SET007 Axioms: SET007+620.ax


%------------------------------------------------------------------------------
% File     : SET007+620 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : A Characterization of Concept Lattices. Dual Concept Lattices
% 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    : conlat_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   50 (   0 unit)
%            Number of atoms       :  351 (  47 equality)
%            Maximal formula depth :   21 (   8 average)
%            Number of connectives :  382 (  81 ~  ;   0  |; 209  &)
%                                         (  14 <=>;  78 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   35 (   0 propositional; 1-3 arity)
%            Number of functors    :   46 (   0 constant; 1-4 arity)
%            Number of variables   :  115 (   0 singleton;  96 !;  19 ?)
%            Maximal term depth    :    5 (   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_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ( ~ v3_struct_0(k11_conlat_1(A))
        & v3_lattices(k11_conlat_1(A))
        & v4_lattices(k11_conlat_1(A))
        & v5_lattices(k11_conlat_1(A))
        & v6_lattices(k11_conlat_1(A))
        & v7_lattices(k11_conlat_1(A))
        & v8_lattices(k11_conlat_1(A))
        & v9_lattices(k11_conlat_1(A))
        & v10_lattices(k11_conlat_1(A))
        & v13_lattices(k11_conlat_1(A))
        & v14_lattices(k11_conlat_1(A))
        & v15_lattices(k11_conlat_1(A))
        & v4_lattice3(k11_conlat_1(A)) ) ) )).

fof(fc2_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ( ~ v3_struct_0(k1_lattice2(A))
        & v3_lattices(k1_lattice2(A))
        & v4_lattices(k1_lattice2(A))
        & v5_lattices(k1_lattice2(A))
        & v6_lattices(k1_lattice2(A))
        & v7_lattices(k1_lattice2(A))
        & v8_lattices(k1_lattice2(A))
        & v9_lattices(k1_lattice2(A))
        & v10_lattices(k1_lattice2(A))
        & v4_lattice3(k1_lattice2(A)) ) ) )).

fof(d1_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] :
          ( ( v6_conlat_1(B,A)
            & ~ v7_conlat_1(B,A)
            & v9_conlat_1(B,A)
            & l3_conlat_1(B,A) )
         => k1_conlat_2(A,B) = B ) ) )).

fof(t1_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ( k5_lattices(k11_conlat_1(A)) = k6_conlat_1(A)
        & k6_lattices(k11_conlat_1(A)) = k5_conlat_1(A) ) ) )).

fof(t4_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A))))
         => ( ~ v7_conlat_1(k16_lattice3(k11_conlat_1(A),B),A)
            & v9_conlat_1(k16_lattice3(k11_conlat_1(A),B),A)
            & l3_conlat_1(k16_lattice3(k11_conlat_1(A),B),A)
            & ~ v7_conlat_1(k15_lattice3(k11_conlat_1(A),B),A)
            & v9_conlat_1(k15_lattice3(k11_conlat_1(A),B),A)
            & l3_conlat_1(k15_lattice3(k11_conlat_1(A),B),A) ) ) ) )).

fof(d2_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A))))
         => k2_conlat_2(A,B) = k16_lattice3(k11_conlat_1(A),B) ) ) )).

fof(d3_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A))))
         => k3_conlat_2(A,B) = k15_lattice3(k11_conlat_1(A),B) ) ) )).

fof(t5_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ( k3_conlat_2(A,k1_pre_topc(k11_conlat_1(A))) = k6_conlat_1(A)
        & k2_conlat_2(A,k1_pre_topc(k11_conlat_1(A))) = k5_conlat_1(A) ) ) )).

fof(t6_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ( k3_conlat_2(A,k2_subset_1(u1_struct_0(k11_conlat_1(A)))) = k5_conlat_1(A)
        & k2_conlat_2(A,k2_subset_1(u1_struct_0(k11_conlat_1(A)))) = k6_conlat_1(A) ) ) )).

