SET007 Axioms: SET007+482.ax


%------------------------------------------------------------------------------
% File     : SET007+482 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Fixpoints in Complete Lattices
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : knaster [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   88 (   6 unit)
%            Number of atoms       :  912 (  64 equality)
%            Maximal formula depth :   24 (  11 average)
%            Number of connectives :  923 (  99 ~  ;   4  |; 529  &)
%                                         (  16 <=>; 275 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   48 (   1 propositional; 0-3 arity)
%            Number of functors    :   44 (   4 constant; 0-4 arity)
%            Number of variables   :  303 (   0 singleton; 280 !;  23 ?)
%            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_knaster,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ? [C] :
          ( m1_relset_1(C,A,B)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & v6_cohsp_1(C) ) ) )).

fof(rc2_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v2_knaster(B,A)
          & v3_knaster(B,A) ) ) )).

fof(cc1_knaster,axiom,(
    ! [A] :
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v4_lattice3(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A)
          & v10_lattices(A)
          & v13_lattices(A)
          & v14_lattices(A)
          & v15_lattices(A) ) ) ) )).

fof(fc1_knaster,axiom,(
    ! [A] :
      ( ~ v3_struct_0(k1_lattice3(A))
      & v3_lattices(k1_lattice3(A))
      & v4_lattices(k1_lattice3(A))
      & v5_lattices(k1_lattice3(A))
      & v6_lattices(k1_lattice3(A))
      & v7_lattices(k1_lattice3(A))
      & v8_lattices(k1_lattice3(A))
      & v9_lattices(k1_lattice3(A))
      & v10_lattices(k1_lattice3(A))
      & v11_lattices(k1_lattice3(A))
      & v12_lattices(k1_lattice3(A))
      & v13_lattices(k1_lattice3(A))
      & v14_lattices(k1_lattice3(A))
      & v15_lattices(k1_lattice3(A))
      & v16_lattices(k1_lattice3(A))
      & v17_lattices(k1_lattice3(A))
      & v4_lattice3(k1_lattice3(A)) ) )).

fof(t1_knaster,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( v2_funct_1(A)
              & v2_funct_1(B)
              & r1_xboole_0(k2_relat_1(A),k2_relat_1(B)) )
           => v2_funct_1(k1_funct_4(A,B)) ) ) ) )).

fof(t2_knaster,axiom,(
    $true )).

fof(t3_knaster,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( A = k2_xboole_0(B,C)
                  & r1_xboole_0(k1_relat_1(B),k1_relat_1(C)) )
               => ( v2_funct_1(A)
                <=> ( v2_funct_1(B)
                    & v2_funct_1(C)
                    & r1_xboole_0(k2_relat_1(B),k2_relat_1(C)) ) ) ) ) ) ) )).

fof(t4_knaster,axiom,(
    ! [A,B,C] :
      ( m2_subset_1(C,k1_numbers,k5_numbers)
     => ! [D] :
          ( ( v1_funct_1(D)
            & v1_funct_2(D,A,A)
            & m2_relset_1(D,A,A) )
         => ( r1_abian(B,k1_abian(A,D,C))
           => r1_abian(k1_funct_1(D,B),k1_abian(A,D,C)) ) ) ) )).

fof(t5_knaster,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & m2_relset_1(C,A,A) )
     => ( ? [D] :
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & r1_abian(B,k1_abian(A,C,D))
            & ! [E] :
                ( r1_abian(E,k1_abian(A,C,D))
               => B = E ) )
       => r1_abian(B,C) ) ) )).

fof(d1_knaster,axiom,(
    $true )).

fof(d2_knaster,axiom,(
    $true )).

fof(d3_knaster,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( v6_cohsp_1(C)
              <=> ! [D] :
                    ( m1_subset_1(D,A)
                   => ! [E] :
                        ( m1_subset_1(E,A)
                       => ( r1_tarski(D,E)
                         => r1_tarski(k8_funct_2(A,B,C,D),k8_funct_2(A,B,C,E)) ) ) ) ) ) ) ) )).

fof(t6_knaster,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
        & v6_cohsp_1(B)
        & m2_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A)) )
     => r2_abian(k1_zfmisc_1(A),k1_knaster(A,B),B) ) )).

