SET007 Axioms: SET007+253.ax


%------------------------------------------------------------------------------
% File     : SET007+253 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Finite Join and Finite Meet, and Dual 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    : lattice2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  108 (   9 unit)
%            Number of atoms       :  919 (  75 equality)
%            Maximal formula depth :   17 (   9 average)
%            Number of connectives :  952 ( 141 ~  ;   8  |; 451  &)
%                                         (   8 <=>; 344 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   39 (   1 propositional; 0-3 arity)
%            Number of functors    :   25 (   1 constant; 0-6 arity)
%            Number of variables   :  300 (   0 singleton; 295 !;   5 ?)
%            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_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( ~ v3_struct_0(k1_lattice2(A))
        & v3_lattices(k1_lattice2(A)) ) ) )).

fof(fc2_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & l2_lattices(A) )
     => ( v1_relat_1(u2_lattices(A))
        & v1_funct_1(u2_lattices(A))
        & v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & v1_binop_1(u2_lattices(A),u1_struct_0(A))
        & v1_partfun1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) )).

fof(fc3_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v5_lattices(A)
        & l2_lattices(A) )
     => ( v1_relat_1(u2_lattices(A))
        & v1_funct_1(u2_lattices(A))
        & v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & v2_binop_1(u2_lattices(A),u1_struct_0(A))
        & v1_partfun1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) )).

fof(fc4_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & l1_lattices(A) )
     => ( v1_relat_1(u1_lattices(A))
        & v1_funct_1(u1_lattices(A))
        & v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & v1_binop_1(u1_lattices(A),u1_struct_0(A))
        & v1_partfun1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) )).

fof(fc5_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v7_lattices(A)
        & l1_lattices(A) )
     => ( v1_relat_1(u1_lattices(A))
        & v1_funct_1(u1_lattices(A))
        & v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & v2_binop_1(u1_lattices(A),u1_struct_0(A))
        & v1_partfun1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) )).

fof(fc6_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(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)) ) ) )).

fof(rc1_lattice2,axiom,(
    ? [A] :
      ( l3_lattices(A)
      & ~ v3_struct_0(A)
      & v4_lattices(A)
      & v5_lattices(A)
      & v6_lattices(A)
      & v7_lattices(A)
      & v8_lattices(A)
      & v9_lattices(A)
      & v10_lattices(A)
      & v1_lattice2(A) ) )).

fof(cc1_lattice2,axiom,(
    ! [A] :
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v1_lattice2(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A)
          & v10_lattices(A)
          & v13_lattices(A)
          & v3_filter_0(A) ) ) ) )).

fof(cc2_lattice2,axiom,(
    ! [A] :
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v13_lattices(A)
          & v3_filter_0(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A)
          & v10_lattices(A)
          & v1_lattice2(A) ) ) ) )).

fof(rc2_lattice2,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)
      & v13_lattices(A)
      & v3_filter_0(A)
      & v1_lattice2(A) ) )).

fof(cc3_lattice2,axiom,(
    ! [A] :
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v6_group_1(A)
          & v10_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A)
          & v10_lattices(A)
          & v13_lattices(A) ) ) ) )).

fof(cc4_lattice2,axiom,(
    ! [A] :
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v6_group_1(A)
          & v10_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A)
          & v10_lattices(A)
          & v14_lattices(A) ) ) ) )).

fof(cc5_lattice2,axiom,(
    ! [A] :
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v6_group_1(A)
          & v10_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A)
          & v10_lattices(A)
          & v13_lattices(A)
          & v14_lattices(A)
          & v15_lattices(A) ) ) ) )).

fof(cc6_lattice2,axiom,(
    ! [A] :
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v6_group_1(A)
          & v10_lattices(A)
          & v11_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A)
          & v10_lattices(A)
          & v13_lattices(A)
          & v3_filter_0(A)
          & v1_lattice2(A) ) ) ) )).

fof(t1_lattice2,axiom,(
    $true )).