fof(d4_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_conlat_1(A),u1_struct_0(k11_conlat_1(A)))
            & m2_relset_1(B,u1_conlat_1(A),u1_struct_0(k11_conlat_1(A))) )
         => ( B = k4_conlat_2(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_conlat_1(A))
               => ? [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_conlat_1(A)))
                    & ? [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u2_conlat_1(A)))
                        & k8_funct_2(u1_conlat_1(A),u1_struct_0(k11_conlat_1(A)),B,C) = g3_conlat_1(A,D,E)
                        & D = k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k6_domain_1(u1_conlat_1(A),C)))
                        & E = k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k6_domain_1(u1_conlat_1(A),C)) ) ) ) ) ) ) )).

fof(d5_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u2_conlat_1(A),u1_struct_0(k11_conlat_1(A)))
            & m2_relset_1(B,u2_conlat_1(A),u1_struct_0(k11_conlat_1(A))) )
         => ( B = k5_conlat_2(A)
          <=> ! [C] :
                ( m1_subset_1(C,u2_conlat_1(A))
               => ? [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_conlat_1(A)))
                    & ? [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u2_conlat_1(A)))
                        & k8_funct_2(u2_conlat_1(A),u1_struct_0(k11_conlat_1(A)),B,C) = g3_conlat_1(A,D,E)
                        & D = k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k6_domain_1(u2_conlat_1(A),C))
                        & E = k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k6_domain_1(u2_conlat_1(A),C))) ) ) ) ) ) ) )).

fof(t11_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_conlat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u2_conlat_1(A))
             => ( ~ v7_conlat_1(k8_funct_2(u1_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k4_conlat_2(A),B),A)
                & v9_conlat_1(k8_funct_2(u1_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k4_conlat_2(A),B),A)
                & l3_conlat_1(k8_funct_2(u1_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k4_conlat_2(A),B),A)
                & ~ v7_conlat_1(k8_funct_2(u2_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k5_conlat_2(A),C),A)
                & v9_conlat_1(k8_funct_2(u2_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k5_conlat_2(A),C),A)
                & l3_conlat_1(k8_funct_2(u2_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k5_conlat_2(A),C),A) ) ) ) ) )).

fof(t12_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ( v8_lattice6(k5_relset_1(u1_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k4_conlat_2(A)),k11_conlat_1(A))
        & v9_lattice6(k5_relset_1(u2_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k5_conlat_2(A)),k11_conlat_1(A)) ) ) )).

fof(t13_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_conlat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u2_conlat_1(A))
             => ( r1_conlat_1(A,B,C)
              <=> r3_lattices(k11_conlat_1(A),k8_funct_2(u1_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k4_conlat_2(A),B),k8_funct_2(u2_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k5_conlat_2(A),C)) ) ) ) ) )).

fof(t14_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_conlat_1(B)
            & l2_conlat_1(B) )
         => ( r1_filter_1(k11_conlat_1(B),A)
          <=> ? [C] :
                ( v1_funct_1(C)
                & v1_funct_2(C,u1_conlat_1(B),u1_struct_0(A))
                & m2_relset_1(C,u1_conlat_1(B),u1_struct_0(A))
                & ? [D] :
                    ( v1_funct_1(D)
                    & v1_funct_2(D,u2_conlat_1(B),u1_struct_0(A))
                    & m2_relset_1(D,u2_conlat_1(B),u1_struct_0(A))
                    & v8_lattice6(k5_relset_1(u1_conlat_1(B),u1_struct_0(A),C),A)
                    & v9_lattice6(k5_relset_1(u2_conlat_1(B),u1_struct_0(A),D),A)
                    & ! [E] :
                        ( m1_subset_1(E,u1_conlat_1(B))
                       => ! [F] :
                            ( m1_subset_1(F,u2_conlat_1(B))
                           => ( r1_conlat_1(B,E,F)
                            <=> r3_lattices(A,k8_funct_2(u1_conlat_1(B),u1_struct_0(A),C,E),k8_funct_2(u2_conlat_1(B),u1_struct_0(A),D,F)) ) ) ) ) ) ) ) ) )).

fof(d6_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => k6_conlat_2(A) = g2_conlat_1(u1_struct_0(A),u1_struct_0(A),k2_lattice3(A)) ) )).

fof(t15_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => r1_filter_1(k11_conlat_1(k6_conlat_2(A)),A) ) )).

fof(t16_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( v4_lattice3(A)
      <=> ? [B] :
            ( ~ v3_conlat_1(B)
            & l2_conlat_1(B)
            & r1_filter_1(k11_conlat_1(B),A) ) ) ) )).

