SET007 Axioms: SET007+335.ax


%------------------------------------------------------------------------------
% File     : SET007+335 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Complete 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    : lattice3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  137 (   4 unit)
%            Number of atoms       :  950 (  88 equality)
%            Maximal formula depth :   18 (   8 average)
%            Number of connectives :  914 ( 101 ~  ;   0  |; 496  &)
%                                         (  52 <=>; 265 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   53 (   1 propositional; 0-3 arity)
%            Number of functors    :   80 (   9 constant; 0-4 arity)
%            Number of variables   :  381 (   0 singleton; 346 !;  35 ?)
%            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_lattice3,axiom,(
    ! [A] :
      ( ~ v3_struct_0(k1_lattice3(A))
      & v3_lattices(k1_lattice3(A)) ) )).

fof(fc2_lattice3,axiom,(
    ! [A] :
      ( ~ v3_struct_0(k1_lattice3(A))
      & v3_lattices(k1_lattice3(A))
      & v4_lattices(k1_lattice3(A))
      & v5_lattices(k1_lattice3(A))
      & v6_lattices(k1_lattice3(A))
      & v7_lattices(k1_lattice3(A))
      & v8_lattices(k1_lattice3(A))
      & v9_lattices(k1_lattice3(A))
      & v10_lattices(k1_lattice3(A)) ) )).

fof(fc3_lattice3,axiom,(
    ! [A] :
      ( ~ v3_struct_0(k1_lattice3(A))
      & v3_lattices(k1_lattice3(A))
      & v4_lattices(k1_lattice3(A))
      & v5_lattices(k1_lattice3(A))
      & v6_lattices(k1_lattice3(A))
      & v7_lattices(k1_lattice3(A))
      & v8_lattices(k1_lattice3(A))
      & v9_lattices(k1_lattice3(A))
      & v10_lattices(k1_lattice3(A))
      & v11_lattices(k1_lattice3(A))
      & v12_lattices(k1_lattice3(A))
      & v13_lattices(k1_lattice3(A))
      & v14_lattices(k1_lattice3(A))
      & v15_lattices(k1_lattice3(A))
      & v16_lattices(k1_lattice3(A))
      & v17_lattices(k1_lattice3(A)) ) )).

fof(fc4_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( ~ v3_struct_0(k3_lattice3(A))
        & v1_orders_2(k3_lattice3(A))
        & v2_orders_2(k3_lattice3(A))
        & v3_orders_2(k3_lattice3(A))
        & v4_orders_2(k3_lattice3(A)) ) ) )).

fof(fc5_lattice3,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_orders_2(k7_lattice3(A))
        & v2_orders_2(k7_lattice3(A))
        & v3_orders_2(k7_lattice3(A))
        & v4_orders_2(k7_lattice3(A)) ) ) )).

fof(fc6_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k7_lattice3(A))
        & v1_orders_2(k7_lattice3(A)) ) ) )).

fof(cc1_lattice3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v1_lattice3(A)
       => ~ v3_struct_0(A) ) ) )).

fof(cc2_lattice3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v2_lattice3(A)
       => ~ v3_struct_0(A) ) ) )).

fof(rc1_lattice3,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)
      & v3_lattice3(A) ) )).

fof(rc2_lattice3,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_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A) ) )).

fof(rc3_lattice3,axiom,(
    ? [A] :
      ( l3_lattices(A)
      & ~ v3_struct_0(A)
      & v3_lattices(A)
      & v4_lattices(A)
      & v5_lattices(A)
      & v6_lattices(A)
      & v7_lattices(A)
      & v8_lattices(A)
      & v9_lattices(A)
      & v10_lattices(A)
      & v4_lattice3(A)
      & v5_lattice3(A)
      & v6_lattice3(A) ) )).

fof(fc7_lattice3,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) )
     => ( ~ v3_struct_0(k14_lattice3(A))
        & v3_lattices(k14_lattice3(A))
        & v4_lattices(k14_lattice3(A))
        & v5_lattices(k14_lattice3(A))
        & v6_lattices(k14_lattice3(A))
        & v7_lattices(k14_lattice3(A))
        & v8_lattices(k14_lattice3(A))
        & v9_lattices(k14_lattice3(A))
        & v10_lattices(k14_lattice3(A))
        & v4_lattice3(k14_lattice3(A)) ) ) )).