fof(t2_lattice2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,B)
                & m2_relset_1(D,A,B) )
             => k1_relat_1(k2_partfun1(A,B,D,C)) = C ) ) ) )).

fof(t3_lattice2,axiom,(
    $true )).

fof(t4_lattice2,axiom,(
    $true )).

fof(t5_lattice2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,B)
                & m2_relset_1(D,A,B) )
             => ! [E] :
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,A,B)
                    & m2_relset_1(E,A,B) )
                 => ( k2_partfun1(A,B,D,C) = k2_partfun1(A,B,E,C)
                  <=> ! [F] :
                        ( m1_subset_1(F,A)
                       => ( r2_hidden(F,C)
                         => k1_funct_1(E,F) = k1_funct_1(D,F) ) ) ) ) ) ) ) )).

fof(t6_lattice2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,B)
            & m2_relset_1(C,A,B) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,B)
                & m2_relset_1(D,A,B) )
             => ! [E] :
                  ( v1_funct_1(k1_funct_4(C,k2_partfun1(A,B,D,E)))
                  & v1_funct_2(k1_funct_4(C,k2_partfun1(A,B,D,E)),A,B)
                  & m2_relset_1(k1_funct_4(C,k2_partfun1(A,B,D,E)),A,B) ) ) ) ) )).

fof(t7_lattice2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,B)
                & m2_relset_1(D,A,B) )
             => ! [E] :
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,A,B)
                    & m2_relset_1(E,A,B) )
                 => k1_funct_4(k2_partfun1(A,B,D,C),E) = E ) ) ) ) )).

fof(t8_lattice2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(B,A)
           => k1_funct_4(A,B) = A ) ) ) )).

fof(t9_lattice2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,B)
                & m2_relset_1(D,A,B) )
             => k1_funct_4(D,k2_partfun1(A,B,D,C)) = D ) ) ) )).

fof(t10_lattice2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,B)
                & m2_relset_1(D,A,B) )
             => ! [E] :
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,A,B)
                    & m2_relset_1(E,A,B) )
                 => ( ! [F] :
                        ( m1_subset_1(F,A)
                       => ( r2_hidden(F,C)
                         => k1_funct_1(D,F) = k1_funct_1(E,F) ) )
                   => k1_funct_4(E,k2_partfun1(A,B,D,C)) = E ) ) ) ) ) )).

fof(t11_lattice2,axiom,(
    $true )).

fof(t12_lattice2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,B)
            & m2_relset_1(C,A,B) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,B)
                & m2_relset_1(D,A,B) )
             => ! [E] :
                  ( m1_subset_1(E,k5_finsub_1(A))
                 => k1_funct_4(k2_partfun1(A,B,C,E),D) = D ) ) ) ) )).

fof(t13_lattice2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,B)
            & m2_relset_1(C,A,B) )
         => ! [D] :
              ( m1_subset_1(D,k5_finsub_1(A))
             => k1_relat_1(k2_partfun1(A,B,C,D)) = D ) ) ) )).

fof(t14_lattice2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,B)
            & m2_relset_1(C,A,B) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,B)
                & m2_relset_1(D,A,B) )
             => ! [E] :
                  ( m1_subset_1(E,k5_finsub_1(A))
                 => ( ! [F] :
                        ( m1_subset_1(F,A)
                       => ( r2_hidden(F,E)
                         => k1_funct_1(C,F) = k1_funct_1(D,F) ) )
                   => k1_funct_4(D,k2_partfun1(A,B,C,E)) = D ) ) ) ) ) )).

fof(t15_lattice2,axiom,(
    $true )).

fof(t16_lattice2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,B)
            & m2_relset_1(C,A,B) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,B)
                & m2_relset_1(D,A,B) )
             => ! [E] :
                  ( m1_subset_1(E,k5_finsub_1(A))
                 => ( k2_partfun1(A,B,C,E) = k2_partfun1(A,B,D,E)
                   => k2_funct_2(A,B,C,E) = k2_funct_2(A,B,D,E) ) ) ) ) ) )).

