SET007 Axioms: SET007+295.ax


%------------------------------------------------------------------------------
% File     : SET007+295 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Filters - Part II.
% Version  : [Urb08] axioms.
% English  : Quotient Lattices Modulo Filters and Direct Product of Two
%            Lattices

% 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    : filter_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  103 (   0 unit)
%            Number of atoms       :  994 (  46 equality)
%            Maximal formula depth :   21 (  10 average)
%            Number of connectives : 1051 ( 160 ~  ;   0  |; 510  &)
%                                         (  29 <=>; 352 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   53 (   0 propositional; 1-3 arity)
%            Number of functors    :   57 (  12 constant; 0-6 arity)
%            Number of variables   :  367 (   0 singleton; 363 !;   4 ?)
%            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_filter_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A) )
     => ~ v1_xboole_0(k7_eqrel_1(A,B)) ) )).

fof(fc2_filter_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A)
        & ~ v3_struct_0(B)
        & l3_lattices(B) )
     => ( ~ v3_struct_0(k8_filter_1(A,B))
        & v3_lattices(k8_filter_1(A,B)) ) ) )).

fof(fc3_filter_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B) )
     => ( ~ v3_struct_0(k8_filter_1(A,B))
        & v3_lattices(k8_filter_1(A,B))
        & v4_lattices(k8_filter_1(A,B))
        & v5_lattices(k8_filter_1(A,B))
        & v6_lattices(k8_filter_1(A,B))
        & v7_lattices(k8_filter_1(A,B))
        & v8_lattices(k8_filter_1(A,B))
        & v9_lattices(k8_filter_1(A,B))
        & v10_lattices(k8_filter_1(A,B)) ) ) )).

fof(t1_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ! [C] :
              ( m1_filter_0(C,A)
             => m1_filter_0(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) )).

fof(t2_filter_1,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_filter_0(A,B) = k2_filter_0(A,C)
               => B = C ) ) ) ) )).

fof(d1_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,A)
                & m2_relset_1(C,A,A) )
             => ( m1_filter_1(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,A)
                   => ! [E] :
                        ( m1_subset_1(E,A)
                       => ( r2_hidden(k1_domain_1(A,A,D,E),B)
                         => r2_hidden(k1_domain_1(A,A,k8_funct_2(A,A,C,D),k8_funct_2(A,A,C,E)),B) ) ) ) ) ) ) ) )).

fof(d2_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ! [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) )
             => ( m2_filter_1(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,A)
                   => ! [E] :
                        ( m1_subset_1(E,A)
                       => ! [F] :
                            ( m1_subset_1(F,A)
                           => ! [G] :
                                ( m1_subset_1(G,A)
                               => ( ( r2_hidden(k1_domain_1(A,A,D,E),B)
                                    & r2_hidden(k1_domain_1(A,A,F,G),B) )
                                 => r2_hidden(k1_domain_1(A,A,k2_binop_1(A,A,A,C,D,F),k2_binop_1(A,A,A,C,E,G)),B) ) ) ) ) ) ) ) ) ) )).

fof(d3_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v3_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,A)
                & m2_relset_1(C,A,A) )
             => ( m1_filter_1(C,A,B)
               => ! [D] :
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,k8_eqrel_1(A,B),k8_eqrel_1(A,B))
                      & m2_relset_1(D,k8_eqrel_1(A,B),k8_eqrel_1(A,B)) )
                   => ( D = k3_filter_1(A,B,C)
                    <=> ! [E,F] :
                          ( ( r2_hidden(E,k8_eqrel_1(A,B))
                            & r2_hidden(F,E) )
                         => k1_funct_1(D,E) = k6_eqrel_1(A,B,k1_funct_1(C,F)) ) ) ) ) ) ) ) )).

fof(d4_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v3_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,A,A)
            & m2_relset_1(B,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) )
             => ( m2_filter_1(C,A,B)
               => ! [D] :
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,k2_zfmisc_1(k8_eqrel_1(A,B),k8_eqrel_1(A,B)),k8_eqrel_1(A,B))
                      & m2_relset_1(D,k2_zfmisc_1(k8_eqrel_1(A,B),k8_eqrel_1(A,B)),k8_eqrel_1(A,B)) )
                   => ( D = k4_filter_1(A,B,C)
                    <=> ! [E,F,G,H] :
                          ( ( r2_hidden(E,k8_eqrel_1(A,B))
                            & r2_hidden(F,k8_eqrel_1(A,B))
                            & r2_hidden(G,E)
                            & r2_hidden(H,F) )
                         => k1_binop_1(D,E,F) = k6_eqrel_1(A,B,k1_binop_1(C,G,H)) ) ) ) ) ) ) ) )).