fof(t7_knaster,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
        & v6_cohsp_1(B)
        & m2_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A)) )
     => r2_abian(k1_zfmisc_1(A),k2_knaster(A,B),B) ) )).

fof(t8_knaster,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
        & v6_cohsp_1(B)
        & m2_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A)) )
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( r1_tarski(k8_funct_2(k1_zfmisc_1(A),k1_zfmisc_1(A),B,C),C)
           => r1_tarski(k1_knaster(A,B),C) ) ) ) )).

fof(t9_knaster,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
        & v6_cohsp_1(B)
        & m2_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A)) )
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( r1_tarski(C,k8_funct_2(k1_zfmisc_1(A),k1_zfmisc_1(A),B,C))
           => r1_tarski(C,k2_knaster(A,B)) ) ) ) )).

fof(t10_knaster,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
        & v6_cohsp_1(B)
        & m2_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A)) )
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( r2_abian(k1_zfmisc_1(A),C,B)
           => ( r1_tarski(k1_knaster(A,B),C)
              & r1_tarski(C,k2_knaster(A,B)) ) ) ) ) )).

fof(t11_knaster,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ? [E,F,G,H] :
                      ( r1_xboole_0(E,F)
                      & r1_xboole_0(G,H)
                      & k2_xboole_0(E,F) = A
                      & k2_xboole_0(G,H) = B
                      & k2_funct_2(A,B,C,E) = G
                      & k2_funct_2(B,A,D,H) = F ) ) ) ) ) )).

fof(t12_knaster,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ~ ( v2_funct_1(C)
                      & v2_funct_1(D)
                      & ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,A,B)
                            & m2_relset_1(E,A,B) )
                         => ~ v3_funct_2(E,A,B) ) ) ) ) ) ) )).

fof(t13_knaster,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ( ? [C] :
                ( v1_funct_1(C)
                & v1_funct_2(C,B,A)
                & m2_relset_1(C,B,A)
                & v3_funct_2(C,B,A) )
           => r2_tarski(B,A) ) ) ) )).

fof(t14_knaster,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ( ( v2_funct_1(C)
                      & v2_funct_1(D) )
                   => r2_tarski(A,B) ) ) ) ) ) )).

fof(d6_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_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)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( v3_ordinal1(D)
                 => ! [E] :
                      ( E = k4_knaster(A,B,C,D)
                    <=> ? [F] :
                          ( v1_relat_1(F)
                          & v1_funct_1(F)
                          & v5_ordinal1(F)
                          & E = k1_ordinal2(F)
                          & k1_relat_1(F) = k1_ordinal1(D)
                          & k1_funct_1(F,k1_xboole_0) = C
                          & ! [G] :
                              ( v3_ordinal1(G)
                             => ( r2_hidden(k1_ordinal1(G),k1_ordinal1(D))
                               => k1_funct_1(F,k1_ordinal1(G)) = k1_funct_1(B,k1_funct_1(F,G)) ) )
                          & ! [G] :
                              ( v3_ordinal1(G)
                             => ( ( r2_hidden(G,k1_ordinal1(D))
                                  & v4_ordinal1(G) )
                               => ( G = k1_xboole_0
                                  | k1_funct_1(F,G) = k15_lattice3(A,k2_relat_1(k2_ordinal1(F,G))) ) ) ) ) ) ) ) ) ) )).

fof(d7_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_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)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( v3_ordinal1(D)
                 => ! [E] :
                      ( E = k5_knaster(A,B,C,D)
                    <=> ? [F] :
                          ( v1_relat_1(F)
                          & v1_funct_1(F)
                          & v5_ordinal1(F)
                          & E = k1_ordinal2(F)
                          & k1_relat_1(F) = k1_ordinal1(D)
                          & k1_funct_1(F,k1_xboole_0) = C
                          & ! [G] :
                              ( v3_ordinal1(G)
                             => ( r2_hidden(k1_ordinal1(G),k1_ordinal1(D))
                               => k1_funct_1(F,k1_ordinal1(G)) = k1_funct_1(B,k1_funct_1(F,G)) ) )
                          & ! [G] :
                              ( v3_ordinal1(G)
                             => ( ( r2_hidden(G,k1_ordinal1(D))
                                  & v4_ordinal1(G) )
                               => ( G = k1_xboole_0
                                  | k1_funct_1(F,G) = k16_lattice3(A,k2_relat_1(k2_ordinal1(F,G))) ) ) ) ) ) ) ) ) ) )).

