SET007 Axioms: SET007+375.ax


%------------------------------------------------------------------------------
% File     : SET007+375 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Homomorphisms of Lattices, Finite Join and Finite Meet
% 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    : lattice4 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   82 (   5 unit)
%            Number of atoms       :  659 (  43 equality)
%            Maximal formula depth :   15 (   8 average)
%            Number of connectives :  701 ( 124 ~  ;   0  |; 339  &)
%                                         (  18 <=>; 220 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   35 (   1 propositional; 0-3 arity)
%            Number of functors    :   35 (   1 constant; 0-5 arity)
%            Number of variables   :  230 (   0 singleton; 217 !;  13 ?)
%            Maximal term depth    :    5 (   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_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ? [B] :
          ( m2_lattice4(B,A)
          & ~ v1_xboole_0(B) ) ) )).

fof(fc1_lattice4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ~ v1_xboole_0(k4_lattice4(A,B)) ) )).

fof(t1_lattice4,axiom,(
    $true )).

fof(t2_lattice4,axiom,(
    $true )).

fof(t3_lattice4,axiom,(
    ! [A] :
      ~ ( A != k1_xboole_0
        & ! [B] :
            ~ ( B != k1_xboole_0
              & r1_tarski(B,A)
              & v6_ordinal1(B)
              & ! [C] :
                  ~ ( r2_hidden(C,A)
                    & ! [D] :
                        ( r2_hidden(D,B)
                       => r1_tarski(D,C) ) ) )
        & ! [B] :
            ~ ( r2_hidden(B,A)
              & ! [C] :
                  ~ ( r2_hidden(C,A)
                    & C != B
                    & r1_tarski(B,C) ) ) ) )).

fof(t4_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => v2_filter_0(k1_filter_0(A),A) ) )).

fof(t5_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ! [C] :
              ( m1_filter_0(C,A)
             => ( r1_tarski(B,k3_filter_0(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),B,C)))
                & r1_tarski(C,k3_filter_0(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),B,C))) ) ) ) ) )).

fof(t6_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ~ ( r2_hidden(C,k3_filter_0(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k2_filter_0(A,D),B)))
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r2_hidden(E,B)
                              & r3_lattices(A,k4_lattices(A,D,E),C) ) ) ) ) ) ) ) )).

fof(d1_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( m1_lattice4(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k3_lattices(A,D,E)) = k3_lattices(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E))
                          & k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k4_lattices(A,D,E)) = k4_lattices(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) ) ) ) ) ) ) ) )).

fof(t7_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_lattice4(E,A,B)
                     => ( r3_lattices(A,C,D)
                       => r3_lattices(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,C),k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,D)) ) ) ) ) ) ) )).

fof(d2_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v1_lattice4(C,A,B)
              <=> v2_funct_1(C) ) ) ) ) )).

fof(d3_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v2_lattice4(C,A,B)
              <=> k2_relat_1(C) = u1_struct_0(B) ) ) ) ) )).

fof(t8_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_lattice4(E,A,B)
                     => ( v1_lattice4(E,A,B)
                       => ( r3_lattices(A,C,D)
                        <=> r3_lattices(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,C),k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,D)) ) ) ) ) ) ) ) )).

fof(t9_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v2_lattice4(C,A,B)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ? [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                        & D = k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E) ) ) ) ) ) ) )).

fof(d4_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ! [C] :
              ( m1_lattice4(C,A,B)
             => ( v3_lattice4(C,A,B)
              <=> ( v1_lattice4(C,A,B)
                  & v2_lattice4(C,A,B) ) ) ) ) ) )).

fof(d5_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ( r1_filter_1(A,B)
          <=> ? [C] :
                ( m1_lattice4(C,A,B)
                & v3_lattice4(C,A,B) ) ) ) ) )).

fof(d6_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ! [C] :
              ( m1_lattice4(C,A,B)
             => ( r1_lattice4(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k4_filter_0(A,D,E)) = k4_filter_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) ) ) ) ) ) ) )).

fof(d7_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ! [C] :
              ( m1_lattice4(C,A,B)
             => ( r2_lattice4(A,B,C)
              <=> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k6_lattices(A)) = k6_lattices(B) ) ) ) ) )).

fof(d8_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ! [C] :
              ( m1_lattice4(C,A,B)
             => ( r3_lattice4(A,B,C)
              <=> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k5_lattices(A)) = k5_lattices(B) ) ) ) ) )).

fof(d9_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ! [C] :
              ( m1_lattice4(C,A,B)
             => ( r4_lattice4(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k7_lattices(A,D)) = k7_lattices(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D)) ) ) ) ) ) )).