fof(t3_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v3_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m2_filter_1(E,A,B)
                     => k2_binop_1(k8_eqrel_1(A,B),k8_eqrel_1(A,B),k8_eqrel_1(A,B),k4_filter_1(A,B,E),k2_filter_1(A,B,C),k2_filter_1(A,B,D)) = k2_filter_1(A,B,k2_binop_1(A,A,A,E,C,D)) ) ) ) ) ) )).

fof(t4_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v3_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( m2_filter_1(C,A,B)
             => ( v1_binop_1(C,A)
               => v1_binop_1(k4_filter_1(A,B,C),k8_eqrel_1(A,B)) ) ) ) ) )).

fof(t5_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v3_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( m2_filter_1(C,A,B)
             => ( v2_binop_1(C,A)
               => v2_binop_1(k4_filter_1(A,B,C),k8_eqrel_1(A,B)) ) ) ) ) )).

fof(t6_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v3_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m2_filter_1(D,A,B)
                 => ( r1_binop_1(A,C,D)
                   => r1_binop_1(k8_eqrel_1(A,B),k2_filter_1(A,B,C),k4_filter_1(A,B,D)) ) ) ) ) ) )).

fof(t7_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v3_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m2_filter_1(D,A,B)
                 => ( r2_binop_1(A,C,D)
                   => r2_binop_1(k8_eqrel_1(A,B),k2_filter_1(A,B,C),k4_filter_1(A,B,D)) ) ) ) ) ) )).

fof(t8_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v3_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m2_filter_1(D,A,B)
                 => ( r3_binop_1(A,C,D)
                   => r3_binop_1(k8_eqrel_1(A,B),k2_filter_1(A,B,C),k4_filter_1(A,B,D)) ) ) ) ) ) )).

fof(t9_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v3_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( m2_filter_1(C,A,B)
             => ! [D] :
                  ( m2_filter_1(D,A,B)
                 => ( r4_binop_1(A,C,D)
                   => r4_binop_1(k8_eqrel_1(A,B),k4_filter_1(A,B,C),k4_filter_1(A,B,D)) ) ) ) ) ) )).

fof(t10_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v3_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( m2_filter_1(C,A,B)
             => ! [D] :
                  ( m2_filter_1(D,A,B)
                 => ( r5_binop_1(A,C,D)
                   => r5_binop_1(k8_eqrel_1(A,B),k4_filter_1(A,B,C),k4_filter_1(A,B,D)) ) ) ) ) ) )).

fof(t11_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v3_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( m2_filter_1(C,A,B)
             => ! [D] :
                  ( m2_filter_1(D,A,B)
                 => ( r6_binop_1(A,C,D)
                   => r6_binop_1(k8_eqrel_1(A,B),k4_filter_1(A,B,C),k4_filter_1(A,B,D)) ) ) ) ) ) )).

fof(t12_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v3_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( m2_filter_1(C,A,B)
             => ! [D] :
                  ( m2_filter_1(D,A,B)
                 => ( r1_lattice2(A,C,D)
                   => r1_lattice2(k8_eqrel_1(A,B),k4_filter_1(A,B,C),k4_filter_1(A,B,D)) ) ) ) ) ) )).

fof(t13_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => m2_filter_1(u2_lattices(A),u1_struct_0(A),k11_filter_0(A,B)) ) ) )).

fof(t14_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => m2_filter_1(u1_lattices(A),u1_struct_0(A),k11_filter_0(A,B)) ) ) )).

fof(d5_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ( ( ~ v3_struct_0(A)
              & v10_lattices(A)
              & v3_filter_0(A)
              & l3_lattices(A) )
           => ! [C] :
                ( ( ~ v3_struct_0(C)
                  & v3_lattices(C)
                  & v10_lattices(C)
                  & l3_lattices(C) )
               => ( C = k5_filter_1(A,B)
                <=> ! [D] :
                      ( ( v3_relat_2(D)
                        & v8_relat_2(D)
                        & v1_partfun1(D,u1_struct_0(A),u1_struct_0(A))
                        & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                     => ( D = k10_filter_0(A,B)
                       => C = g3_lattices(k8_eqrel_1(u1_struct_0(A),D),k4_filter_1(u1_struct_0(A),D,u2_lattices(A)),k4_filter_1(u1_struct_0(A),D,u1_lattices(A))) ) ) ) ) ) ) ) )).

fof(d6_filter_1,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))
             => ( ( ~ v3_struct_0(A)
                  & v10_lattices(A)
                  & v3_filter_0(A)
                  & l3_lattices(A) )
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(k5_filter_1(A,B)))
                   => ( D = k6_filter_1(A,B,C)
                    <=> ! [E] :
                          ( ( v3_relat_2(E)
                            & v8_relat_2(E)
                            & v1_partfun1(E,u1_struct_0(A),u1_struct_0(A))
                            & m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
                         => ( E = k10_filter_0(A,B)
                           => D = k2_filter_1(u1_struct_0(A),E,C) ) ) ) ) ) ) ) ) )).