fof(t15_knaster,axiom,(
    $true )).

fof(t16_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_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)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k4_knaster(A,B,C,k1_xboole_0) = C ) ) ) )).

fof(t17_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_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)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k5_knaster(A,B,C,k1_xboole_0) = C ) ) ) )).

fof(t18_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_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)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( v3_ordinal1(D)
                 => k4_knaster(A,B,C,k1_ordinal1(D)) = k1_funct_1(B,k4_knaster(A,B,C,D)) ) ) ) ) )).

fof(t19_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_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)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( v3_ordinal1(D)
                 => k5_knaster(A,B,C,k1_ordinal1(D)) = k1_funct_1(B,k5_knaster(A,B,C,D)) ) ) ) ) )).

fof(t20_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_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)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( v3_ordinal1(D)
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E)
                        & v5_ordinal1(E) )
                     => ( ( v4_ordinal1(D)
                          & k1_relat_1(E) = D
                          & ! [F] :
                              ( v3_ordinal1(F)
                             => ( r2_hidden(F,D)
                               => k1_funct_1(E,F) = k4_knaster(A,B,C,F) ) ) )
                       => ( D = k1_xboole_0
                          | k4_knaster(A,B,C,D) = k15_lattice3(A,k2_relat_1(E)) ) ) ) ) ) ) ) )).

fof(t21_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_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)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( v3_ordinal1(D)
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E)
                        & v5_ordinal1(E) )
                     => ( ( v4_ordinal1(D)
                          & k1_relat_1(E) = D
                          & ! [F] :
                              ( v3_ordinal1(F)
                             => ( r2_hidden(F,D)
                               => k1_funct_1(E,F) = k5_knaster(A,B,C,F) ) ) )
                       => ( D = k1_xboole_0
                          | k5_knaster(A,B,C,D) = k16_lattice3(A,k2_relat_1(E)) ) ) ) ) ) ) ) )).

fof(t22_knaster,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => k3_knaster(B,k1_abian(u1_struct_0(B),C,A),D) = k4_knaster(B,C,D,A) ) ) ) ) )).

fof(t23_knaster,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => k3_knaster(B,k1_abian(u1_struct_0(B),C,A),D) = k5_knaster(B,C,D,A) ) ) ) ) )).

fof(d8_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_knaster(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)
                        & ! [E] :
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ~ ( r2_hidden(E,B)
                                & r1_lattices(A,C,E)
                                & r1_lattices(A,D,E)
                                & ! [F] :
                                    ( m1_subset_1(F,u1_struct_0(A))
                                   => ( ( r2_hidden(F,B)
                                        & r1_lattices(A,C,F)
                                        & r1_lattices(A,D,F) )
                                     => r1_lattices(A,E,F) ) ) ) ) ) ) ) ) ) ) )).

fof(d9_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_knaster(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)
                        & ! [E] :
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ~ ( r2_hidden(E,B)
                                & r1_lattices(A,E,C)
                                & r1_lattices(A,E,D)
                                & ! [F] :
                                    ( m1_subset_1(F,u1_struct_0(A))
                                   => ( ( r2_hidden(F,B)
                                        & r1_lattices(A,F,C)
                                        & r1_lattices(A,F,D) )
                                     => r1_lattices(A,F,E) ) ) ) ) ) ) ) ) ) ) )).

fof(d10_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v2_knaster(B,A)
            & v3_knaster(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_lattices(C)
                & v10_lattices(C)
                & l3_lattices(C) )
             => ( C = k8_knaster(A,B)
              <=> ( u1_struct_0(C) = B
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(C))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(C))
                         => ? [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                              & ? [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                  & D = F
                                  & E = G
                                  & ( r3_lattices(C,D,E)
                                   => r3_lattices(A,F,G) )
                                  & ( r3_lattices(A,F,G)
                                   => r3_lattices(C,D,E) ) ) ) ) ) ) ) ) ) ) )).

