,B)
          & p1_s4_yellow_3(B) ) ) )).

fof(fraenkel_a_0_4_yellow_3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_4_yellow_3)
    <=> ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s4_yellow_3)))
          & A = B
          & p1_s4_yellow_3(B) ) ) )).

fof(fraenkel_a_0_5_yellow_3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_5_yellow_3)
    <=> ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s5_yellow_3)))
          & A = k1_yellow_0(f1_s5_yellow_3,B)
          & p1_s5_yellow_3(B) ) ) )).

fof(fraenkel_a_0_6_yellow_3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_6_yellow_3)
    <=> ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s5_yellow_3)))
          & A = B
          & p1_s5_yellow_3(B) ) ) )).

fof(fraenkel_a_0_7_yellow_3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_7_yellow_3)
    <=> ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s6_yellow_3)))
          & A = k1_yellow_0(f1_s6_yellow_3,B)
          & p1_s6_yellow_3(B) ) ) )).

fof(fraenkel_a_0_8_yellow_3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_8_yellow_3)
    <=> ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s6_yellow_3)))
          & A = B
          & p1_s6_yellow_3(B) ) ) )).
%------------------------------------------------------------------------------