fof(t15_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(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))
                 => ( k3_lattices(k5_filter_1(A,B),k6_filter_1(A,B,C),k6_filter_1(A,B,D)) = k6_filter_1(A,B,k3_lattices(A,C,D))
                    & k4_lattices(k5_filter_1(A,B),k6_filter_1(A,B,C),k6_filter_1(A,B,D)) = k6_filter_1(A,B,k4_lattices(A,C,D)) ) ) ) ) ) )).

fof(t16_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(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))
                 => ( r3_lattices(k5_filter_1(A,B),k6_filter_1(A,B,C),k6_filter_1(A,B,D))
                  <=> r2_hidden(k4_filter_0(A,C,D),B) ) ) ) ) ) )).

fof(t17_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(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_filter_0(A,k4_lattices(A,B,C),D) = k4_filter_0(A,B,k4_filter_0(A,C,D)) ) ) ) ) )).

fof(t18_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ( v13_lattices(A)
           => ( ~ v3_struct_0(k5_filter_1(A,B))
              & v10_lattices(k5_filter_1(A,B))
              & v13_lattices(k5_filter_1(A,B))
              & l3_lattices(k5_filter_1(A,B))
              & k5_lattices(k5_filter_1(A,B)) = k6_filter_1(A,B,k5_lattices(A)) ) ) ) ) )).

fof(t19_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ( ~ v3_struct_0(k5_filter_1(A,B))
            & v10_lattices(k5_filter_1(A,B))
            & v14_lattices(k5_filter_1(A,B))
            & l3_lattices(k5_filter_1(A,B))
            & k6_lattices(k5_filter_1(A,B)) = k6_filter_1(A,B,k6_lattices(A)) ) ) ) )).

fof(t20_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => v3_filter_0(k5_filter_1(A,B)) ) ) )).

fof(t21_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_filter_0(B,A)
         => ( ~ v3_struct_0(k5_filter_1(A,B))
            & v10_lattices(k5_filter_1(A,B))
            & v17_lattices(k5_filter_1(A,B))
            & l3_lattices(k5_filter_1(A,B)) ) ) ) )).

fof(t22_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ! [F] :
                          ( m1_subset_1(F,B)
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k2_zfmisc_1(A,A),A)
                                & m2_relset_1(G,k2_zfmisc_1(A,A),A) )
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,k2_zfmisc_1(B,B),B)
                                    & m2_relset_1(H,k2_zfmisc_1(B,B),B) )
                                 => k2_binop_1(k2_zfmisc_1(A,B),k2_zfmisc_1(A,B),k2_zfmisc_1(A,B),k7_filter_1(A,B,G,H),k1_domain_1(A,B,C,E),k1_domain_1(A,B,D,F)) = k1_domain_1(A,B,k2_binop_1(A,A,A,G,C,D),k2_binop_1(B,B,B,H,E,F)) ) ) ) ) ) ) ) ) )).

fof(t23_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [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) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(B,B),B)
                    & m2_relset_1(D,k2_zfmisc_1(B,B),B) )
                 => ( ( v1_binop_1(C,A)
                      & v1_binop_1(D,B) )
                  <=> v1_binop_1(k7_filter_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ) ) ) ) )).

fof(t24_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [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) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(B,B),B)
                    & m2_relset_1(D,k2_zfmisc_1(B,B),B) )
                 => ( ( v2_binop_1(C,A)
                      & v2_binop_1(D,B) )
                  <=> v2_binop_1(k7_filter_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ) ) ) ) )).

fof(t25_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,B)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,A),A)
                        & m2_relset_1(E,k2_zfmisc_1(A,A),A) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(B,B),B)
                            & m2_relset_1(F,k2_zfmisc_1(B,B),B) )
                         => ( ( r1_binop_1(A,C,E)
                              & r1_binop_1(B,D,F) )
                          <=> r1_binop_1(k2_zfmisc_1(A,B),k1_domain_1(A,B,C,D),k7_filter_1(A,B,E,F)) ) ) ) ) ) ) ) )).

fof(t26_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,B)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,A),A)
                        & m2_relset_1(E,k2_zfmisc_1(A,A),A) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(B,B),B)
                            & m2_relset_1(F,k2_zfmisc_1(B,B),B) )
                         => ( ( r2_binop_1(A,C,E)
                              & r2_binop_1(B,D,F) )
                          <=> r2_binop_1(k2_zfmisc_1(A,B),k1_domain_1(A,B,C,D),k7_filter_1(A,B,E,F)) ) ) ) ) ) ) ) )).