fof(t24_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ? [C] :
              ( m1_subset_1(C,u1_struct_0(A))
              & r2_abian(u1_struct_0(A),C,B) ) ) ) )).

fof(t25_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_lattices(A,C,k3_knaster(A,B,C))
               => ! [D] :
                    ( v3_ordinal1(D)
                   => r3_lattices(A,C,k6_knaster(A,B,C,D)) ) ) ) ) ) )).

fof(t26_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_lattices(A,k3_knaster(A,B,C),C)
               => ! [D] :
                    ( v3_ordinal1(D)
                   => r3_lattices(A,k7_knaster(A,B,C,D),C) ) ) ) ) ) )).

fof(t27_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_lattices(A,C,k3_knaster(A,B,C))
               => ! [D] :
                    ( v3_ordinal1(D)
                   => ! [E] :
                        ( v3_ordinal1(E)
                       => ( r1_ordinal1(D,E)
                         => r3_lattices(A,k6_knaster(A,B,C,D),k6_knaster(A,B,C,E)) ) ) ) ) ) ) ) )).

fof(t28_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_lattices(A,k3_knaster(A,B,C),C)
               => ! [D] :
                    ( v3_ordinal1(D)
                   => ! [E] :
                        ( v3_ordinal1(E)
                       => ( r1_ordinal1(D,E)
                         => r3_lattices(A,k7_knaster(A,B,C,E),k7_knaster(A,B,C,D)) ) ) ) ) ) ) ) )).

fof(t29_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_lattices(A,C,k3_knaster(A,B,C))
               => ! [D] :
                    ( v3_ordinal1(D)
                   => ! [E] :
                        ( v3_ordinal1(E)
                       => ~ ( r2_xboole_0(D,E)
                            & ~ r2_abian(u1_struct_0(A),k6_knaster(A,B,C,E),B)
                            & k6_knaster(A,B,C,D) = k6_knaster(A,B,C,E) ) ) ) ) ) ) ) )).

fof(t30_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_lattices(A,k3_knaster(A,B,C),C)
               => ! [D] :
                    ( v3_ordinal1(D)
                   => ! [E] :
                        ( v3_ordinal1(E)
                       => ~ ( r2_xboole_0(D,E)
                            & ~ r2_abian(u1_struct_0(A),k7_knaster(A,B,C,E),B)
                            & k7_knaster(A,B,C,D) = k7_knaster(A,B,C,E) ) ) ) ) ) ) ) )).

fof(t31_knaster,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & v4_lattice3(B)
            & l3_lattices(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
                & v14_quantal1(C,B)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( ( r3_lattices(B,D,k3_knaster(B,C,D))
                      & r2_abian(u1_struct_0(B),k6_knaster(B,C,D,A),C) )
                   => ! [E] :
                        ( v3_ordinal1(E)
                       => ( r1_ordinal1(A,E)
                         => k6_knaster(B,C,D,A) = k6_knaster(B,C,D,E) ) ) ) ) ) ) ) )).

fof(t32_knaster,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & v4_lattice3(B)
            & l3_lattices(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
                & v14_quantal1(C,B)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( ( r3_lattices(B,k3_knaster(B,C,D),D)
                      & r2_abian(u1_struct_0(B),k7_knaster(B,C,D,A),C) )
                   => ! [E] :
                        ( v3_ordinal1(E)
                       => ( r1_ordinal1(A,E)
                         => k7_knaster(B,C,D,A) = k7_knaster(B,C,D,E) ) ) ) ) ) ) ) )).

fof(t33_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( r3_lattices(A,C,k3_knaster(A,B,C))
                  & ! [D] :
                      ( v3_ordinal1(D)
                     => ~ ( r1_tarski(k1_card_1(D),k1_card_1(u1_struct_0(A)))
                          & r2_abian(u1_struct_0(A),k6_knaster(A,B,C,D),B) ) ) ) ) ) ) )).