fof(d1_lattice3,axiom,(
    ! [A,B] :
      ( ( v3_lattices(B)
        & l3_lattices(B) )
     => ( B = k1_lattice3(A)
      <=> ( u1_struct_0(B) = k1_zfmisc_1(A)
          & ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(A))
                 => ( k1_binop_1(u2_lattices(B),C,D) = k4_subset_1(A,C,D)
                    & k1_binop_1(u1_lattices(B),C,D) = k5_subset_1(A,C,D) ) ) ) ) ) ) )).

fof(t1_lattice3,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,u1_struct_0(k1_lattice3(A)))
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(k1_lattice3(A)))
         => ( k1_lattices(k1_lattice3(A),B,C) = k2_xboole_0(B,C)
            & k2_lattices(k1_lattice3(A),B,C) = k3_xboole_0(B,C) ) ) ) )).

fof(t2_lattice3,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,u1_struct_0(k1_lattice3(A)))
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(k1_lattice3(A)))
         => ( r1_lattices(k1_lattice3(A),B,C)
          <=> r1_tarski(B,C) ) ) ) )).

fof(t3_lattice3,axiom,(
    ! [A] :
      ( v13_lattices(k1_lattice3(A))
      & k5_lattices(k1_lattice3(A)) = k1_xboole_0 ) )).

fof(t4_lattice3,axiom,(
    ! [A] :
      ( v14_lattices(k1_lattice3(A))
      & k6_lattices(k1_lattice3(A)) = A ) )).

fof(t5_lattice3,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,u1_struct_0(k1_lattice3(A)))
     => k7_lattices(k1_lattice3(A),B) = k4_xboole_0(A,B) ) )).

fof(d2_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => k3_lattice3(A) = g1_orders_2(u1_struct_0(A),k2_lattice3(A)) ) )).

fof(t6_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ( k3_lattice3(A) = k3_lattice3(B)
           => g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) ) ) ) )).

fof(d3_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k4_lattice3(A,B) = B ) ) )).

fof(d4_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k3_lattice3(A)))
         => k5_lattice3(A,B) = B ) ) )).

fof(t7_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_lattices(A,B,C)
              <=> r3_orders_2(k3_lattice3(A),k4_lattice3(A,B),k4_lattice3(A,C)) ) ) ) ) )).

fof(d5_lattice3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => k7_lattice3(A) = g1_orders_2(u1_struct_0(A),k6_relset_1(u1_struct_0(A),u1_struct_0(A),u1_orders_2(A))) ) )).

fof(t8_lattice3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => k7_lattice3(k7_lattice3(A)) = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) )).

fof(d6_lattice3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k8_lattice3(A,B) = B ) ) )).

fof(d7_lattice3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k7_lattice3(A)))
         => k9_lattice3(A,B) = B ) ) )).

fof(t9_lattice3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_orders_2(A,B,C)
              <=> r1_orders_2(k7_lattice3(A),k8_lattice3(A,C),k8_lattice3(A,B)) ) ) ) ) )).

fof(d8_lattice3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B,C] :
          ( m1_subset_1(C,u1_struct_0(A))
         => ( r1_lattice3(A,B,C)
          <=> ! [D] :
                ( m1_subset_1(D,u1_struct_0(A))
               => ( r2_hidden(D,B)
                 => r1_orders_2(A,C,D) ) ) ) ) ) )).

fof(d9_lattice3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B,C] :
          ( m1_subset_1(C,u1_struct_0(A))
         => ( r2_lattice3(A,B,C)
          <=> ! [D] :
                ( m1_subset_1(D,u1_struct_0(A))
               => ( r2_hidden(D,B)
                 => r1_orders_2(A,D,C) ) ) ) ) ) )).

fof(d10_lattice3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v1_lattice3(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))
                    & r1_orders_2(A,B,D)
                    & r1_orders_2(A,C,D)
                    & ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( ( r1_orders_2(A,B,E)
                            & r1_orders_2(A,C,E) )
                         => r1_orders_2(A,D,E) ) ) ) ) ) ) ) )).

fof(d11_lattice3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v2_lattice3(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))
                    & r1_orders_2(A,D,B)
                    & r1_orders_2(A,D,C)
                    & ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( ( r1_orders_2(A,E,B)
                            & r1_orders_2(A,E,C) )
                         => r1_orders_2(A,E,D) ) ) ) ) ) ) ) )).