fof(d10_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( m2_lattice4(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r2_hidden(C,B)
                        & r2_hidden(D,B) )
                     => ( r2_hidden(k4_lattices(A,C,D),B)
                        & r2_hidden(k3_lattices(A,C,D),B) ) ) ) ) ) ) ) )).

fof(t10_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => m2_lattice4(u1_struct_0(A),A) ) )).

fof(t11_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => m2_lattice4(B,A) ) ) )).

fof(d11_lattice4,axiom,(
    $true )).

fof(d12_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
         => k1_lattice4(A,B) = k2_lattice2(u1_struct_0(A),A,B,k7_grcat_1(A)) ) ) )).

fof(d13_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
         => k2_lattice4(A,B) = k3_lattice2(u1_struct_0(A),A,B,k7_grcat_1(A)) ) ) )).

fof(t12_lattice4,axiom,(
    $true )).

fof(t13_lattice4,axiom,(
    $true )).

fof(t14_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
         => k2_lattice4(A,B) = k7_setwiseo(u1_struct_0(A),u1_struct_0(A),u1_lattices(A),B,k7_grcat_1(A)) ) ) )).

fof(t15_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
         => k1_lattice4(A,B) = k7_setwiseo(u1_struct_0(A),u1_struct_0(A),u2_lattices(A),B,k7_grcat_1(A)) ) ) )).

fof(t16_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_lattice4(A,k2_setwiseo(u1_struct_0(A),B)) = B ) ) )).

fof(t17_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k2_lattice4(A,k2_setwiseo(u1_struct_0(A),B)) = B ) ) )).

fof(t18_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & v11_lattices(B)
            & l3_lattices(B) )
         => ! [C] :
              ( m1_lattice4(C,B,A)
             => ( v2_lattice4(C,B,A)
               => v11_lattices(A) ) ) ) ) )).

fof(t19_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & v13_lattices(B)
            & l3_lattices(B) )
         => ! [C] :
              ( m1_lattice4(C,B,A)
             => ( v2_lattice4(C,B,A)
               => ( v13_lattices(A)
                  & r3_lattice4(B,A,C) ) ) ) ) ) )).

fof(t20_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => k2_lattice2(u1_struct_0(A),A,k5_setwiseo(u1_struct_0(A),B,k2_setwiseo(u1_struct_0(A),C)),D) = k3_lattices(A,k2_lattice2(u1_struct_0(A),A,B,D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C)) ) ) ) ) )).

fof(t21_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_lattice4(A,k5_setwiseo(u1_struct_0(A),B,k2_setwiseo(u1_struct_0(A),C))) = k3_lattices(A,k1_lattice4(A,B),C) ) ) ) )).

fof(t22_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(u1_struct_0(A)))
             => k3_lattices(A,k1_lattice4(A,B),k1_lattice4(A,C)) = k1_lattice4(A,k5_setwiseo(u1_struct_0(A),B,C)) ) ) ) )).

fof(t23_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => k1_lattice4(A,k1_setwiseo(u1_struct_0(A))) = k5_lattices(A) ) )).

fof(t24_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m2_lattice4(B,A)
         => ( r2_hidden(k5_lattices(A),B)
           => ! [C] :
                ( m1_subset_1(C,k5_finsub_1(u1_struct_0(A)))
               => ( r1_tarski(C,B)
                 => r2_hidden(k1_lattice4(A,C),B) ) ) ) ) ) )).

fof(t25_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & v14_lattices(B)
            & l3_lattices(B) )
         => ! [C] :
              ( m1_lattice4(C,B,A)
             => ( v2_lattice4(C,B,A)
               => ( v14_lattices(A)
                  & r2_lattice4(B,A,C) ) ) ) ) ) )).

fof(t26_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v14_lattices(A)
        & l3_lattices(A) )
     => k2_lattice4(A,k1_setwiseo(u1_struct_0(A))) = k6_lattices(A) ) )).

fof(t27_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v14_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => k3_lattice2(u1_struct_0(A),A,k5_setwiseo(u1_struct_0(A),B,k2_setwiseo(u1_struct_0(A),C)),D) = k4_lattices(A,k3_lattice2(u1_struct_0(A),A,B,D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C)) ) ) ) ) )).

fof(t28_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v14_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_lattice4(A,k5_setwiseo(u1_struct_0(A),B,k2_setwiseo(u1_struct_0(A),C))) = k4_lattices(A,k2_lattice4(A,B),C) ) ) ) )).

fof(t29_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v14_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => k3_lattice2(u1_struct_0(A),A,k8_setwiseo(u1_struct_0(A),u1_struct_0(A),C,B),D) = k3_lattice2(u1_struct_0(A),A,B,k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C,D)) ) ) ) ) )).