fof(d7_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => k7_conlat_2(A) = g2_conlat_1(u2_conlat_1(A),u1_conlat_1(A),k6_relset_1(u1_conlat_1(A),u2_conlat_1(A),u3_conlat_1(A))) ) )).

fof(t17_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & v4_conlat_1(A)
        & l2_conlat_1(A) )
     => k7_conlat_2(k7_conlat_2(A)) = A ) )).

fof(t18_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A)))
         => k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B) = k1_funct_1(k2_conlat_1(k7_conlat_2(A)),B) ) ) )).

fof(t19_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u2_conlat_1(A)))
         => k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B) = k1_funct_1(k1_conlat_1(k7_conlat_2(A)),B) ) ) )).

fof(d8_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] :
          ( l3_conlat_1(B,A)
         => ! [C] :
              ( ( v6_conlat_1(C,k7_conlat_2(A))
                & l3_conlat_1(C,k7_conlat_2(A)) )
             => ( C = k8_conlat_2(A,B)
              <=> ( u4_conlat_1(k7_conlat_2(A),C) = u5_conlat_1(A,B)
                  & u5_conlat_1(k7_conlat_2(A),C) = u4_conlat_1(A,B) ) ) ) ) ) )).

fof(t20_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & v4_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] :
          ( ( v6_conlat_1(B,A)
            & ~ v7_conlat_1(B,A)
            & v9_conlat_1(B,A)
            & l3_conlat_1(B,A) )
         => k9_conlat_2(k7_conlat_2(A),k9_conlat_2(A,B)) = B ) ) )).

fof(d9_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] :
          ( m1_lattice4(B,k1_lattice2(k11_conlat_1(A)),k11_conlat_1(k7_conlat_2(A)))
         => ( B = k10_conlat_2(A)
          <=> ! [C] :
                ( ( v6_conlat_1(C,A)
                  & ~ v7_conlat_1(C,A)
                  & v9_conlat_1(C,A)
                  & l3_conlat_1(C,A) )
               => k1_funct_1(B,C) = k9_conlat_2(A,C) ) ) ) ) )).

fof(t21_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => v3_lattice4(k10_conlat_2(A),k1_lattice2(k11_conlat_1(A)),k11_conlat_1(k7_conlat_2(A))) ) )).

fof(t22_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => r1_filter_1(k11_conlat_1(k7_conlat_2(A)),k1_lattice2(k11_conlat_1(A))) ) )).

fof(dt_k1_conlat_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A)
        & v6_conlat_1(B,A)
        & ~ v7_conlat_1(B,A)
        & v9_conlat_1(B,A)
        & l3_conlat_1(B,A) )
     => m1_subset_1(k1_conlat_2(A,B),u1_struct_0(k11_conlat_1(A))) ) )).

fof(dt_k2_conlat_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) )
     => ( ~ v7_conlat_1(k2_conlat_2(A,B),A)
        & v9_conlat_1(k2_conlat_2(A,B),A)
        & l3_conlat_1(k2_conlat_2(A,B),A) ) ) )).

fof(dt_k3_conlat_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) )
     => ( ~ v7_conlat_1(k3_conlat_2(A,B),A)
        & v9_conlat_1(k3_conlat_2(A,B),A)
        & l3_conlat_1(k3_conlat_2(A,B),A) ) ) )).

fof(dt_k4_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ( v1_funct_1(k4_conlat_2(A))
        & v1_funct_2(k4_conlat_2(A),u1_conlat_1(A),u1_struct_0(k11_conlat_1(A)))
        & m2_relset_1(k4_conlat_2(A),u1_conlat_1(A),u1_struct_0(k11_conlat_1(A))) ) ) )).

fof(dt_k5_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ( v1_funct_1(k5_conlat_2(A))
        & v1_funct_2(k5_conlat_2(A),u2_conlat_1(A),u1_struct_0(k11_conlat_1(A)))
        & m2_relset_1(k5_conlat_2(A),u2_conlat_1(A),u1_struct_0(k11_conlat_1(A))) ) ) )).