fof(t27_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,B)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,A),A)
                        & m2_relset_1(E,k2_zfmisc_1(A,A),A) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(B,B),B)
                            & m2_relset_1(F,k2_zfmisc_1(B,B),B) )
                         => ( ( r3_binop_1(A,C,E)
                              & r3_binop_1(B,D,F) )
                          <=> r3_binop_1(k2_zfmisc_1(A,B),k1_domain_1(A,B,C,D),k7_filter_1(A,B,E,F)) ) ) ) ) ) ) ) )).

fof(t28_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [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) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(B,B),B)
                        & m2_relset_1(E,k2_zfmisc_1(B,B),B) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(B,B),B)
                            & m2_relset_1(F,k2_zfmisc_1(B,B),B) )
                         => ( ( r4_binop_1(A,C,D)
                              & r4_binop_1(B,E,F) )
                          <=> r4_binop_1(k2_zfmisc_1(A,B),k7_filter_1(A,B,C,E),k7_filter_1(A,B,D,F)) ) ) ) ) ) ) ) )).

fof(t29_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [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) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(B,B),B)
                        & m2_relset_1(E,k2_zfmisc_1(B,B),B) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(B,B),B)
                            & m2_relset_1(F,k2_zfmisc_1(B,B),B) )
                         => ( ( r5_binop_1(A,C,D)
                              & r5_binop_1(B,E,F) )
                          <=> r5_binop_1(k2_zfmisc_1(A,B),k7_filter_1(A,B,C,E),k7_filter_1(A,B,D,F)) ) ) ) ) ) ) ) )).

fof(t30_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [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) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(B,B),B)
                        & m2_relset_1(E,k2_zfmisc_1(B,B),B) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(B,B),B)
                            & m2_relset_1(F,k2_zfmisc_1(B,B),B) )
                         => ( ( r6_binop_1(A,C,D)
                              & r6_binop_1(B,E,F) )
                          <=> r6_binop_1(k2_zfmisc_1(A,B),k7_filter_1(A,B,C,E),k7_filter_1(A,B,D,F)) ) ) ) ) ) ) ) )).

fof(t31_filter_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [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) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(B,B),B)
                        & m2_relset_1(E,k2_zfmisc_1(B,B),B) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(B,B),B)
                            & m2_relset_1(F,k2_zfmisc_1(B,B),B) )
                         => ( ( r1_lattice2(A,C,D)
                              & r1_lattice2(B,E,F) )
                          <=> r1_lattice2(k2_zfmisc_1(A,B),k7_filter_1(A,B,C,E),k7_filter_1(A,B,D,F)) ) ) ) ) ) ) ) )).

fof(d7_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l3_lattices(B) )
         => k8_filter_1(A,B) = g3_lattices(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k7_filter_1(u1_struct_0(A),u1_struct_0(B),u2_lattices(A),u2_lattices(B)),k7_filter_1(u1_struct_0(A),u1_struct_0(B),u1_lattices(A),u1_lattices(B))) ) ) )).

fof(t32_filter_1,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))
             => ( r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k9_filter_1(A))
              <=> r3_lattices(A,B,C) ) ) ) ) )).

fof(t33_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( k1_relat_1(k9_filter_1(A)) = u1_struct_0(A)
        & k2_relat_1(k9_filter_1(A)) = u1_struct_0(A)
        & k3_relat_1(k9_filter_1(A)) = u1_struct_0(A) ) ) )).

fof(d9_filter_1,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)
          <=> r4_wellord1(k9_filter_1(A),k9_filter_1(B)) ) ) ) )).

fof(t34_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v10_lattices(C)
                & l3_lattices(C) )
             => ( ( r1_filter_1(A,B)
                  & r1_filter_1(B,C) )
               => r1_filter_1(A,C) ) ) ) ) )).

fof(t35_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l3_lattices(B) )
         => ( ( ~ v3_struct_0(k8_filter_1(A,B))
              & v10_lattices(k8_filter_1(A,B))
              & l3_lattices(k8_filter_1(A,B)) )
           => ( ~ v3_struct_0(A)
              & v10_lattices(A)
              & l3_lattices(A)
              & ~ v3_struct_0(B)
              & v10_lattices(B)
              & l3_lattices(B) ) ) ) ) )).

fof(t36_filter_1,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_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( k3_lattices(k8_filter_1(A,B),k10_filter_1(A,B,C,E),k10_filter_1(A,B,D,F)) = k10_filter_1(A,B,k3_lattices(A,C,D),k3_lattices(B,E,F))
                            & k4_lattices(k8_filter_1(A,B),k10_filter_1(A,B,C,E),k10_filter_1(A,B,D,F)) = k10_filter_1(A,B,k4_lattices(A,C,D),k4_lattices(B,E,F)) ) ) ) ) ) ) ) )).

fof(t37_filter_1,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_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( r3_lattices(k8_filter_1(A,B),k10_filter_1(A,B,C,E),k10_filter_1(A,B,D,F))
                          <=> ( r3_lattices(A,C,D)
                              & r3_lattices(B,E,F) ) ) ) ) ) ) ) ) )).