fof(t30_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v14_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(u1_struct_0(A)))
             => k4_lattices(A,k2_lattice4(A,B),k2_lattice4(A,C)) = k2_lattice4(A,k5_setwiseo(u1_struct_0(A),B,C)) ) ) ) )).

fof(t31_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v14_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m2_lattice4(B,A)
         => ( r2_hidden(k6_lattices(A),B)
           => ! [C] :
                ( m1_subset_1(C,k5_finsub_1(u1_struct_0(A)))
               => ( r1_tarski(C,B)
                 => r2_hidden(k2_lattice4(A,C),B) ) ) ) ) ) )).

fof(t32_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v11_lattices(A)
        & v14_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k3_lattices(A,k2_lattice4(A,B),C) = k2_lattice4(A,k8_setwiseo(u1_struct_0(A),u1_struct_0(A),k7_funcop_1(u1_struct_0(A),u1_struct_0(A),u2_lattices(A),k7_grcat_1(A),C),B)) ) ) ) )).

fof(t33_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v15_lattices(A)
        & v16_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & v3_filter_0(B)
            & l3_lattices(B) )
         => ! [C] :
              ( m1_lattice4(C,B,A)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => r3_lattices(A,k4_lattices(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,D),k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,k4_filter_0(B,D,E))),k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,E)) ) ) ) ) ) )).

fof(t34_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v15_lattices(A)
        & v16_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & v3_filter_0(B)
            & l3_lattices(B) )
         => ! [C] :
              ( m1_lattice4(C,B,A)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( v1_lattice4(C,B,A)
                              & r3_lattices(A,k4_lattices(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,D),k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,E)),k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,F)) )
                           => r3_lattices(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,E),k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,k4_filter_0(B,D,F))) ) ) ) ) ) ) ) )).

fof(t35_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v15_lattices(A)
        & v16_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & v3_filter_0(B)
            & l3_lattices(B) )
         => ! [C] :
              ( m1_lattice4(C,B,A)
             => ( v3_lattice4(C,B,A)
               => ( v3_filter_0(A)
                  & r1_lattice4(B,A,C) ) ) ) ) ) )).

fof(t36_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => k7_lattices(A,k6_lattices(A)) = k5_lattices(A) ) )).

fof(t37_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => k7_lattices(A,k5_lattices(A)) = k6_lattices(A) ) )).

fof(t38_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v15_lattices(A)
        & v16_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & v17_lattices(B)
            & l3_lattices(B) )
         => ! [C] :
              ( m1_lattice4(C,B,A)
             => ( v2_lattice4(C,B,A)
               => ( v17_lattices(A)
                  & r4_lattice4(B,A,C) ) ) ) ) ) )).

fof(d14_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( m3_lattice4(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r2_hidden(C,B)
                        & r2_hidden(D,B) )
                     => ( r2_hidden(k4_lattices(A,C,D),B)
                        & r2_hidden(k7_lattices(A,C),B) ) ) ) ) ) ) ) )).

fof(t39_lattice4,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))
             => ! [D] :
                  ( m3_lattice4(D,A)
                 => ( ( r2_hidden(B,D)
                      & r2_hidden(C,D) )
                   => r2_hidden(k3_lattices(A,B,C),D) ) ) ) ) ) )).

fof(t40_lattice4,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))
             => ! [D] :
                  ( m3_lattice4(D,A)
                 => ( ( r2_hidden(B,D)
                      & r2_hidden(C,D) )
                   => r2_hidden(k4_filter_0(A,B,C),D) ) ) ) ) ) )).

fof(t41_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => m3_lattice4(u1_struct_0(A),A) ) )).

fof(t42_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m3_lattice4(B,A)
         => m2_lattice4(B,A) ) ) )).

fof(d15_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m3_lattice4(C,A)
             => ( C = k3_lattice4(A,B)
              <=> ( r1_tarski(B,C)
                  & ! [D] :
                      ( m3_lattice4(D,A)
                     => ( r1_tarski(B,D)
                       => r1_tarski(C,D) ) ) ) ) ) ) ) )).

fof(t43_lattice4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & v17_lattices(B)
        & l3_lattices(B) )
     => ! [C] :
          ( ( ~ v1_xboole_0(C)
            & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
         => ( r2_hidden(A,k4_lattice4(B,C))
          <=> ? [D] :
                ( m1_subset_1(D,u1_struct_0(B))
                & ? [E] :
                    ( m1_subset_1(E,u1_struct_0(B))
                    & A = k4_filter_0(B,D,E)
                    & r2_hidden(D,C)
                    & r2_hidden(E,C) ) ) ) ) ) )).

fof(t44_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,k4_lattice4(A,B))
              <=> ? [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                    & ? [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                        & C = k3_lattices(A,k7_lattices(A,D),E)
                        & r2_hidden(D,B)
                        & r2_hidden(E,B) ) ) ) ) ) ) )).