fof(t34_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( r3_lattices(A,k3_knaster(A,B,C),C)
                  & ! [D] :
                      ( v3_ordinal1(D)
                     => ~ ( r1_tarski(k1_card_1(D),k1_card_1(u1_struct_0(A)))
                          & r2_abian(u1_struct_0(A),k7_knaster(A,B,C,D),B) ) ) ) ) ) ) )).

fof(t35_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ~ ( r2_abian(u1_struct_0(A),C,B)
                      & r2_abian(u1_struct_0(A),D,B)
                      & ! [E] :
                          ( v3_ordinal1(E)
                         => ~ ( r1_tarski(k1_card_1(E),k1_card_1(u1_struct_0(A)))
                              & r2_abian(u1_struct_0(A),k6_knaster(A,B,k3_lattices(A,C,D),E),B)
                              & r3_lattices(A,C,k6_knaster(A,B,k3_lattices(A,C,D),E))
                              & r3_lattices(A,D,k6_knaster(A,B,k3_lattices(A,C,D),E)) ) ) ) ) ) ) ) )).

fof(t36_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ~ ( r2_abian(u1_struct_0(A),C,B)
                      & r2_abian(u1_struct_0(A),D,B)
                      & ! [E] :
                          ( v3_ordinal1(E)
                         => ~ ( r1_tarski(k1_card_1(E),k1_card_1(u1_struct_0(A)))
                              & r2_abian(u1_struct_0(A),k7_knaster(A,B,k4_lattices(A,C,D),E),B)
                              & r3_lattices(A,k7_knaster(A,B,k4_lattices(A,C,D),E),C)
                              & r3_lattices(A,k7_knaster(A,B,k4_lattices(A,C,D),E),D) ) ) ) ) ) ) ) )).

fof(t37_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),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,C,k3_knaster(A,B,C))
                      & r3_lattices(A,C,D)
                      & r2_abian(u1_struct_0(A),D,B) )
                   => ! [E] :
                        ( v3_ordinal1(E)
                       => r3_lattices(A,k6_knaster(A,B,C,E),D) ) ) ) ) ) ) )).

fof(t38_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),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,k3_knaster(A,B,C),C)
                      & r3_lattices(A,D,C)
                      & r2_abian(u1_struct_0(A),D,B) )
                   => ! [E] :
                        ( v3_ordinal1(E)
                       => r3_lattices(A,D,k7_knaster(A,B,C,E)) ) ) ) ) ) ) )).

fof(t40_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => r1_tarski(u1_struct_0(k9_knaster(A,B)),u1_struct_0(A)) ) ) )).

fof(t41_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,u1_struct_0(k9_knaster(A,B)))
              <=> r2_abian(u1_struct_0(A),C,B) ) ) ) ) )).

fof(t42_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k9_knaster(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k9_knaster(A,B)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( C = E
                              & D = F )
                           => ( r3_lattices(k9_knaster(A,B),C,D)
                            <=> r3_lattices(A,E,F) ) ) ) ) ) ) ) ) )).

fof(t43_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => v4_lattice3(k9_knaster(A,B)) ) ) )).

fof(d12_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => k10_knaster(A,B) = k6_knaster(A,B,k5_lattices(A),k2_card_1(u1_struct_0(A))) ) ) )).

fof(d13_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => k11_knaster(A,B) = k7_knaster(A,B,k6_lattices(A),k2_card_1(u1_struct_0(A))) ) ) )).

fof(t44_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( r2_abian(u1_struct_0(A),k10_knaster(A,B),B)
            & ? [C] :
                ( v3_ordinal1(C)
                & r1_tarski(k1_card_1(C),k1_card_1(u1_struct_0(A)))
                & k6_knaster(A,B,k5_lattices(A),C) = k10_knaster(A,B) ) ) ) ) )).

fof(t45_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( r2_abian(u1_struct_0(A),k11_knaster(A,B),B)
            & ? [C] :
                ( v3_ordinal1(C)
                & r1_tarski(k1_card_1(C),k1_card_1(u1_struct_0(A)))
                & k7_knaster(A,B,k6_lattices(A),C) = k11_knaster(A,B) ) ) ) ) )).