fof(t38_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ( ( v12_lattices(A)
              & v12_lattices(B) )
          <=> v12_lattices(k8_filter_1(A,B)) ) ) ) )).

fof(t39_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ( ( ~ v3_struct_0(A)
              & v10_lattices(A)
              & v11_lattices(A)
              & l3_lattices(A)
              & ~ v3_struct_0(B)
              & v10_lattices(B)
              & v11_lattices(B)
              & l3_lattices(B) )
          <=> ( ~ v3_struct_0(k8_filter_1(A,B))
              & v10_lattices(k8_filter_1(A,B))
              & v11_lattices(k8_filter_1(A,B))
              & l3_lattices(k8_filter_1(A,B)) ) ) ) ) )).

fof(t40_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ( ( v13_lattices(A)
              & v13_lattices(B) )
          <=> v13_lattices(k8_filter_1(A,B)) ) ) ) )).

fof(t41_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ( ( v14_lattices(A)
              & v14_lattices(B) )
          <=> v14_lattices(k8_filter_1(A,B)) ) ) ) )).

fof(t42_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ( ( v15_lattices(A)
              & v15_lattices(B) )
          <=> v15_lattices(k8_filter_1(A,B)) ) ) ) )).

fof(t43_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ( ( ~ v3_struct_0(A)
              & v10_lattices(A)
              & v13_lattices(A)
              & l3_lattices(A)
              & ~ v3_struct_0(B)
              & v10_lattices(B)
              & v13_lattices(B)
              & l3_lattices(B) )
           => k5_lattices(k8_filter_1(A,B)) = k10_filter_1(A,B,k5_lattices(A),k5_lattices(B)) ) ) ) )).

fof(t44_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ( ( ~ v3_struct_0(A)
              & v10_lattices(A)
              & v14_lattices(A)
              & l3_lattices(A)
              & ~ v3_struct_0(B)
              & v10_lattices(B)
              & v14_lattices(B)
              & l3_lattices(B) )
           => k6_lattices(k8_filter_1(A,B)) = k10_filter_1(A,B,k6_lattices(A),k6_lattices(B)) ) ) ) )).

fof(t45_filter_1,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_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( ~ v3_struct_0(A)
                              & v10_lattices(A)
                              & v15_lattices(A)
                              & l3_lattices(A)
                              & ~ v3_struct_0(B)
                              & v10_lattices(B)
                              & v15_lattices(B)
                              & l3_lattices(B) )
                           => ( ( r2_lattices(A,C,D)
                                & r2_lattices(B,E,F) )
                            <=> r2_lattices(k8_filter_1(A,B),k10_filter_1(A,B,C,E),k10_filter_1(A,B,D,F)) ) ) ) ) ) ) ) ) )).

fof(t46_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ( ( ~ v3_struct_0(A)
              & v10_lattices(A)
              & v15_lattices(A)
              & v16_lattices(A)
              & l3_lattices(A)
              & ~ v3_struct_0(B)
              & v10_lattices(B)
              & v15_lattices(B)
              & v16_lattices(B)
              & l3_lattices(B) )
          <=> ( ~ v3_struct_0(k8_filter_1(A,B))
              & v10_lattices(k8_filter_1(A,B))
              & v15_lattices(k8_filter_1(A,B))
              & v16_lattices(k8_filter_1(A,B))
              & l3_lattices(k8_filter_1(A,B)) ) ) ) ) )).

fof(t47_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ( ( ~ v3_struct_0(A)
              & v10_lattices(A)
              & v17_lattices(A)
              & l3_lattices(A)
              & ~ v3_struct_0(B)
              & v10_lattices(B)
              & v17_lattices(B)
              & l3_lattices(B) )
          <=> ( ~ v3_struct_0(k8_filter_1(A,B))
              & v10_lattices(k8_filter_1(A,B))
              & v17_lattices(k8_filter_1(A,B))
              & l3_lattices(k8_filter_1(A,B)) ) ) ) ) )).

fof(t48_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ( ( v3_filter_0(A)
              & v3_filter_0(B) )
          <=> v3_filter_0(k8_filter_1(A,B)) ) ) ) )).

fof(t49_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => k1_lattice2(k8_filter_1(A,B)) = k8_filter_1(k1_lattice2(A),k1_lattice2(B)) ) ) )).

fof(t50_filter_1,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(k8_filter_1(A,B),k8_filter_1(B,A)) ) ) )).

fof(t51_filter_1,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))
             => k9_filter_0(A,B,C) = k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,k7_lattices(A,B),k7_lattices(A,C))) ) ) ) )).