fof(d1_lattice2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ( r1_lattice2(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,A)
                   => ! [E] :
                        ( m1_subset_1(E,A)
                       => k2_binop_1(A,A,A,B,D,k2_binop_1(A,A,A,C,D,E)) = D ) ) ) ) ) ) )).

fof(t17_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( ( v1_binop_1(u2_lattices(A),u1_struct_0(A))
          & v2_binop_1(u2_lattices(A),u1_struct_0(A))
          & v1_binop_1(u1_lattices(A),u1_struct_0(A))
          & v2_binop_1(u1_lattices(A),u1_struct_0(A))
          & r1_lattice2(u1_struct_0(A),u2_lattices(A),u1_lattices(A))
          & r1_lattice2(u1_struct_0(A),u1_lattices(A),u2_lattices(A)) )
       => v10_lattices(A) ) ) )).

fof(d2_lattice2,axiom,(
    ! [A] :
      ( l3_lattices(A)
     => k1_lattice2(A) = g3_lattices(u1_struct_0(A),u1_lattices(A),u2_lattices(A)) ) )).

fof(t18_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( u1_struct_0(A) = u1_struct_0(k1_lattice2(A))
        & u2_lattices(A) = u1_lattices(k1_lattice2(A))
        & u1_lattices(A) = u2_lattices(k1_lattice2(A)) ) ) )).

fof(t19_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_lattices(A)
        & l3_lattices(A) )
     => k1_lattice2(k1_lattice2(A)) = A ) )).

fof(t20_lattice2,axiom,(
    $true )).

fof(t21_lattice2,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))
               => k3_lattices(A,B,C) = C )
           => B = k5_lattices(A) ) ) ) )).

fof(t22_lattice2,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))
               => k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u2_lattices(A),B,C) = C )
           => B = k5_lattices(A) ) ) ) )).

fof(t23_lattice2,axiom,(
    $true )).

fof(t24_lattice2,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))
               => k4_lattices(A,B,C) = C )
           => B = k6_lattices(A) ) ) ) )).

fof(t25_lattice2,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))
               => k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_lattices(A),B,C) = C )
           => B = k6_lattices(A) ) ) ) )).

fof(t26_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => v3_binop_1(u2_lattices(A),u1_struct_0(A)) ) )).

fof(t27_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & l2_lattices(A) )
     => v1_binop_1(u2_lattices(A),u1_struct_0(A)) ) )).

fof(t28_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( v1_setwiseo(u2_lattices(A),u1_struct_0(A))
       => k5_lattices(A) = k3_binop_1(u1_struct_0(A),u2_lattices(A)) ) ) )).

fof(t29_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v5_lattices(A)
        & l2_lattices(A) )
     => v2_binop_1(u2_lattices(A),u1_struct_0(A)) ) )).

fof(t30_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => v3_binop_1(u1_lattices(A),u1_struct_0(A)) ) )).

fof(t31_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & l1_lattices(A) )
     => v1_binop_1(u1_lattices(A),u1_struct_0(A)) ) )).

fof(t32_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v7_lattices(A)
        & l1_lattices(A) )
     => v2_binop_1(u1_lattices(A),u1_struct_0(A)) ) )).

fof(t33_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( v1_setwiseo(u1_lattices(A),u1_struct_0(A))
       => k6_lattices(A) = k3_binop_1(u1_struct_0(A),u1_lattices(A)) ) ) )).

fof(t34_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => r6_binop_1(u1_struct_0(A),u2_lattices(A),u2_lattices(A)) ) )).

fof(t35_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v11_lattices(A)
          & l3_lattices(A) )
       => r6_binop_1(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ) ) )).

fof(t36_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( r6_binop_1(u1_struct_0(A),u2_lattices(A),u1_lattices(A))
       => v11_lattices(A) ) ) )).