fof(t10_lattice3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v1_lattice3(A)
      <=> v2_lattice3(k7_lattice3(A)) ) ) )).

fof(t11_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( v1_lattice3(k3_lattice3(A))
        & v2_lattice3(k3_lattice3(A)) ) ) )).

fof(d12_lattice3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v3_lattice3(A)
      <=> ! [B] :
          ? [C] :
            ( m1_subset_1(C,u1_struct_0(A))
            & r2_lattice3(A,B,C)
            & ! [D] :
                ( m1_subset_1(D,u1_struct_0(A))
               => ( r2_lattice3(A,B,D)
                 => r1_orders_2(A,C,D) ) ) ) ) ) )).

fof(t12_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v3_lattice3(A)
       => ( v1_lattice3(A)
          & v2_lattice3(A) ) ) ) )).

fof(d13_lattice3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v4_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))
                      & r1_orders_2(A,B,D)
                      & r1_orders_2(A,C,D)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( ( r1_orders_2(A,B,E)
                              & r1_orders_2(A,C,E) )
                           => r1_orders_2(A,D,E) ) ) )
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( D = k10_lattice3(A,B,C)
                      <=> ( r1_orders_2(A,B,D)
                          & r1_orders_2(A,C,D)
                          & ! [E] :
                              ( m1_subset_1(E,u1_struct_0(A))
                             => ( ( r1_orders_2(A,B,E)
                                  & r1_orders_2(A,C,E) )
                               => r1_orders_2(A,D,E) ) ) ) ) ) ) ) ) ) ) )).

fof(d14_lattice3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v4_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))
                      & r1_orders_2(A,D,B)
                      & r1_orders_2(A,D,C)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( ( r1_orders_2(A,E,B)
                              & r1_orders_2(A,E,C) )
                           => r1_orders_2(A,E,D) ) ) )
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( D = k11_lattice3(A,B,C)
                      <=> ( r1_orders_2(A,D,B)
                          & r1_orders_2(A,D,C)
                          & ! [E] :
                              ( m1_subset_1(E,u1_struct_0(A))
                             => ( ( r1_orders_2(A,E,B)
                                  & r1_orders_2(A,E,C) )
                               => r1_orders_2(A,E,D) ) ) ) ) ) ) ) ) ) ) )).

fof(t13_lattice3,axiom,(
    ! [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))
             => k10_lattice3(A,B,C) = k10_lattice3(A,C,B) ) ) ) )).

fof(t14_lattice3,axiom,(
    ! [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))
                 => ( v3_orders_2(A)
                   => k10_lattice3(A,k10_lattice3(A,B,C),D) = k10_lattice3(A,B,k10_lattice3(A,C,D)) ) ) ) ) ) )).

fof(t15_lattice3,axiom,(
    ! [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))
             => k11_lattice3(A,B,C) = k11_lattice3(A,C,B) ) ) ) )).

fof(t16_lattice3,axiom,(
    ! [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))
                 => ( v3_orders_2(A)
                   => k11_lattice3(A,k11_lattice3(A,B,C),D) = k11_lattice3(A,B,k11_lattice3(A,C,D)) ) ) ) ) ) )).

fof(t17_lattice3,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(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))
             => k13_lattice3(A,k12_lattice3(A,B,C),C) = C ) ) ) )).

fof(t18_lattice3,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(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))
             => k12_lattice3(A,B,k13_lattice3(A,B,C)) = B ) ) ) )).

fof(t19_lattice3,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( ~ v3_struct_0(B)
          & v3_lattices(B)
          & v10_lattices(B)
          & l3_lattices(B)
          & g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = k3_lattice3(B) ) ) )).

fof(d15_lattice3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & l1_orders_2(A) )
       => ! [B] :
            ( ( ~ v3_struct_0(B)
              & v3_lattices(B)
              & v10_lattices(B)
              & l3_lattices(B) )
           => ( B = k14_lattice3(A)
            <=> g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = k3_lattice3(B) ) ) ) ) )).

fof(t20_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( k6_lattice3(u1_struct_0(A),k2_lattice3(A)) = k2_lattice3(k1_lattice2(A))
        & k7_lattice3(k3_lattice3(A)) = k3_lattice3(k1_lattice2(A)) ) ) )).

fof(d16_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( r3_lattice3(A,B,C)
            <=> ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_hidden(D,C)
                   => r1_lattices(A,B,D) ) ) ) ) ) )).