fof(t46_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_abian(u1_struct_0(A),C,B)
               => ( r3_lattices(A,k10_knaster(A,B),C)
                  & r3_lattices(A,C,k11_knaster(A,B)) ) ) ) ) ) )).

fof(t47_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_lattices(A,k3_knaster(A,B,C),C)
               => r3_lattices(A,k10_knaster(A,B),C) ) ) ) ) )).

fof(t48_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_lattices(A,C,k3_knaster(A,B,C))
               => r3_lattices(A,C,k11_knaster(A,B)) ) ) ) ) )).

fof(t49_knaster,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k1_lattice3(A)),u1_struct_0(k1_lattice3(A)))
            & m2_relset_1(B,u1_struct_0(k1_lattice3(A)),u1_struct_0(k1_lattice3(A))) )
         => ( v14_quantal1(B,k1_lattice3(A))
          <=> v6_cohsp_1(B) ) ) ) )).

fof(t50_knaster,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k1_lattice3(A)),u1_struct_0(k1_lattice3(A)))
            & v14_quantal1(B,k1_lattice3(A))
            & m2_relset_1(B,u1_struct_0(k1_lattice3(A)),u1_struct_0(k1_lattice3(A))) )
         => ? [C] :
              ( v1_funct_1(C)
              & v1_funct_2(C,k1_zfmisc_1(A),k1_zfmisc_1(A))
              & v6_cohsp_1(C)
              & m2_relset_1(C,k1_zfmisc_1(A),k1_zfmisc_1(A))
              & k1_knaster(A,C) = k10_knaster(k1_lattice3(A),B) ) ) ) )).

fof(t51_knaster,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k1_lattice3(A)),u1_struct_0(k1_lattice3(A)))
            & v14_quantal1(B,k1_lattice3(A))
            & m2_relset_1(B,u1_struct_0(k1_lattice3(A)),u1_struct_0(k1_lattice3(A))) )
         => ? [C] :
              ( v1_funct_1(C)
              & v1_funct_2(C,k1_zfmisc_1(A),k1_zfmisc_1(A))
              & v6_cohsp_1(C)
              & m2_relset_1(C,k1_zfmisc_1(A),k1_zfmisc_1(A))
              & k2_knaster(A,C) = k11_knaster(k1_lattice3(A),B) ) ) ) )).

fof(s1_knaster,axiom,
    ( ( ! [A,B] :
          ( r1_tarski(A,B)
         => r1_tarski(f2_s1_knaster(A),f2_s1_knaster(B)) )
      & r1_tarski(f2_s1_knaster(f1_s1_knaster),f1_s1_knaster) )
   => ? [A] :
        ( f2_s1_knaster(A) = A
        & r1_tarski(A,f1_s1_knaster) ) )).

fof(redefinition_v1_knaster,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => ( v1_knaster(C,A,B)
      <=> v6_cohsp_1(C) ) ) )).

fof(dt_k1_knaster,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
        & v6_cohsp_1(B)
        & m1_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A)) )
     => m1_subset_1(k1_knaster(A,B),k1_zfmisc_1(A)) ) )).

fof(dt_k2_knaster,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
        & v6_cohsp_1(B)
        & m1_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A)) )
     => m1_subset_1(k2_knaster(A,B),k1_zfmisc_1(A)) ) )).

fof(dt_k3_knaster,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A)
        & v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k3_knaster(A,B,C),u1_struct_0(A)) ) )).

fof(redefinition_k3_knaster,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A)
        & v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k3_knaster(A,B,C) = k1_funct_1(B,C) ) )).

fof(dt_k4_knaster,axiom,(
    $true )).

fof(dt_k5_knaster,axiom,(
    $true )).

fof(dt_k6_knaster,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A))
        & v3_ordinal1(D) )
     => m1_subset_1(k6_knaster(A,B,C,D),u1_struct_0(A)) ) )).

fof(redefinition_k6_knaster,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A))
        & v3_ordinal1(D) )
     => k6_knaster(A,B,C,D) = k4_knaster(A,B,C,D) ) )).