fof(dt_k6_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( ~ v3_conlat_1(k6_conlat_2(A))
        & v4_conlat_1(k6_conlat_2(A))
        & l2_conlat_1(k6_conlat_2(A)) ) ) )).

fof(dt_k7_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ( ~ v3_conlat_1(k7_conlat_2(A))
        & v4_conlat_1(k7_conlat_2(A))
        & l2_conlat_1(k7_conlat_2(A)) ) ) )).

fof(dt_k8_conlat_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A)
        & l3_conlat_1(B,A) )
     => ( v6_conlat_1(k8_conlat_2(A,B),k7_conlat_2(A))
        & l3_conlat_1(k8_conlat_2(A,B),k7_conlat_2(A)) ) ) )).

fof(dt_k9_conlat_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A)
        & ~ v7_conlat_1(B,A)
        & v9_conlat_1(B,A)
        & l3_conlat_1(B,A) )
     => ( v6_conlat_1(k9_conlat_2(A,B),k7_conlat_2(A))
        & ~ v7_conlat_1(k9_conlat_2(A,B),k7_conlat_2(A))
        & v9_conlat_1(k9_conlat_2(A,B),k7_conlat_2(A))
        & l3_conlat_1(k9_conlat_2(A,B),k7_conlat_2(A)) ) ) )).

fof(redefinition_k9_conlat_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A)
        & ~ v7_conlat_1(B,A)
        & v9_conlat_1(B,A)
        & l3_conlat_1(B,A) )
     => k9_conlat_2(A,B) = k8_conlat_2(A,B) ) )).

fof(dt_k10_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => m1_lattice4(k10_conlat_2(A),k1_lattice2(k11_conlat_1(A)),k11_conlat_1(k7_conlat_2(A))) ) )).

fof(t2_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_conlat_1(A)))) )
         => k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k5_setfam_1(u1_conlat_1(A),B)) = k1_setfam_1(a_2_0_conlat_2(A,B)) ) ) )).

fof(t3_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u2_conlat_1(A)))) )
         => k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k5_setfam_1(u2_conlat_1(A),B)) = k1_setfam_1(a_2_1_conlat_2(A,B)) ) ) )).

fof(t7_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) )
         => ( u4_conlat_1(A,k3_conlat_2(A,B)) = k1_funct_1(k2_conlat_1(A),k1_funct_1(k1_conlat_1(A),k3_tarski(a_2_2_conlat_2(A,B))))
            & u5_conlat_1(A,k3_conlat_2(A,B)) = k1_setfam_1(a_2_3_conlat_2(A,B)) ) ) ) )).

fof(t8_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) )
         => ( u4_conlat_1(A,k2_conlat_2(A,B)) = k1_setfam_1(a_2_2_conlat_2(A,B))
            & u5_conlat_1(A,k2_conlat_2(A,B)) = k1_funct_1(k1_conlat_1(A),k1_funct_1(k2_conlat_1(A),k3_tarski(a_2_3_conlat_2(A,B)))) ) ) ) )).

fof(t9_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] :
          ( ( v6_conlat_1(B,A)
            & ~ v7_conlat_1(B,A)
            & v9_conlat_1(B,A)
            & l3_conlat_1(B,A) )
         => k15_lattice3(k11_conlat_1(A),a_2_4_conlat_2(A,B)) = B ) ) )).

fof(t10_conlat_2,axiom,(
    ! [A] :
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] :
          ( ( v6_conlat_1(B,A)
            & ~ v7_conlat_1(B,A)
            & v9_conlat_1(B,A)
            & l3_conlat_1(B,A) )
         => k16_lattice3(k11_conlat_1(A),a_2_5_conlat_2(A,B)) = B ) ) )).

fof(fraenkel_a_2_0_conlat_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_conlat_1(B)
        & l2_conlat_1(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_conlat_1(B)))) )
     => ( r2_hidden(A,a_2_0_conlat_2(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_conlat_1(B)))
            & A = k8_funct_2(k1_zfmisc_1(u1_conlat_1(B)),k1_zfmisc_1(u2_conlat_1(B)),k1_conlat_1(B),D)
            & r2_hidden(D,C) ) ) ) )).