fof(t52_filter_1,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_filter_0(A,B,C)) = k4_lattices(A,B,k7_lattices(A,C))
                & k7_lattices(A,k9_filter_0(A,B,C)) = k3_lattices(A,k4_lattices(A,B,k7_lattices(A,C)),k4_lattices(A,k7_lattices(A,B),C))
                & k7_lattices(A,k9_filter_0(A,B,C)) = k9_filter_0(A,B,k7_lattices(A,C))
                & k7_lattices(A,k9_filter_0(A,B,C)) = k9_filter_0(A,k7_lattices(A,B),C) ) ) ) ) )).

fof(t53_filter_1,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] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( k9_filter_0(A,B,C) = k9_filter_0(A,B,D)
                   => C = D ) ) ) ) ) )).

fof(t54_filter_1,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))
             => k9_filter_0(A,B,k9_filter_0(A,B,C)) = C ) ) ) )).

fof(t55_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k4_filter_0(A,k3_lattices(A,B,C),B) = k4_filter_0(A,C,B)
                & k4_filter_0(A,B,k4_lattices(A,B,C)) = k4_filter_0(A,B,C) ) ) ) ) )).

fof(t56_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(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_filter_0(A,B,C),k4_filter_0(A,B,k3_lattices(A,C,D)))
                    & r3_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,k4_lattices(A,B,D),C))
                    & r3_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,B,k3_lattices(A,D,C)))
                    & r3_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,k4_lattices(A,D,B),C)) ) ) ) ) ) )).

fof(t57_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(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,k4_filter_0(A,B,C),k4_filter_0(A,D,C)),k4_filter_0(A,k3_lattices(A,B,D),C)) ) ) ) ) )).

fof(t58_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(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,k4_filter_0(A,B,C),k4_filter_0(A,B,D)),k4_filter_0(A,B,k4_lattices(A,C,D))) ) ) ) ) )).

fof(t59_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(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))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r2_hidden(k9_filter_0(A,C,D),B)
                              & r2_hidden(k9_filter_0(A,E,F),B) )
                           => ( r2_hidden(k9_filter_0(A,k3_lattices(A,C,E),k3_lattices(A,D,F)),B)
                              & r2_hidden(k9_filter_0(A,k4_lattices(A,C,E),k4_lattices(A,D,F)),B) ) ) ) ) ) ) ) ) )).

fof(t60_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(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))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r2_hidden(C,k2_filter_1(u1_struct_0(A),k11_filter_0(A,B),D))
                          & r2_hidden(E,k2_filter_1(u1_struct_0(A),k11_filter_0(A,B),D)) )
                       => ( r2_hidden(k3_lattices(A,C,E),k2_filter_1(u1_struct_0(A),k11_filter_0(A,B),D))
                          & r2_hidden(k4_lattices(A,C,E),k2_filter_1(u1_struct_0(A),k11_filter_0(A,B),D)) ) ) ) ) ) ) ) )).

fof(t61_filter_1,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))
             => ( r2_hidden(k3_lattices(A,B,k9_filter_0(A,B,C)),k2_filter_1(u1_struct_0(A),k12_filter_0(A,k2_filter_0(A,C)),B))
                & ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(D,k2_filter_1(u1_struct_0(A),k12_filter_0(A,k2_filter_0(A,C)),B))
                     => r3_lattices(A,D,k3_lattices(A,B,k9_filter_0(A,B,C))) ) ) ) ) ) ) )).

fof(t62_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_filter_1(A,k8_filter_1(k5_filter_1(A,k2_filter_0(A,B)),k8_filter_0(A,k2_filter_0(A,B)))) ) ) )).

fof(s1_filter_1,axiom,
    ( ! [A] :
        ( m1_subset_1(A,f1_s1_filter_1)
       => p1_s1_filter_1(k2_filter_1(f1_s1_filter_1,f2_s1_filter_1,A)) )
   => ! [A] :
        ( m2_subset_1(A,k1_zfmisc_1(f1_s1_filter_1),k8_eqrel_1(f1_s1_filter_1,f2_s1_filter_1))
       => p1_s1_filter_1(A) ) )).

fof(s2_filter_1,axiom,
    ( ! [A] :
        ( m1_subset_1(A,f1_s2_filter_1)
       => ! [B] :
            ( m1_subset_1(B,f1_s2_filter_1)
           => p1_s2_filter_1(k2_filter_1(f1_s2_filter_1,f2_s2_filter_1,A),k2_filter_1(f1_s2_filter_1,f2_s2_filter_1,B)) ) )
   => ! [A] :
        ( m2_subset_1(A,k1_zfmisc_1(f1_s2_filter_1),k8_eqrel_1(f1_s2_filter_1,f2_s2_filter_1))
       => ! [B] :
            ( m2_subset_1(B,k1_zfmisc_1(f1_s2_filter_1),k8_eqrel_1(f1_s2_filter_1,f2_s2_filter_1))
           => p1_s2_filter_1(A,B) ) ) )).

