SET007 Axioms: SET007+205.ax


%------------------------------------------------------------------------------
% File     : SET007+205 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Introduction to Lattice Theory
% 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    : lattices [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  127 (  30 unit)
%            Number of atoms       :  680 (  65 equality)
%            Maximal formula depth :   17 (   6 average)
%            Number of connectives :  644 (  91 ~  ;   0  |; 335  &)
%                                         (  23 <=>; 195 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   33 (   1 propositional; 0-3 arity)
%            Number of functors    :   15 (   0 constant; 1-6 arity)
%            Number of variables   :  231 (   0 singleton; 212 !;  19 ?)
%            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(rc1_lattices,axiom,(
    ? [A] :
      ( l1_lattices(A)
      & v1_lattices(A) ) )).

fof(rc2_lattices,axiom,(
    ? [A] :
      ( l2_lattices(A)
      & v2_lattices(A) ) )).

fof(rc3_lattices,axiom,(
    ? [A] :
      ( l3_lattices(A)
      & v3_lattices(A) ) )).

fof(fc1_lattices,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ( ~ v3_struct_0(g2_lattices(A,B))
        & v2_lattices(g2_lattices(A,B)) ) ) )).

fof(fc2_lattices,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ( ~ v3_struct_0(g1_lattices(A,B))
        & v1_lattices(g1_lattices(A,B)) ) ) )).

fof(fc3_lattices,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A) )
     => ( ~ v3_struct_0(g3_lattices(A,B,C))
        & v3_lattices(g3_lattices(A,B,C)) ) ) )).

fof(rc4_lattices,axiom,(
    ? [A] :
      ( l2_lattices(A)
      & ~ v3_struct_0(A)
      & v2_lattices(A) ) )).

fof(rc5_lattices,axiom,(
    ? [A] :
      ( l1_lattices(A)
      & ~ v3_struct_0(A)
      & v1_lattices(A) ) )).

fof(rc6_lattices,axiom,(
    ? [A] :
      ( l3_lattices(A)
      & ~ v3_struct_0(A)
      & v3_lattices(A) ) )).

fof(cc1_lattices,axiom,(
    ! [A] :
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(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) ) ) ) )).

fof(cc2_lattices,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) )
       => ( ~ v3_struct_0(A)
          & v10_lattices(A) ) ) ) )).

fof(rc7_lattices,axiom,(
    ? [A] :
      ( l2_lattices(A)
      & ~ v3_struct_0(A)
      & v2_lattices(A)
      & v4_lattices(A)
      & v5_lattices(A) ) )).

fof(rc8_lattices,axiom,(
    ? [A] :
      ( l1_lattices(A)
      & ~ v3_struct_0(A)
      & v1_lattices(A)
      & v6_lattices(A)
      & v7_lattices(A) ) )).

fof(rc9_lattices,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) ) )).

fof(rc10_lattices,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)
      & v11_lattices(A)
      & v12_lattices(A)
      & v13_lattices(A)
      & v14_lattices(A) ) )).

fof(cc3_lattices,axiom,(
    ! [A] :
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v13_lattices(A)
          & v14_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v15_lattices(A) ) ) ) )).

fof(cc4_lattices,axiom,(
    ! [A] :
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v15_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v13_lattices(A)
          & v14_lattices(A) ) ) ) )).

fof(rc11_lattices,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)
      & v14_lattices(A)
      & v15_lattices(A) ) )).

fof(rc12_lattices,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)
      & v14_lattices(A)
      & v15_lattices(A)
      & v16_lattices(A) ) )).

fof(cc5_lattices,axiom,(
    ! [A] :
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v17_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v11_lattices(A)
          & v13_lattices(A)
          & v14_lattices(A)
          & v15_lattices(A)
          & v16_lattices(A) ) ) ) )).

fof(cc6_lattices,axiom,(
    ! [A] :
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v11_lattices(A)
          & v15_lattices(A)
          & v16_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v17_lattices(A) ) ) ) )).

fof(rc13_lattices,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)
      & v11_lattices(A)
      & v13_lattices(A)
      & v14_lattices(A)
      & v15_lattices(A)
      & v16_lattices(A)
      & v17_lattices(A) ) )).

fof(cc7_lattices,axiom,(
    ! [A] :
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(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)
          & v12_lattices(A) ) ) ) )).

fof(d1_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_lattices(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u2_lattices(A),B,C) ) ) ) )).

fof(d2_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_lattices(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_lattices(A),B,C) ) ) ) )).

fof(d3_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_lattices(A,B,C)
              <=> k1_lattices(A,B,C) = C ) ) ) ) )).