fof(d17_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( r4_lattice3(A,B,C)
            <=> ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_hidden(D,C)
                   => r1_lattices(A,D,B) ) ) ) ) ) )).

fof(t21_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(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))
                 => ( r3_lattice3(A,B,k2_struct_0(A,C,D))
                  <=> r3_lattices(A,B,k4_lattices(A,C,D)) ) ) ) ) ) )).

fof(t22_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(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))
                 => ( r4_lattice3(A,B,k2_struct_0(A,C,D))
                  <=> r3_lattices(A,k3_lattices(A,C,D),B) ) ) ) ) ) )).

fof(d18_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( v4_lattice3(A)
      <=> ! [B] :
          ? [C] :
            ( m1_subset_1(C,u1_struct_0(A))
            & r4_lattice3(A,C,B)
            & ! [D] :
                ( m1_subset_1(D,u1_struct_0(A))
               => ( r4_lattice3(A,D,B)
                 => r1_lattices(A,C,D) ) ) ) ) ) )).

fof(t25_lattice3,axiom,(
    ! [A] : v4_lattice3(k1_lattice3(A)) )).

fof(t26_lattice3,axiom,(
    ! [A] : v5_lattice3(k1_lattice3(A)) )).

fof(t27_lattice3,axiom,(
    ! [A] : v6_lattice3(k1_lattice3(A)) )).

fof(t28_lattice3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(B))
         => ( r3_lattice3(B,C,A)
          <=> r1_lattice3(k3_lattice3(B),A,k4_lattice3(B,C)) ) ) ) )).

fof(t29_lattice3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(k3_lattice3(B)))
         => ( r1_lattice3(k3_lattice3(B),A,C)
          <=> r3_lattice3(B,k5_lattice3(B,C),A) ) ) ) )).

fof(t30_lattice3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(B))
         => ( r4_lattice3(B,C,A)
          <=> r2_lattice3(k3_lattice3(B),A,k4_lattice3(B,C)) ) ) ) )).

fof(t31_lattice3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(k3_lattice3(B)))
         => ( r2_lattice3(k3_lattice3(B),A,C)
          <=> r4_lattice3(B,k5_lattice3(B,C),A) ) ) ) )).

fof(d21_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v4_lattice3(A)
          & l3_lattices(A) )
       => ! [B,C] :
            ( m1_subset_1(C,u1_struct_0(A))
           => ( C = k15_lattice3(A,B)
            <=> ( r4_lattice3(A,C,B)
                & ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r4_lattice3(A,D,B)
                     => r1_lattices(A,C,D) ) ) ) ) ) ) ) )).

fof(t34_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( B = k16_lattice3(A,C)
            <=> ( r3_lattice3(A,B,C)
                & ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r3_lattice3(A,D,C)
                     => r3_lattices(A,D,B) ) ) ) ) ) ) )).

fof(t38_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( r2_hidden(B,C)
             => ( r3_lattices(A,B,k15_lattice3(A,C))
                & r3_lattices(A,k16_lattice3(A,C),B) ) ) ) ) )).

fof(t39_lattice3,axiom,(
    $true )).

fof(t40_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( r3_lattice3(A,B,C)
             => r3_lattices(A,B,k16_lattice3(A,C)) ) ) ) )).

fof(t41_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( r2_hidden(B,C)
                & r4_lattice3(A,B,C) )
             => k15_lattice3(A,C) = B ) ) ) )).

fof(t42_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( r2_hidden(B,C)
                & r3_lattice3(A,B,C) )
             => k16_lattice3(A,C) = B ) ) ) )).

fof(t43_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k15_lattice3(A,k1_struct_0(A,B)) = B
            & k16_lattice3(A,k1_struct_0(A,B)) = B ) ) ) )).

fof(t44_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k3_lattices(A,B,C) = k15_lattice3(A,k2_struct_0(A,B,C))
                & k4_lattices(A,B,C) = k16_lattice3(A,k2_struct_0(A,B,C)) ) ) ) ) )).

fof(t46_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B,C] :
          ( r1_tarski(B,C)
         => ( r3_lattices(A,k15_lattice3(A,B),k15_lattice3(A,C))
            & r3_lattices(A,k16_lattice3(A,C),k16_lattice3(A,B)) ) ) ) )).

fof(t48_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(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))
                     => ~ ( r3_lattices(A,D,E)
                          & r2_hidden(E,C) ) ) ) )
         => r3_lattices(A,k15_lattice3(A,B),k15_lattice3(A,C)) ) ) )).