fof(t37_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v11_lattices(A)
          & l3_lattices(A) )
       => r6_binop_1(u1_struct_0(A),u1_lattices(A),u2_lattices(A)) ) ) )).

fof(t38_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( r6_binop_1(u1_struct_0(A),u1_lattices(A),u2_lattices(A))
       => v11_lattices(A) ) ) )).

fof(t39_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => r6_binop_1(u1_struct_0(A),u1_lattices(A),u1_lattices(A)) ) )).

fof(t40_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => r1_lattice2(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ) )).

fof(t41_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => r1_lattice2(u1_struct_0(A),u1_lattices(A),u2_lattices(A)) ) )).

fof(d3_lattice2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,u1_struct_0(B))
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => k2_lattice2(A,B,C,D) = k7_setwiseo(A,u1_struct_0(B),u2_lattices(B),C,D) ) ) ) ) )).

fof(d4_lattice2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,u1_struct_0(B))
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => k3_lattice2(A,B,C,D) = k7_setwiseo(A,u1_struct_0(B),u1_lattices(B),C,D) ) ) ) ) )).

fof(t42_lattice2,axiom,(
    $true )).

fof(t43_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,B)
             => ! [D] :
                  ( m1_subset_1(D,k5_finsub_1(B))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,u1_struct_0(A))
                        & m2_relset_1(E,B,u1_struct_0(A)) )
                     => ( r2_hidden(C,D)
                       => r3_lattices(A,k8_funct_2(B,u1_struct_0(A),E,C),k2_lattice2(B,A,D,E)) ) ) ) ) ) ) )).

fof(t44_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,k5_finsub_1(C))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,C,u1_struct_0(A))
                        & m2_relset_1(E,C,u1_struct_0(A)) )
                     => ( ? [F] :
                            ( m1_subset_1(F,C)
                            & r2_hidden(F,D)
                            & r3_lattices(A,B,k8_funct_2(C,u1_struct_0(A),E,F)) )
                       => r3_lattices(A,B,k2_lattice2(C,A,D,E)) ) ) ) ) ) ) )).

fof(t45_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,k5_finsub_1(C))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,C,u1_struct_0(A))
                        & m2_relset_1(E,C,u1_struct_0(A)) )
                     => ( ! [F] :
                            ( m1_subset_1(F,C)
                           => ( r2_hidden(F,D)
                             => k8_funct_2(C,u1_struct_0(A),E,F) = B ) )
                       => ( D = k1_xboole_0
                          | k2_lattice2(C,A,D,E) = B ) ) ) ) ) ) ) )).

fof(t46_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,k5_finsub_1(C))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,C,u1_struct_0(A))
                        & m2_relset_1(E,C,u1_struct_0(A)) )
                     => ( r3_lattices(A,k2_lattice2(C,A,D,E),B)
                       => ! [F] :
                            ( m1_subset_1(F,C)
                           => ( r2_hidden(F,D)
                             => r3_lattices(A,k8_funct_2(C,u1_struct_0(A),E,F),B) ) ) ) ) ) ) ) ) )).

fof(t47_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,k5_finsub_1(C))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,C,u1_struct_0(A))
                        & m2_relset_1(E,C,u1_struct_0(A)) )
                     => ( ! [F] :
                            ( m1_subset_1(F,C)
                           => ( r2_hidden(F,D)
                             => r3_lattices(A,k8_funct_2(C,u1_struct_0(A),E,F),B) ) )
                       => ( D = k1_xboole_0
                          | r3_lattices(A,k2_lattice2(C,A,D,E),B) ) ) ) ) ) ) ) )).

fof(t48_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(B))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,u1_struct_0(A))
                    & m2_relset_1(D,B,u1_struct_0(A)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,u1_struct_0(A))
                        & m2_relset_1(E,B,u1_struct_0(A)) )
                     => ( ! [F] :
                            ( m1_subset_1(F,B)
                           => ( r2_hidden(F,C)
                             => r3_lattices(A,k8_funct_2(B,u1_struct_0(A),D,F),k8_funct_2(B,u1_struct_0(A),E,F)) ) )
                       => ( C = k1_xboole_0
                          | r3_lattices(A,k2_lattice2(B,A,C,D),k2_lattice2(B,A,C,E)) ) ) ) ) ) ) ) )).