fof(d4_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_lattices(A) )
     => ( v4_lattices(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k1_lattices(A,B,C) = k1_lattices(A,C,B) ) ) ) ) )).

fof(d5_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_lattices(A) )
     => ( v5_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))
                   => k1_lattices(A,B,k1_lattices(A,C,D)) = k1_lattices(A,k1_lattices(A,B,C),D) ) ) ) ) ) )).

fof(d6_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_lattices(A) )
     => ( v6_lattices(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k2_lattices(A,B,C) = k2_lattices(A,C,B) ) ) ) ) )).

fof(d7_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_lattices(A) )
     => ( v7_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))
                   => k2_lattices(A,B,k2_lattices(A,C,D)) = k2_lattices(A,k2_lattices(A,B,C),D) ) ) ) ) ) )).

fof(d8_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( v8_lattices(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k1_lattices(A,k2_lattices(A,B,C),C) = C ) ) ) ) )).

fof(d9_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( v9_lattices(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k2_lattices(A,B,k1_lattices(A,B,C)) = B ) ) ) ) )).

fof(d10_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( v10_lattices(A)
      <=> ( v4_lattices(A)
          & v5_lattices(A)
          & v8_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v9_lattices(A) ) ) ) )).

fof(d11_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( v11_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))
                   => k2_lattices(A,B,k1_lattices(A,C,D)) = k1_lattices(A,k2_lattices(A,B,C),k2_lattices(A,B,D)) ) ) ) ) ) )).

fof(d12_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( v12_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))
                   => ( r1_lattices(A,B,D)
                     => k1_lattices(A,B,k2_lattices(A,C,D)) = k2_lattices(A,k1_lattices(A,B,C),D) ) ) ) ) ) ) )).

fof(d13_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_lattices(A) )
     => ( v13_lattices(A)
      <=> ? [B] :
            ( m1_subset_1(B,u1_struct_0(A))
            & ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( k2_lattices(A,B,C) = B
                  & k2_lattices(A,C,B) = B ) ) ) ) ) )).

fof(d14_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_lattices(A) )
     => ( v14_lattices(A)
      <=> ? [B] :
            ( m1_subset_1(B,u1_struct_0(A))
            & ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( k1_lattices(A,B,C) = B
                  & k1_lattices(A,C,B) = B ) ) ) ) ) )).

fof(d15_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( v15_lattices(A)
      <=> ( v13_lattices(A)
          & v14_lattices(A) ) ) ) )).

fof(d16_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_lattices(A) )
     => ( v13_lattices(A)
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ( B = k5_lattices(A)
            <=> ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ( k2_lattices(A,B,C) = B
                    & k2_lattices(A,C,B) = B ) ) ) ) ) ) )).

fof(d17_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_lattices(A) )
     => ( v14_lattices(A)
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ( B = k6_lattices(A)
            <=> ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ( k1_lattices(A,B,C) = B
                    & k1_lattices(A,C,B) = B ) ) ) ) ) ) )).

fof(d18_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_lattices(A,B,C)
              <=> ( k1_lattices(A,B,C) = k6_lattices(A)
                  & k1_lattices(A,C,B) = k6_lattices(A)
                  & k2_lattices(A,B,C) = k5_lattices(A)
                  & k2_lattices(A,C,B) = k5_lattices(A) ) ) ) ) ) )).

fof(d19_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( v16_lattices(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ? [C] :
                ( m1_subset_1(C,u1_struct_0(A))
                & r2_lattices(A,C,B) ) ) ) ) )).

fof(d20_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( v17_lattices(A)
      <=> ( v15_lattices(A)
          & v16_lattices(A)
          & v11_lattices(A) ) ) ) )).

fof(t1_lattices,axiom,(
    $true )).

fof(t2_lattices,axiom,(
    $true )).

fof(t3_lattices,axiom,(
    $true )).

fof(t4_lattices,axiom,(
    $true )).

fof(t5_lattices,axiom,(
    $true )).

fof(t6_lattices,axiom,(
    $true )).

fof(t7_lattices,axiom,(
    $true )).

fof(t8_lattices,axiom,(
    $true )).

fof(t9_lattices,axiom,(
    $true )).

fof(t10_lattices,axiom,(
    $true )).

fof(t11_lattices,axiom,(
    $true )).

fof(t12_lattices,axiom,(
    $true )).

fof(t13_lattices,axiom,(
    $true )).

fof(t14_lattices,axiom,(
    $true )).

fof(t15_lattices,axiom,(
    $true )).

fof(t16_lattices,axiom,(
    $true )).