fof(fraenkel_a_2_1_conlat_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_conlat_1(B)
        & l2_conlat_1(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u2_conlat_1(B)))) )
     => ( r2_hidden(A,a_2_1_conlat_2(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(u2_conlat_1(B)))
            & A = k8_funct_2(k1_zfmisc_1(u2_conlat_1(B)),k1_zfmisc_1(u1_conlat_1(B)),k2_conlat_1(B),D)
            & r2_hidden(D,C) ) ) ) )).

fof(fraenkel_a_2_2_conlat_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_conlat_1(B)
        & l2_conlat_1(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k11_conlat_1(B)))) )
     => ( r2_hidden(A,a_2_2_conlat_2(B,C))
      <=> ? [D,E] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_conlat_1(B)))
            & m1_subset_1(E,k1_zfmisc_1(u2_conlat_1(B)))
            & A = u4_conlat_1(B,g3_conlat_1(B,D,E))
            & r2_hidden(g3_conlat_1(B,D,E),C) ) ) ) )).

fof(fraenkel_a_2_3_conlat_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_conlat_1(B)
        & l2_conlat_1(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k11_conlat_1(B)))) )
     => ( r2_hidden(A,a_2_3_conlat_2(B,C))
      <=> ? [D,E] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_conlat_1(B)))
            & m1_subset_1(E,k1_zfmisc_1(u2_conlat_1(B)))
            & A = u5_conlat_1(B,g3_conlat_1(B,D,E))
            & r2_hidden(g3_conlat_1(B,D,E),C) ) ) ) )).

fof(fraenkel_a_2_4_conlat_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_conlat_1(B)
        & l2_conlat_1(B)
        & v6_conlat_1(C,B)
        & ~ v7_conlat_1(C,B)
        & v9_conlat_1(C,B)
        & l3_conlat_1(C,B) )
     => ( r2_hidden(A,a_2_4_conlat_2(B,C))
      <=> ? [D,E] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_conlat_1(B)))
            & m1_subset_1(E,k1_zfmisc_1(u2_conlat_1(B)))
            & A = g3_conlat_1(B,D,E)
            & ? [F] :
                ( m1_subset_1(F,u1_conlat_1(B))
                & r2_hidden(F,u4_conlat_1(B,C))
                & D = k8_funct_2(k1_zfmisc_1(u2_conlat_1(B)),k1_zfmisc_1(u1_conlat_1(B)),k2_conlat_1(B),k8_funct_2(k1_zfmisc_1(u1_conlat_1(B)),k1_zfmisc_1(u2_conlat_1(B)),k1_conlat_1(B),k6_domain_1(u1_conlat_1(B),F)))
                & E = k8_funct_2(k1_zfmisc_1(u1_conlat_1(B)),k1_zfmisc_1(u2_conlat_1(B)),k1_conlat_1(B),k6_domain_1(u1_conlat_1(B),F)) ) ) ) ) )).

fof(fraenkel_a_2_5_conlat_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_conlat_1(B)
        & l2_conlat_1(B)
        & v6_conlat_1(C,B)
        & ~ v7_conlat_1(C,B)
        & v9_conlat_1(C,B)
        & l3_conlat_1(C,B) )
     => ( r2_hidden(A,a_2_5_conlat_2(B,C))
      <=> ? [D,E] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_conlat_1(B)))
            & m1_subset_1(E,k1_zfmisc_1(u2_conlat_1(B)))
            & A = g3_conlat_1(B,D,E)
            & ? [F] :
                ( m1_subset_1(F,u2_conlat_1(B))
                & r2_hidden(F,u5_conlat_1(B,C))
                & D = k8_funct_2(k1_zfmisc_1(u2_conlat_1(B)),k1_zfmisc_1(u1_conlat_1(B)),k2_conlat_1(B),k6_domain_1(u2_conlat_1(B),F))
                & E = k8_funct_2(k1_zfmisc_1(u1_conlat_1(B)),k1_zfmisc_1(u2_conlat_1(B)),k1_conlat_1(B),k8_funct_2(k1_zfmisc_1(u2_conlat_1(B)),k1_zfmisc_1(u1_conlat_1(B)),k2_conlat_1(B),k6_domain_1(u2_conlat_1(B),F))) ) ) ) ) )).
%------------------------------------------------------------------------------