fof(t49_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(B))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,u1_struct_0(A))
                    & m2_relset_1(D,B,u1_struct_0(A)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,u1_struct_0(A))
                        & m2_relset_1(E,B,u1_struct_0(A)) )
                     => ( k2_partfun1(B,u1_struct_0(A),D,C) = k2_partfun1(B,u1_struct_0(A),E,C)
                       => ( C = k1_xboole_0
                          | k2_lattice2(B,A,C,D) = k2_lattice2(B,A,C,E) ) ) ) ) ) ) ) )).

fof(t50_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,k5_finsub_1(C))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,C,u1_struct_0(A))
                        & m2_relset_1(E,C,u1_struct_0(A)) )
                     => ( D != k1_xboole_0
                       => k3_lattices(A,B,k2_lattice2(C,A,D,E)) = k2_lattice2(C,A,D,k8_funcop_1(u1_struct_0(A),C,u2_lattices(A),B,E)) ) ) ) ) ) ) )).

fof(t51_lattice2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,u1_struct_0(B))
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,u1_struct_0(k1_lattice2(B)))
                        & m2_relset_1(E,A,u1_struct_0(k1_lattice2(B))) )
                     => ( D = E
                       => ( k2_lattice2(A,B,C,D) = k3_lattice2(A,k1_lattice2(B),C,E)
                          & k3_lattice2(A,B,C,D) = k2_lattice2(A,k1_lattice2(B),C,E) ) ) ) ) ) ) ) )).

fof(t52_lattice2,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(k1_lattice2(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k1_lattice2(A)))
                     => ( ( B = D
                          & C = E )
                       => ( k4_lattices(A,B,C) = k3_lattices(k1_lattice2(A),D,E)
                          & k3_lattices(A,B,C) = k4_lattices(k1_lattice2(A),D,E) ) ) ) ) ) ) ) )).

fof(t53_lattice2,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)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(k1_lattice2(A)))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(k1_lattice2(A)))
                       => ( ( B = D
                            & C = E )
                         => r3_lattices(k1_lattice2(A),E,D) ) ) ) ) ) ) ) )).

fof(t54_lattice2,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(k1_lattice2(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k1_lattice2(A)))
                     => ( ( r3_lattices(k1_lattice2(A),D,E)
                          & B = D
                          & C = E )
                       => r3_lattices(A,C,B) ) ) ) ) ) ) )).

fof(t55_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,B)
             => ! [D] :
                  ( m1_subset_1(D,k5_finsub_1(B))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,u1_struct_0(A))
                        & m2_relset_1(E,B,u1_struct_0(A)) )
                     => ( r2_hidden(C,D)
                       => r3_lattices(A,k3_lattice2(B,A,D,E),k8_funct_2(B,u1_struct_0(A),E,C)) ) ) ) ) ) ) )).

fof(t56_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,k5_finsub_1(C))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,C,u1_struct_0(A))
                        & m2_relset_1(E,C,u1_struct_0(A)) )
                     => ( ? [F] :
                            ( m1_subset_1(F,C)
                            & r2_hidden(F,D)
                            & r3_lattices(A,k8_funct_2(C,u1_struct_0(A),E,F),B) )
                       => r3_lattices(A,k3_lattice2(C,A,D,E),B) ) ) ) ) ) ) )).

fof(t57_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,k5_finsub_1(C))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,C,u1_struct_0(A))
                        & m2_relset_1(E,C,u1_struct_0(A)) )
                     => ( ! [F] :
                            ( m1_subset_1(F,C)
                           => ( r2_hidden(F,D)
                             => k8_funct_2(C,u1_struct_0(A),E,F) = B ) )
                       => ( D = k1_xboole_0
                          | k3_lattice2(C,A,D,E) = B ) ) ) ) ) ) ) )).