fof(t17_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & v8_lattices(A)
        & v9_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_lattices(A,B,B) = B ) ) )).

fof(t18_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & v8_lattices(A)
        & v9_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k4_lattices(A,B,B) = B ) ) )).

fof(t19_lattices,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))
                   => k4_lattices(A,B,k3_lattices(A,C,D)) = k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,B,D)) ) ) )
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k3_lattices(A,B,k4_lattices(A,C,D)) = k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,B,D)) ) ) ) ) ) )).

fof(t20_lattices,axiom,(
    $true )).

fof(t21_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v8_lattices(A)
        & v9_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_lattices(A,B,C)
              <=> k2_lattices(A,B,C) = B ) ) ) ) )).

fof(t22_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v5_lattices(A)
        & v6_lattices(A)
        & v8_lattices(A)
        & v9_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_lattices(A,B,k1_lattices(A,B,C)) ) ) ) )).

fof(t23_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & v8_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_lattices(A,k4_lattices(A,B,C),B) ) ) ) )).

fof(t24_lattices,axiom,(
    $true )).

fof(t25_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v5_lattices(A)
        & l2_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))
                 => ( ( r1_lattices(A,B,C)
                      & r1_lattices(A,C,D) )
                   => r1_lattices(A,B,D) ) ) ) ) ) )).

fof(t26_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & l2_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( r1_lattices(A,B,C)
                  & r1_lattices(A,C,B) )
               => B = C ) ) ) ) )).

fof(t27_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v7_lattices(A)
        & v8_lattices(A)
        & v9_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))
                 => ( r1_lattices(A,B,C)
                   => r1_lattices(A,k2_lattices(A,B,D),k2_lattices(A,C,D)) ) ) ) ) ) )).

fof(t28_lattices,axiom,(
    $true )).

fof(t29_lattices,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))
                   => k3_lattices(A,k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,C,D)),k4_lattices(A,D,B)) = k4_lattices(A,k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,C,D)),k3_lattices(A,D,B)) ) ) )
       => v11_lattices(A) ) ) )).

fof(t30_lattices,axiom,(
    $true )).

fof(t31_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v11_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))
                 => k3_lattices(A,B,k4_lattices(A,C,D)) = k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,B,D)) ) ) ) ) )).

fof(t32_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v11_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))
                 => ( ( k4_lattices(A,B,C) = k4_lattices(A,B,D)
                      & k3_lattices(A,B,C) = k3_lattices(A,B,D) )
                   => C = D ) ) ) ) ) )).

fof(t33_lattices,axiom,(
    $true )).

fof(t34_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v11_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))
                 => k4_lattices(A,k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,C,D)),k3_lattices(A,D,B)) = k3_lattices(A,k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,C,D)),k4_lattices(A,D,B)) ) ) ) ) )).

fof(t35_lattices,axiom,(
    $true )).

fof(t36_lattices,axiom,(
    $true )).

fof(t37_lattices,axiom,(
    $true )).

fof(t38_lattices,axiom,(
    $true )).

fof(t39_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k3_lattices(A,k5_lattices(A),B) = B ) ) )).

fof(t40_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k4_lattices(A,k5_lattices(A),B) = k5_lattices(A) ) ) )).

fof(t41_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r3_lattices(A,k5_lattices(A),B) ) ) )).

fof(t42_lattices,axiom,(
    $true )).

fof(t43_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v14_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k4_lattices(A,k6_lattices(A),B) = B ) ) )).

fof(t44_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v14_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k3_lattices(A,k6_lattices(A),B) = k6_lattices(A) ) ) )).

fof(t45_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v14_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r3_lattices(A,B,k6_lattices(A)) ) ) )).

fof(d21_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( ( ~ v3_struct_0(A)
              & v10_lattices(A)
              & v11_lattices(A)
              & v16_lattices(A)
              & l3_lattices(A) )
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( C = k7_lattices(A,B)
                <=> r2_lattices(A,C,B) ) ) ) ) ) )).

fof(t46_lattices,axiom,(
    $true )).

fof(t47_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k4_lattices(A,k7_lattices(A,B),B) = k5_lattices(A) ) ) )).

fof(t48_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k3_lattices(A,k7_lattices(A,B),B) = k6_lattices(A) ) ) )).

fof(t49_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k7_lattices(A,k7_lattices(A,B)) = B ) ) )).

fof(t50_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k7_lattices(A,k4_lattices(A,B,C)) = k3_lattices(A,k7_lattices(A,B),k7_lattices(A,C)) ) ) ) )).