fof(t50_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A)
        & k5_lattices(A) = k15_lattice3(A,k1_xboole_0) ) ) )).

fof(t51_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v14_lattices(A)
        & l3_lattices(A)
        & k6_lattices(A) = k15_lattice3(A,u1_struct_0(A)) ) ) )).

fof(t53_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v3_filter_0(A)
          & l3_lattices(A) )
       => v5_lattice3(A) ) ) )).

fof(t56_lattice3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zfmisc_1(A),A)
            & m2_relset_1(B,k1_zfmisc_1(A),A) )
         => ~ ( ! [C] :
                  ( m1_subset_1(C,A)
                 => k8_funct_2(k1_zfmisc_1(A),A,B,k6_domain_1(A,C)) = C )
              & ! [C] :
                  ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
                 => k8_funct_2(k1_zfmisc_1(A),A,B,k10_relset_1(k1_zfmisc_1(A),A,B,C)) = k1_funct_1(B,k3_tarski(C)) )
              & ! [C] :
                  ( ( ~ v3_struct_0(C)
                    & v3_lattices(C)
                    & v10_lattices(C)
                    & v4_lattice3(C)
                    & l3_lattices(C) )
                 => ~ ( u1_struct_0(C) = A
                      & ! [D] :
                          ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C)))
                         => k15_lattice3(C,D) = k1_funct_1(B,D) ) ) ) ) ) ) )).

fof(dt_k1_lattice3,axiom,(
    ! [A] :
      ( v3_lattices(k1_lattice3(A))
      & l3_lattices(k1_lattice3(A)) ) )).

fof(dt_k2_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( v1_relat_2(k2_lattice3(A))
        & v4_relat_2(k2_lattice3(A))
        & v8_relat_2(k2_lattice3(A))
        & v1_partfun1(k2_lattice3(A),u1_struct_0(A),u1_struct_0(A))
        & m2_relset_1(k2_lattice3(A),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(redefinition_k2_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => k2_lattice3(A) = k9_filter_1(A) ) )).

fof(dt_k3_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( v1_orders_2(k3_lattice3(A))
        & v2_orders_2(k3_lattice3(A))
        & v3_orders_2(k3_lattice3(A))
        & v4_orders_2(k3_lattice3(A))
        & l1_orders_2(k3_lattice3(A)) ) ) )).

fof(dt_k4_lattice3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k4_lattice3(A,B),u1_struct_0(k3_lattice3(A))) ) )).

fof(dt_k5_lattice3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(k3_lattice3(A))) )
     => m1_subset_1(k5_lattice3(A,B),u1_struct_0(A)) ) )).

fof(dt_k6_lattice3,axiom,(
    ! [A,B] :
      ( ( v1_relat_2(B)
        & v4_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A) )
     => ( v1_relat_2(k6_lattice3(A,B))
        & v4_relat_2(k6_lattice3(A,B))
        & v8_relat_2(k6_lattice3(A,B))
        & v1_partfun1(k6_lattice3(A,B),A,A)
        & m2_relset_1(k6_lattice3(A,B),A,A) ) ) )).

fof(involutiveness_k6_lattice3,axiom,(
    ! [A,B] :
      ( ( v1_relat_2(B)
        & v4_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A) )
     => k6_lattice3(A,k6_lattice3(A,B)) = B ) )).

fof(redefinition_k6_lattice3,axiom,(
    ! [A,B] :
      ( ( v1_relat_2(B)
        & v4_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A) )
     => k6_lattice3(A,B) = k4_relat_1(B) ) )).

fof(dt_k7_lattice3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v1_orders_2(k7_lattice3(A))
        & l1_orders_2(k7_lattice3(A)) ) ) )).

fof(dt_k8_lattice3,axiom,(
    ! [A,B] :
      ( ( l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k8_lattice3(A,B),u1_struct_0(k7_lattice3(A))) ) )).

fof(dt_k9_lattice3,axiom,(
    ! [A,B] :
      ( ( l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(k7_lattice3(A))) )
     => m1_subset_1(k9_lattice3(A,B),u1_struct_0(A)) ) )).