fof(t58_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,k5_finsub_1(C))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,C,u1_struct_0(A))
                        & m2_relset_1(E,C,u1_struct_0(A)) )
                     => ( D != k1_xboole_0
                       => k4_lattices(A,B,k3_lattice2(C,A,D,E)) = k3_lattice2(C,A,D,k8_funcop_1(u1_struct_0(A),C,u1_lattices(A),B,E)) ) ) ) ) ) ) )).

fof(t59_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,k5_finsub_1(C))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,C,u1_struct_0(A))
                        & m2_relset_1(E,C,u1_struct_0(A)) )
                     => ( r3_lattices(A,B,k3_lattice2(C,A,D,E))
                       => ! [F] :
                            ( m1_subset_1(F,C)
                           => ( r2_hidden(F,D)
                             => r3_lattices(A,B,k8_funct_2(C,u1_struct_0(A),E,F)) ) ) ) ) ) ) ) ) )).

fof(t60_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(B))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,u1_struct_0(A))
                    & m2_relset_1(D,B,u1_struct_0(A)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,u1_struct_0(A))
                        & m2_relset_1(E,B,u1_struct_0(A)) )
                     => ( k2_partfun1(B,u1_struct_0(A),D,C) = k2_partfun1(B,u1_struct_0(A),E,C)
                       => ( C = k1_xboole_0
                          | k3_lattice2(B,A,C,D) = k3_lattice2(B,A,C,E) ) ) ) ) ) ) ) )).

fof(t61_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,k5_finsub_1(C))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,C,u1_struct_0(A))
                        & m2_relset_1(E,C,u1_struct_0(A)) )
                     => ( ! [F] :
                            ( m1_subset_1(F,C)
                           => ( r2_hidden(F,D)
                             => r3_lattices(A,B,k8_funct_2(C,u1_struct_0(A),E,F)) ) )
                       => ( D = k1_xboole_0
                          | r3_lattices(A,B,k3_lattice2(C,A,D,E)) ) ) ) ) ) ) ) )).

fof(t62_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(B))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,u1_struct_0(A))
                    & m2_relset_1(D,B,u1_struct_0(A)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,u1_struct_0(A))
                        & m2_relset_1(E,B,u1_struct_0(A)) )
                     => ( ! [F] :
                            ( m1_subset_1(F,B)
                           => ( r2_hidden(F,C)
                             => r3_lattices(A,k8_funct_2(B,u1_struct_0(A),D,F),k8_funct_2(B,u1_struct_0(A),E,F)) ) )
                       => ( C = k1_xboole_0
                          | r3_lattices(A,k3_lattice2(B,A,C,D),k3_lattice2(B,A,C,E)) ) ) ) ) ) ) ) )).

fof(t63_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( v13_lattices(A)
      <=> v14_lattices(k1_lattice2(A)) ) ) )).

fof(t64_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( v14_lattices(A)
      <=> v13_lattices(k1_lattice2(A)) ) ) )).

fof(t65_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v11_lattices(A)
          & l3_lattices(A) )
      <=> ( ~ v3_struct_0(k1_lattice2(A))
          & v10_lattices(k1_lattice2(A))
          & v11_lattices(k1_lattice2(A))
          & l3_lattices(k1_lattice2(A)) ) ) ) )).

fof(t66_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => r3_binop_1(u1_struct_0(A),k5_lattices(A),u2_lattices(A)) ) )).

fof(t67_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => v1_setwiseo(u2_lattices(A),u1_struct_0(A)) ) )).

fof(t68_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => k5_lattices(A) = k3_binop_1(u1_struct_0(A),u2_lattices(A)) ) )).