fof(t51_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k7_lattices(A,k3_lattices(A,B,C)) = k4_lattices(A,k7_lattices(A,B),k7_lattices(A,C)) ) ) ) )).

fof(t52_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_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) = k5_lattices(A)
              <=> r3_lattices(A,B,k7_lattices(A,C)) ) ) ) ) )).

fof(t53_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_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_lattices(A,k7_lattices(A,C),k7_lattices(A,B)) ) ) ) ) )).

fof(dt_l1_lattices,axiom,(
    ! [A] :
      ( l1_lattices(A)
     => l1_struct_0(A) ) )).

fof(existence_l1_lattices,axiom,(
    ? [A] : l1_lattices(A) )).

fof(dt_l2_lattices,axiom,(
    ! [A] :
      ( l2_lattices(A)
     => l1_struct_0(A) ) )).

fof(existence_l2_lattices,axiom,(
    ? [A] : l2_lattices(A) )).

fof(dt_l3_lattices,axiom,(
    ! [A] :
      ( l3_lattices(A)
     => ( l1_lattices(A)
        & l2_lattices(A) ) ) )).

fof(existence_l3_lattices,axiom,(
    ? [A] : l3_lattices(A) )).

fof(abstractness_v1_lattices,axiom,(
    ! [A] :
      ( l1_lattices(A)
     => ( v1_lattices(A)
       => A = g1_lattices(u1_struct_0(A),u1_lattices(A)) ) ) )).

fof(abstractness_v2_lattices,axiom,(
    ! [A] :
      ( l2_lattices(A)
     => ( v2_lattices(A)
       => A = g2_lattices(u1_struct_0(A),u2_lattices(A)) ) ) )).

fof(abstractness_v3_lattices,axiom,(
    ! [A] :
      ( l3_lattices(A)
     => ( v3_lattices(A)
       => A = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ) ) )).

fof(reflexivity_r3_lattices,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & v8_lattices(A)
        & v9_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => r3_lattices(A,B,B) ) )).

fof(redefinition_r3_lattices,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & v8_lattices(A)
        & v9_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r3_lattices(A,B,C)
      <=> r1_lattices(A,B,C) ) ) )).

fof(dt_k1_lattices,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l2_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k1_lattices(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k2_lattices,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k2_lattices(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k3_lattices,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & l2_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k3_lattices(A,B,C),u1_struct_0(A)) ) )).

fof(commutativity_k3_lattices,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & l2_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k3_lattices(A,B,C) = k3_lattices(A,C,B) ) )).

fof(redefinition_k3_lattices,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & l2_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k3_lattices(A,B,C) = k1_lattices(A,B,C) ) )).

fof(dt_k4_lattices,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & l1_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k4_lattices(A,B,C),u1_struct_0(A)) ) )).

fof(commutativity_k4_lattices,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & l1_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_lattices(A,B,C) = k4_lattices(A,C,B) ) )).

fof(redefinition_k4_lattices,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & l1_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_lattices(A,B,C) = k2_lattices(A,B,C) ) )).

fof(dt_k5_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_lattices(A) )
     => m1_subset_1(k5_lattices(A),u1_struct_0(A)) ) )).

fof(dt_k6_lattices,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_lattices(A) )
     => m1_subset_1(k6_lattices(A),u1_struct_0(A)) ) )).

fof(dt_k7_lattices,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k7_lattices(A,B),u1_struct_0(A)) ) )).

fof(dt_u1_lattices,axiom,(
    ! [A] :
      ( l1_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))
        & m2_relset_1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) )).

fof(dt_u2_lattices,axiom,(
    ! [A] :
      ( l2_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))
        & m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) )).

fof(dt_g1_lattices,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ( v1_lattices(g1_lattices(A,B))
        & l1_lattices(g1_lattices(A,B)) ) ) )).

fof(free_g1_lattices,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ! [C,D] :
          ( g1_lattices(A,B) = g1_lattices(C,D)
         => ( A = C
            & B = D ) ) ) )).

fof(dt_g2_lattices,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ( v2_lattices(g2_lattices(A,B))
        & l2_lattices(g2_lattices(A,B)) ) ) )).

fof(free_g2_lattices,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ! [C,D] :
          ( g2_lattices(A,B) = g2_lattices(C,D)
         => ( A = C
            & B = D ) ) ) )).

fof(dt_g3_lattices,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A) )
     => ( v3_lattices(g3_lattices(A,B,C))
        & l3_lattices(g3_lattices(A,B,C)) ) ) )).

fof(free_g3_lattices,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A) )
     => ! [D,E,F] :
          ( g3_lattices(A,B,C) = g3_lattices(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) )).
%------------------------------------------------------------------------------