fof(dt_k10_lattice3,axiom,(
    ! [A,B,C] :
      ( ( l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k10_lattice3(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k11_lattice3,axiom,(
    ! [A,B,C] :
      ( ( l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k11_lattice3(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k12_lattice3,axiom,(
    ! [A,B,C] :
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k12_lattice3(A,B,C),u1_struct_0(A)) ) )).

fof(commutativity_k12_lattice3,axiom,(
    ! [A,B,C] :
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k12_lattice3(A,B,C) = k12_lattice3(A,C,B) ) )).

fof(redefinition_k12_lattice3,axiom,(
    ! [A,B,C] :
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k12_lattice3(A,B,C) = k11_lattice3(A,B,C) ) )).

fof(dt_k13_lattice3,axiom,(
    ! [A,B,C] :
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k13_lattice3(A,B,C),u1_struct_0(A)) ) )).

fof(commutativity_k13_lattice3,axiom,(
    ! [A,B,C] :
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k13_lattice3(A,B,C) = k13_lattice3(A,C,B) ) )).

fof(redefinition_k13_lattice3,axiom,(
    ! [A,B,C] :
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k13_lattice3(A,B,C) = k10_lattice3(A,B,C) ) )).

fof(dt_k14_lattice3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ~ v3_struct_0(k14_lattice3(A))
        & v3_lattices(k14_lattice3(A))
        & v10_lattices(k14_lattice3(A))
        & l3_lattices(k14_lattice3(A)) ) ) )).

fof(dt_k15_lattice3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => m1_subset_1(k15_lattice3(A,B),u1_struct_0(A)) ) )).

fof(dt_k16_lattice3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => m1_subset_1(k16_lattice3(A,B),u1_struct_0(A)) ) )).

fof(d19_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( v5_lattice3(A)
      <=> ! [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(A))
                   => ( ( r4_lattice3(A,C,B)
                        & ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( r4_lattice3(A,F,B)
                             => r1_lattices(A,C,F) ) )
                        & r4_lattice3(A,E,a_3_0_lattice3(A,B,D))
                        & ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( r4_lattice3(A,F,a_3_0_lattice3(A,B,D))
                             => r1_lattices(A,E,F) ) ) )
                     => r1_lattices(A,k2_lattices(A,D,C),E) ) ) ) ) ) ) )).

fof(d20_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( v6_lattice3(A)
      <=> ! [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(A))
                   => ( ( r3_lattice3(A,C,B)
                        & ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( r3_lattice3(A,F,B)
                             => r1_lattices(A,F,C) ) )
                        & r3_lattice3(A,E,a_3_1_lattice3(A,B,D))
                        & ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( r3_lattice3(A,F,a_3_1_lattice3(A,B,D))
                             => r1_lattices(A,F,E) ) ) )
                     => r1_lattices(A,E,k1_lattices(A,D,C)) ) ) ) ) ) ) )).

fof(t23_lattice3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & v17_lattices(B)
        & l3_lattices(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(B))
         => ( r4_lattice3(B,C,A)
          <=> r3_lattice3(B,k7_lattices(B,C),a_2_0_lattice3(A,B)) ) ) ) )).

fof(t24_lattice3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & v17_lattices(B)
        & l3_lattices(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(B))
         => ( r3_lattice3(B,C,A)
          <=> r4_lattice3(B,k7_lattices(B,C),a_2_0_lattice3(A,B)) ) ) ) )).

fof(d22_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ! [B] : k16_lattice3(A,B) = k15_lattice3(A,a_2_1_lattice3(A,B)) ) )).

fof(t32_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : r3_lattices(A,k15_lattice3(A,a_3_2_lattice3(A,B,C)),k4_lattices(A,B,k15_lattice3(A,C))) ) ) )).

fof(t33_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ( v5_lattice3(A)
      <=> ! [B,C] :
            ( m1_subset_1(C,u1_struct_0(A))
           => r3_lattices(A,k4_lattices(A,C,k15_lattice3(A,B)),k15_lattice3(A,a_3_3_lattice3(A,B,C))) ) ) ) )).

fof(t35_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : r3_lattices(A,k3_lattices(A,B,k16_lattice3(A,C)),k16_lattice3(A,a_3_4_lattice3(A,B,C))) ) ) )).

fof(t36_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ( v6_lattice3(A)
      <=> ! [B,C] :
            ( m1_subset_1(C,u1_struct_0(A))
           => r3_lattices(A,k16_lattice3(A,a_3_5_lattice3(A,B,C)),k3_lattices(A,C,k16_lattice3(A,B))) ) ) ) )).