fof(d17_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( B = k5_lattice4(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) = k7_lattices(A,C) ) ) ) ) )).

fof(t45_lattice4,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,k5_finsub_1(u1_struct_0(A)))
             => k2_lattice2(u1_struct_0(A),A,k5_setwiseo(u1_struct_0(A),C,k2_setwiseo(u1_struct_0(A),B)),k5_lattice4(A)) = k3_lattices(A,k2_lattice2(u1_struct_0(A),A,C,k5_lattice4(A)),k7_lattices(A,B)) ) ) ) )).

fof(t46_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
         => k7_lattices(A,k1_lattice4(A,B)) = k3_lattice2(u1_struct_0(A),A,B,k5_lattice4(A)) ) ) )).

fof(t47_lattice4,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,k5_finsub_1(u1_struct_0(A)))
             => k3_lattice2(u1_struct_0(A),A,k5_setwiseo(u1_struct_0(A),C,k2_setwiseo(u1_struct_0(A),B)),k5_lattice4(A)) = k4_lattices(A,k3_lattice2(u1_struct_0(A),A,C,k5_lattice4(A)),k7_lattices(A,B)) ) ) ) )).

fof(t48_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A)))
         => k7_lattices(A,k2_lattice4(A,B)) = k2_lattice2(u1_struct_0(A),A,B,k5_lattice4(A)) ) ) )).

fof(t49_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m2_lattice4(B,A) )
         => ( ( r2_hidden(k5_lattices(A),B)
              & r2_hidden(k6_lattices(A),B) )
           => ! [C] :
                ( m1_subset_1(C,k5_finsub_1(u1_struct_0(A)))
               => ~ ( r1_tarski(C,k4_lattice4(A,B))
                    & ! [D] :
                        ( m1_subset_1(D,k5_finsub_1(u1_struct_0(A)))
                       => ~ ( r1_tarski(D,k4_lattice4(A,B))
                            & k2_lattice2(u1_struct_0(A),A,C,k5_lattice4(A)) = k2_lattice4(A,D) ) ) ) ) ) ) ) )).

fof(dt_m1_lattice4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B) )
     => ! [C] :
          ( m1_lattice4(C,A,B)
         => ( v1_funct_1(C)
            & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
            & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) )).

fof(existence_m1_lattice4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B) )
     => ? [C] : m1_lattice4(C,A,B) ) )).

fof(dt_m2_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m2_lattice4(B,A)
         => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(existence_m2_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ? [B] : m2_lattice4(B,A) ) )).

fof(dt_m3_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m3_lattice4(B,A)
         => ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).

fof(existence_m3_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ? [B] : m3_lattice4(B,A) ) )).

fof(dt_k1_lattice4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) )
     => m1_subset_1(k1_lattice4(A,B),u1_struct_0(A)) ) )).

fof(dt_k2_lattice4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) )
     => m1_subset_1(k2_lattice4(A,B),u1_struct_0(A)) ) )).

fof(dt_k3_lattice4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m3_lattice4(k3_lattice4(A,B),A) ) )).

fof(dt_k4_lattice4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k4_lattice4(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k5_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ( v1_funct_1(k5_lattice4(A))
        & v1_funct_2(k5_lattice4(A),u1_struct_0(A),u1_struct_0(A))
        & m2_relset_1(k5_lattice4(A),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(d16_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => k4_lattice4(A,B) = a_2_0_lattice4(A,B) ) ) )).

fof(t50_lattice4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m2_lattice4(B,A) )
         => ( ( r2_hidden(k5_lattices(A),B)
              & r2_hidden(k6_lattices(A),B) )
           => a_2_1_lattice4(A,B) = k3_lattice4(A,B) ) ) ) )).

fof(fraenkel_a_2_0_lattice4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & v17_lattices(B)
        & l3_lattices(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_0_lattice4(B,C))
      <=> ? [D,E] :
            ( m1_subset_1(D,u1_struct_0(B))
            & m1_subset_1(E,u1_struct_0(B))
            & A = k4_filter_0(B,D,E)
            & r2_hidden(D,C)
            & r2_hidden(E,C) ) ) ) )).

fof(fraenkel_a_2_1_lattice4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & v17_lattices(B)
        & l3_lattices(B)
        & ~ v1_xboole_0(C)
        & m2_lattice4(C,B) )
     => ( r2_hidden(A,a_2_1_lattice4(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k5_finsub_1(u1_struct_0(B)))
            & A = k2_lattice4(B,D)
            & r1_tarski(D,k4_lattice4(B,C)) ) ) ) )).
%------------------------------------------------------------------------------