fof(s3_filter_1,axiom,
    ( ! [A] :
        ( m1_subset_1(A,f1_s3_filter_1)
       => ! [B] :
            ( m1_subset_1(B,f1_s3_filter_1)
           => ! [C] :
                ( m1_subset_1(C,f1_s3_filter_1)
               => p1_s3_filter_1(k2_filter_1(f1_s3_filter_1,f2_s3_filter_1,A),k2_filter_1(f1_s3_filter_1,f2_s3_filter_1,B),k2_filter_1(f1_s3_filter_1,f2_s3_filter_1,C)) ) ) )
   => ! [A] :
        ( m2_subset_1(A,k1_zfmisc_1(f1_s3_filter_1),k8_eqrel_1(f1_s3_filter_1,f2_s3_filter_1))
       => ! [B] :
            ( m2_subset_1(B,k1_zfmisc_1(f1_s3_filter_1),k8_eqrel_1(f1_s3_filter_1,f2_s3_filter_1))
           => ! [C] :
                ( m2_subset_1(C,k1_zfmisc_1(f1_s3_filter_1),k8_eqrel_1(f1_s3_filter_1,f2_s3_filter_1))
               => p1_s3_filter_1(A,B,C) ) ) ) )).

fof(s4_filter_1,axiom,
    ( ! [A] :
        ( m1_subset_1(A,f1_s4_filter_1)
       => ! [B] :
            ( m1_subset_1(B,f2_s4_filter_1)
           => p1_s4_filter_1(k1_domain_1(f1_s4_filter_1,f2_s4_filter_1,A,B)) ) )
   => ! [A] :
        ( m1_subset_1(A,k2_zfmisc_1(f1_s4_filter_1,f2_s4_filter_1))
       => p1_s4_filter_1(A) ) )).

fof(s5_filter_1,axiom,
    ( ! [A] :
        ( m1_subset_1(A,f1_s5_filter_1)
       => ! [B] :
            ( m1_subset_1(B,f1_s5_filter_1)
           => ! [C] :
                ( m1_subset_1(C,f2_s5_filter_1)
               => ! [D] :
                    ( m1_subset_1(D,f2_s5_filter_1)
                   => p1_s5_filter_1(k1_domain_1(f1_s5_filter_1,f2_s5_filter_1,A,C),k1_domain_1(f1_s5_filter_1,f2_s5_filter_1,B,D)) ) ) ) )
   => ! [A] :
        ( m1_subset_1(A,k2_zfmisc_1(f1_s5_filter_1,f2_s5_filter_1))
       => ! [B] :
            ( m1_subset_1(B,k2_zfmisc_1(f1_s5_filter_1,f2_s5_filter_1))
           => p1_s5_filter_1(A,B) ) ) )).

fof(s6_filter_1,axiom,
    ( ! [A] :
        ( m1_subset_1(A,f1_s6_filter_1)
       => ! [B] :
            ( m1_subset_1(B,f1_s6_filter_1)
           => ! [C] :
                ( m1_subset_1(C,f1_s6_filter_1)
               => ! [D] :
                    ( m1_subset_1(D,f2_s6_filter_1)
                   => ! [E] :
                        ( m1_subset_1(E,f2_s6_filter_1)
                       => ! [F] :
                            ( m1_subset_1(F,f2_s6_filter_1)
                           => p1_s6_filter_1(k1_domain_1(f1_s6_filter_1,f2_s6_filter_1,A,D),k1_domain_1(f1_s6_filter_1,f2_s6_filter_1,B,E),k1_domain_1(f1_s6_filter_1,f2_s6_filter_1,C,F)) ) ) ) ) ) )
   => ! [A] :
        ( m1_subset_1(A,k2_zfmisc_1(f1_s6_filter_1,f2_s6_filter_1))
       => ! [B] :
            ( m1_subset_1(B,k2_zfmisc_1(f1_s6_filter_1,f2_s6_filter_1))
           => ! [C] :
                ( m1_subset_1(C,k2_zfmisc_1(f1_s6_filter_1,f2_s6_filter_1))
               => p1_s6_filter_1(A,B,C) ) ) ) )).

fof(dt_m1_filter_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(B) )
     => ! [C] :
          ( m1_filter_1(C,A,B)
         => ( v1_funct_1(C)
            & v1_funct_2(C,A,A)
            & m2_relset_1(C,A,A) ) ) ) )).

fof(existence_m1_filter_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(B) )
     => ? [C] : m1_filter_1(C,A,B) ) )).

fof(dt_m2_filter_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(B) )
     => ! [C] :
          ( m2_filter_1(C,A,B)
         => ( v1_funct_1(C)
            & v1_funct_2(C,k2_zfmisc_1(A,A),A)
            & m2_relset_1(C,k2_zfmisc_1(A,A),A) ) ) ) )).

fof(existence_m2_filter_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(B) )
     => ? [C] : m2_filter_1(C,A,B) ) )).