fof(t37_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] : k15_lattice3(A,B) = k16_lattice3(A,a_2_2_lattice3(A,B)) ) )).

fof(t45_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( B = k15_lattice3(A,a_2_3_lattice3(A,B))
            & B = k16_lattice3(A,a_2_4_lattice3(A,B)) ) ) ) )).

fof(t47_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( k15_lattice3(A,B) = k15_lattice3(A,a_2_5_lattice3(A,B))
          & k16_lattice3(A,B) = k16_lattice3(A,a_2_6_lattice3(A,B)) ) ) )).

fof(t49_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( r1_tarski(B,k1_zfmisc_1(u1_struct_0(A)))
         => k15_lattice3(A,k3_tarski(B)) = k15_lattice3(A,a_2_7_lattice3(A,B)) ) ) )).

fof(t52_lattice3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( ~ v3_struct_0(A)
                  & v10_lattices(A)
                  & v3_filter_0(A)
                  & l3_lattices(A) )
               => k4_filter_0(A,B,C) = k15_lattice3(A,a_3_6_lattice3(A,B,C)) ) ) ) ) )).

fof(t54_lattice3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & v4_lattice3(B)
        & v5_lattice3(B)
        & l3_lattices(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(B))
         => ( k4_lattices(B,C,k15_lattice3(B,A)) = k15_lattice3(B,a_3_7_lattice3(A,B,C))
            & k4_lattices(B,k15_lattice3(B,A),C) = k15_lattice3(B,a_3_8_lattice3(A,B,C)) ) ) ) )).

fof(t55_lattice3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & v4_lattice3(B)
        & v6_lattice3(B)
        & l3_lattices(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(B))
         => ( k3_lattices(B,C,k16_lattice3(B,A)) = k16_lattice3(B,a_3_9_lattice3(A,B,C))
            & k3_lattices(B,k16_lattice3(B,A),C) = k16_lattice3(B,a_3_10_lattice3(A,B,C)) ) ) ) )).

fof(s1_lattice3,axiom,
    ( ? [A] :
        ( m1_subset_1(A,f2_s1_lattice3)
        & p1_s1_lattice3(A) )
   => a_0_0_lattice3 = k1_tarski(f1_s1_lattice3) )).

fof(s2_lattice3,axiom,
    ( r1_tarski(f2_s2_lattice3,k1_relat_1(f4_s2_lattice3))
   => k9_relat_1(f4_s2_lattice3,a_0_1_lattice3) = a_0_2_lattice3 )).

fof(fraenkel_a_3_0_lattice3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & l3_lattices(B)
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_0_lattice3(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = k2_lattices(B,D,E)
            & r2_hidden(E,C) ) ) ) )).

fof(fraenkel_a_3_1_lattice3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & l3_lattices(B)
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_1_lattice3(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = k1_lattices(B,D,E)
            & r2_hidden(E,C) ) ) ) )).

fof(fraenkel_a_2_0_lattice3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(C)
        & v10_lattices(C)
        & v17_lattices(C)
        & l3_lattices(C) )
     => ( r2_hidden(A,a_2_0_lattice3(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(C))
            & A = k7_lattices(C,D)
            & r2_hidden(D,B) ) ) ) )).

fof(fraenkel_a_2_1_lattice3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & l3_lattices(B) )
     => ( r2_hidden(A,a_2_1_lattice3(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & r3_lattice3(B,D,C) ) ) ) )).

fof(fraenkel_a_3_2_lattice3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & v4_lattice3(B)
        & l3_lattices(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_2_lattice3(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = k4_lattices(B,C,E)
            & r2_hidden(E,D) ) ) ) )).

fof(fraenkel_a_3_3_lattice3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & v4_lattice3(B)
        & l3_lattices(B)
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_3_lattice3(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = k4_lattices(B,D,E)
            & r2_hidden(E,C) ) ) ) )).

fof(fraenkel_a_3_4_lattice3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & v4_lattice3(B)
        & l3_lattices(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_4_lattice3(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = k3_lattices(B,C,E)
            & r2_hidden(E,D) ) ) ) )).

fof(fraenkel_a_3_5_lattice3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & v4_lattice3(B)
        & l3_lattices(B)
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_5_lattice3(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = k3_lattices(B,D,E)
            & r2_hidden(E,C) ) ) ) )).