fof(t69_lattice2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v10_lattices(C)
                & v13_lattices(C)
                & l3_lattices(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,u1_struct_0(C))
                    & m2_relset_1(D,A,u1_struct_0(C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,u1_struct_0(C))
                        & m2_relset_1(E,A,u1_struct_0(C)) )
                     => ( k2_partfun1(A,u1_struct_0(C),D,B) = k2_partfun1(A,u1_struct_0(C),E,B)
                       => k2_lattice2(A,C,B,D) = k2_lattice2(A,C,B,E) ) ) ) ) ) ) )).

fof(t70_lattice2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v10_lattices(C)
                & v13_lattices(C)
                & l3_lattices(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,u1_struct_0(C))
                    & m2_relset_1(D,A,u1_struct_0(C)) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ( ! [F] :
                            ( m1_subset_1(F,A)
                           => ( r2_hidden(F,B)
                             => r3_lattices(C,k8_funct_2(A,u1_struct_0(C),D,F),E) ) )
                       => r3_lattices(C,k2_lattice2(A,C,B,D),E) ) ) ) ) ) ) )).

fof(t71_lattice2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v10_lattices(C)
                & v13_lattices(C)
                & l3_lattices(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,u1_struct_0(C))
                    & m2_relset_1(D,A,u1_struct_0(C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,u1_struct_0(C))
                        & m2_relset_1(E,A,u1_struct_0(C)) )
                     => ( ! [F] :
                            ( m1_subset_1(F,A)
                           => ( r2_hidden(F,B)
                             => r3_lattices(C,k8_funct_2(A,u1_struct_0(C),D,F),k8_funct_2(A,u1_struct_0(C),E,F)) ) )
                       => r3_lattices(C,k2_lattice2(A,C,B,D),k2_lattice2(A,C,B,E)) ) ) ) ) ) ) )).

fof(t72_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v14_lattices(A)
        & l3_lattices(A) )
     => r3_binop_1(u1_struct_0(A),k6_lattices(A),u1_lattices(A)) ) )).

fof(t73_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v14_lattices(A)
        & l3_lattices(A) )
     => v1_setwiseo(u1_lattices(A),u1_struct_0(A)) ) )).

fof(t74_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v14_lattices(A)
        & l3_lattices(A) )
     => k6_lattices(A) = k3_binop_1(u1_struct_0(A),u1_lattices(A)) ) )).

fof(t75_lattice2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v10_lattices(C)
                & v14_lattices(C)
                & l3_lattices(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,u1_struct_0(C))
                    & m2_relset_1(D,A,u1_struct_0(C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,u1_struct_0(C))
                        & m2_relset_1(E,A,u1_struct_0(C)) )
                     => ( k2_partfun1(A,u1_struct_0(C),D,B) = k2_partfun1(A,u1_struct_0(C),E,B)
                       => k3_lattice2(A,C,B,D) = k3_lattice2(A,C,B,E) ) ) ) ) ) ) )).

fof(t76_lattice2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v10_lattices(C)
                & v14_lattices(C)
                & l3_lattices(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,u1_struct_0(C))
                    & m2_relset_1(D,A,u1_struct_0(C)) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ( ! [F] :
                            ( m1_subset_1(F,A)
                           => ( r2_hidden(F,B)
                             => r3_lattices(C,E,k8_funct_2(A,u1_struct_0(C),D,F)) ) )
                       => r3_lattices(C,E,k3_lattice2(A,C,B,D)) ) ) ) ) ) ) )).

fof(t77_lattice2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v10_lattices(C)
                & v14_lattices(C)
                & l3_lattices(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,u1_struct_0(C))
                    & m2_relset_1(D,A,u1_struct_0(C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,u1_struct_0(C))
                        & m2_relset_1(E,A,u1_struct_0(C)) )
                     => ( ! [F] :
                            ( m1_subset_1(F,A)
                           => ( r2_hidden(F,B)
                             => r3_lattices(C,k8_funct_2(A,u1_struct_0(C),D,F),k8_funct_2(A,u1_struct_0(C),E,F)) ) )
                       => r3_lattices(C,k3_lattice2(A,C,B,D),k3_lattice2(A,C,B,E)) ) ) ) ) ) ) )).