fof(symmetry_r1_filter_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B) )
     => ( r1_filter_1(A,B)
       => r1_filter_1(B,A) ) ) )).

fof(reflexivity_r1_filter_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B) )
     => r1_filter_1(A,A) ) )).

fof(dt_k1_filter_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_filter_0(B,A)
        & m1_filter_0(C,A) )
     => m1_filter_0(k1_filter_1(A,B,C),A) ) )).

fof(commutativity_k1_filter_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_filter_0(B,A)
        & m1_filter_0(C,A) )
     => k1_filter_1(A,B,C) = k1_filter_1(A,C,B) ) )).

fof(idempotence_k1_filter_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_filter_0(B,A)
        & m1_filter_0(C,A) )
     => k1_filter_1(A,B,B) = B ) )).

fof(redefinition_k1_filter_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_filter_0(B,A)
        & m1_filter_0(C,A) )
     => k1_filter_1(A,B,C) = k3_xboole_0(B,C) ) )).

fof(dt_k2_filter_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A)
        & m1_subset_1(C,A) )
     => m2_subset_1(k2_filter_1(A,B,C),k1_zfmisc_1(A),k8_eqrel_1(A,B)) ) )).

fof(redefinition_k2_filter_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A)
        & m1_subset_1(C,A) )
     => k2_filter_1(A,B,C) = k6_eqrel_1(A,B,C) ) )).

fof(dt_k3_filter_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & m1_relset_1(C,A,A) )
     => ( v1_funct_1(k3_filter_1(A,B,C))
        & v1_funct_2(k3_filter_1(A,B,C),k8_eqrel_1(A,B),k8_eqrel_1(A,B))
        & m2_relset_1(k3_filter_1(A,B,C),k8_eqrel_1(A,B),k8_eqrel_1(A,B)) ) ) )).

fof(dt_k4_filter_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,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) )
     => ( v1_funct_1(k4_filter_1(A,B,C))
        & v1_funct_2(k4_filter_1(A,B,C),k2_zfmisc_1(k8_eqrel_1(A,B),k8_eqrel_1(A,B)),k8_eqrel_1(A,B))
        & m2_relset_1(k4_filter_1(A,B,C),k2_zfmisc_1(k8_eqrel_1(A,B),k8_eqrel_1(A,B)),k8_eqrel_1(A,B)) ) ) )).

fof(dt_k5_filter_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_filter_0(B,A) )
     => ( ~ v3_struct_0(k5_filter_1(A,B))
        & v3_lattices(k5_filter_1(A,B))
        & v10_lattices(k5_filter_1(A,B))
        & l3_lattices(k5_filter_1(A,B)) ) ) )).

fof(dt_k6_filter_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_filter_0(B,A)
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k6_filter_1(A,B,C),u1_struct_0(k5_filter_1(A,B))) ) )).

fof(dt_k7_filter_1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(B,B),B)
        & m1_relset_1(D,k2_zfmisc_1(B,B),B) )
     => ( v1_funct_1(k7_filter_1(A,B,C,D))
        & v1_funct_2(k7_filter_1(A,B,C,D),k2_zfmisc_1(k2_zfmisc_1(A,B),k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B))
        & m2_relset_1(k7_filter_1(A,B,C,D),k2_zfmisc_1(k2_zfmisc_1(A,B),k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B)) ) ) )).

fof(redefinition_k7_filter_1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(B,B),B)
        & m1_relset_1(D,k2_zfmisc_1(B,B),B) )
     => k7_filter_1(A,B,C,D) = k3_funct_4(C,D) ) )).

fof(dt_k8_filter_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A)
        & ~ v3_struct_0(B)
        & l3_lattices(B) )
     => ( v3_lattices(k8_filter_1(A,B))
        & l3_lattices(k8_filter_1(A,B)) ) ) )).

fof(dt_k9_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => v1_relat_1(k9_filter_1(A)) ) )).

fof(dt_k10_filter_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B)) )
     => m1_subset_1(k10_filter_1(A,B,C,D),u1_struct_0(k8_filter_1(A,B))) ) )).

fof(redefinition_k10_filter_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B)) )
     => k10_filter_1(A,B,C,D) = k4_tarski(C,D) ) )).

fof(d8_filter_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => k9_filter_1(A) = a_1_0_filter_1(A) ) )).

fof(fraenkel_a_1_0_filter_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B) )
     => ( r2_hidden(A,a_1_0_filter_1(B))
      <=> ? [C,D] :
            ( m1_subset_1(C,u1_struct_0(B))
            & m1_subset_1(D,u1_struct_0(B))
            & A = k1_domain_1(u1_struct_0(B),u1_struct_0(B),C,D)
            & r3_lattices(B,C,D) ) ) ) )).
%------------------------------------------------------------------------------