fof(dt_k7_knaster,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A))
        & v3_ordinal1(D) )
     => m1_subset_1(k7_knaster(A,B,C,D),u1_struct_0(A)) ) )).

fof(redefinition_k7_knaster,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A))
        & v3_ordinal1(D) )
     => k7_knaster(A,B,C,D) = k5_knaster(A,B,C,D) ) )).

fof(dt_k8_knaster,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & ~ v1_xboole_0(B)
        & v2_knaster(B,A)
        & v3_knaster(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v3_struct_0(k8_knaster(A,B))
        & v3_lattices(k8_knaster(A,B))
        & v10_lattices(k8_knaster(A,B))
        & l3_lattices(k8_knaster(A,B)) ) ) )).

fof(dt_k9_knaster,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A)
        & v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
     => ( ~ v3_struct_0(k9_knaster(A,B))
        & v3_lattices(k9_knaster(A,B))
        & v10_lattices(k9_knaster(A,B))
        & l3_lattices(k9_knaster(A,B)) ) ) )).

fof(dt_k10_knaster,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A)
        & v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
        & v14_quantal1(B,A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
     => m1_subset_1(k10_knaster(A,B),u1_struct_0(A)) ) )).

fof(dt_k11_knaster,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A)
        & v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
        & v14_quantal1(B,A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
     => m1_subset_1(k11_knaster(A,B),u1_struct_0(A)) ) )).

fof(d4_knaster,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
        & v6_cohsp_1(B)
        & m2_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A)) )
     => k1_knaster(A,B) = k1_setfam_1(a_2_0_knaster(A,B)) ) )).

fof(d5_knaster,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k1_zfmisc_1(A),k1_zfmisc_1(A))
        & v6_cohsp_1(B)
        & m2_relset_1(B,k1_zfmisc_1(A),k1_zfmisc_1(A)) )
     => k2_knaster(A,B) = k3_tarski(a_2_1_knaster(A,B)) ) )).

fof(d11_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(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)) )
         => ( v14_quantal1(B,A)
           => ! [C] :
                ( ( ~ v3_struct_0(C)
                  & v3_lattices(C)
                  & v10_lattices(C)
                  & l3_lattices(C) )
               => ( C = k9_knaster(A,B)
                <=> ? [D] :
                      ( ~ v1_xboole_0(D)
                      & v2_knaster(D,A)
                      & v3_knaster(D,A)
                      & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                      & D = a_2_2_knaster(A,B)
                      & C = k8_knaster(A,D) ) ) ) ) ) ) )).

fof(t39_knaster,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v14_quantal1(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => u1_struct_0(k9_knaster(A,B)) = a_2_3_knaster(A,B) ) ) )).

fof(fraenkel_a_2_0_knaster,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,k1_zfmisc_1(B),k1_zfmisc_1(B))
        & v6_cohsp_1(C)
        & m2_relset_1(C,k1_zfmisc_1(B),k1_zfmisc_1(B)) )
     => ( r2_hidden(A,a_2_0_knaster(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(B))
            & A = D
            & r1_tarski(k8_funct_2(k1_zfmisc_1(B),k1_zfmisc_1(B),C,D),D) ) ) ) )).

fof(fraenkel_a_2_1_knaster,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,k1_zfmisc_1(B),k1_zfmisc_1(B))
        & v6_cohsp_1(C)
        & m2_relset_1(C,k1_zfmisc_1(B),k1_zfmisc_1(B)) )
     => ( r2_hidden(A,a_2_1_knaster(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(B))
            & A = D
            & r1_tarski(D,k8_funct_2(k1_zfmisc_1(B),k1_zfmisc_1(B),C,D)) ) ) ) )).

fof(fraenkel_a_2_2_knaster,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & v4_lattice3(B)
        & l3_lattices(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
        & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_2_knaster(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & r2_abian(u1_struct_0(B),D,C) ) ) ) )).

fof(fraenkel_a_2_3_knaster,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & v4_lattice3(B)
        & l3_lattices(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
        & v14_quantal1(C,B)
        & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_3_knaster(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & r2_abian(u1_struct_0(B),D,C) ) ) ) )).
%------------------------------------------------------------------------------