fof(fraenkel_a_2_2_lattice3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & v4_lattice3(B)
        & l3_lattices(B) )
     => ( r2_hidden(A,a_2_2_lattice3(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & r4_lattice3(B,D,C) ) ) ) )).

fof(fraenkel_a_2_3_lattice3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & v4_lattice3(B)
        & l3_lattices(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_3_lattice3(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & r3_lattices(B,D,C) ) ) ) )).

fof(fraenkel_a_2_4_lattice3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & v4_lattice3(B)
        & l3_lattices(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_4_lattice3(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & r3_lattices(B,C,D) ) ) ) )).

fof(fraenkel_a_2_5_lattice3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & v4_lattice3(B)
        & l3_lattices(B) )
     => ( r2_hidden(A,a_2_5_lattice3(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & ? [E] :
                ( m1_subset_1(E,u1_struct_0(B))
                & r3_lattices(B,D,E)
                & r2_hidden(E,C) ) ) ) ) )).

fof(fraenkel_a_2_6_lattice3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & v4_lattice3(B)
        & l3_lattices(B) )
     => ( r2_hidden(A,a_2_6_lattice3(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & ? [E] :
                ( m1_subset_1(E,u1_struct_0(B))
                & r3_lattices(B,E,D)
                & r2_hidden(E,C) ) ) ) ) )).

fof(fraenkel_a_2_7_lattice3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & v4_lattice3(B)
        & l3_lattices(B) )
     => ( r2_hidden(A,a_2_7_lattice3(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = k15_lattice3(B,D)
            & r2_hidden(D,C) ) ) ) )).

fof(fraenkel_a_3_6_lattice3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & v4_lattice3(B)
        & l3_lattices(B)
        & m1_subset_1(C,u1_struct_0(B))
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_6_lattice3(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = E
            & r3_lattices(B,k4_lattices(B,C,E),D) ) ) ) )).

fof(fraenkel_a_3_7_lattice3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(C)
        & v10_lattices(C)
        & v4_lattice3(C)
        & v5_lattice3(C)
        & l3_lattices(C)
        & m1_subset_1(D,u1_struct_0(C)) )
     => ( r2_hidden(A,a_3_7_lattice3(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(C))
            & A = k4_lattices(C,D,E)
            & r2_hidden(E,B) ) ) ) )).

fof(fraenkel_a_3_8_lattice3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(C)
        & v10_lattices(C)
        & v4_lattice3(C)
        & v5_lattice3(C)
        & l3_lattices(C)
        & m1_subset_1(D,u1_struct_0(C)) )
     => ( r2_hidden(A,a_3_8_lattice3(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(C))
            & A = k4_lattices(C,E,D)
            & r2_hidden(E,B) ) ) ) )).

fof(fraenkel_a_3_9_lattice3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(C)
        & v10_lattices(C)
        & v4_lattice3(C)
        & v6_lattice3(C)
        & l3_lattices(C)
        & m1_subset_1(D,u1_struct_0(C)) )
     => ( r2_hidden(A,a_3_9_lattice3(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(C))
            & A = k3_lattices(C,D,E)
            & r2_hidden(E,B) ) ) ) )).

fof(fraenkel_a_3_10_lattice3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(C)
        & v10_lattices(C)
        & v4_lattice3(C)
        & v6_lattice3(C)
        & l3_lattices(C)
        & m1_subset_1(D,u1_struct_0(C)) )
     => ( r2_hidden(A,a_3_10_lattice3(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(C))
            & A = k3_lattices(C,E,D)
            & r2_hidden(E,B) ) ) ) )).

fof(fraenkel_a_0_0_lattice3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_lattice3)
    <=> ? [B] :
          ( m1_subset_1(B,f2_s1_lattice3)
          & A = f1_s1_lattice3
          & p1_s1_lattice3(B) ) ) )).

fof(fraenkel_a_0_1_lattice3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_1_lattice3)
    <=> ? [B] :
          ( m1_subset_1(B,f1_s2_lattice3)
          & A = f3_s2_lattice3(B)
          & p1_s2_lattice3(B) ) ) )).

fof(fraenkel_a_0_2_lattice3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_2_lattice3)
    <=> ? [B] :
          ( m1_subset_1(B,f1_s2_lattice3)
          & A = k1_funct_1(f4_s2_lattice3,f3_s2_lattice3(B))
          & p1_s2_lattice3(B) ) ) )).
%------------------------------------------------------------------------------