fof(t78_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => k5_lattices(A) = k6_lattices(k1_lattice2(A)) ) )).

fof(t79_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v14_lattices(A)
        & l3_lattices(A) )
     => k6_lattices(A) = k5_lattices(k1_lattice2(A)) ) )).

fof(t80_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v11_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => r6_binop_1(u1_struct_0(A),u1_lattices(A),u2_lattices(A)) ) )).

fof(t81_lattice2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v10_lattices(C)
                & v11_lattices(C)
                & v13_lattices(C)
                & l3_lattices(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,u1_struct_0(C))
                    & m2_relset_1(D,A,u1_struct_0(C)) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => k2_binop_1(u1_struct_0(C),u1_struct_0(C),u1_struct_0(C),u1_lattices(C),E,k2_lattice2(A,C,B,D)) = k2_lattice2(A,C,B,k8_funcop_1(u1_struct_0(C),A,u1_lattices(C),E,D)) ) ) ) ) ) )).

fof(t82_lattice2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v10_lattices(C)
                & v11_lattices(C)
                & v13_lattices(C)
                & l3_lattices(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,u1_struct_0(C))
                    & m2_relset_1(D,A,u1_struct_0(C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,u1_struct_0(C))
                        & m2_relset_1(E,A,u1_struct_0(C)) )
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(C))
                         => ( ! [G] :
                                ( m1_subset_1(G,A)
                               => ( r2_hidden(G,B)
                                 => k8_funct_2(A,u1_struct_0(C),D,G) = k4_lattices(C,F,k8_funct_2(A,u1_struct_0(C),E,G)) ) )
                           => k4_lattices(C,F,k2_lattice2(A,C,B,E)) = k2_lattice2(A,C,B,D) ) ) ) ) ) ) ) )).

fof(t83_lattice2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v10_lattices(C)
                & v11_lattices(C)
                & v13_lattices(C)
                & l3_lattices(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,u1_struct_0(C))
                    & m2_relset_1(D,A,u1_struct_0(C)) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => k4_lattices(C,E,k2_lattice2(A,C,B,D)) = k2_lattice2(A,C,B,k8_funcop_1(u1_struct_0(C),A,u1_lattices(C),E,D)) ) ) ) ) ) )).

fof(d5_lattice2,axiom,(
    $true )).

fof(d6_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( v1_lattice2(A)
      <=> ( v3_filter_0(A)
          & v13_lattices(A) ) ) ) )).

fof(t84_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v1_lattice2(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_lattices(A,k4_lattices(A,B,D),C)
                    & ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( r3_lattices(A,k4_lattices(A,B,E),C)
                         => r3_lattices(A,E,D) ) ) ) ) ) ) ) )).

fof(t85_lattice2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( v6_group_1(A)
      <=> v6_group_1(k1_lattice2(A)) ) ) )).

fof(dt_k1_lattice2,axiom,(
    ! [A] :
      ( l3_lattices(A)
     => ( v3_lattices(k1_lattice2(A))
        & l3_lattices(k1_lattice2(A)) ) ) )).

fof(dt_k2_lattice2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B)
        & m1_subset_1(C,k5_finsub_1(A))
        & v1_funct_1(D)
        & v1_funct_2(D,A,u1_struct_0(B))
        & m1_relset_1(D,A,u1_struct_0(B)) )
     => m1_subset_1(k2_lattice2(A,B,C,D),u1_struct_0(B)) ) )).

fof(dt_k3_lattice2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B)
        & m1_subset_1(C,k5_finsub_1(A))
        & v1_funct_1(D)
        & v1_funct_2(D,A,u1_struct_0(B))
        & m1_relset_1(D,A,u1_struct_0(B)) )
     => m1_subset_1(k3_lattice2(A,B,C,D),u1_struct_0(B)) ) )).
%------------------------------------------------------------------------------