SET007 Axioms: SET007+373.ax


%------------------------------------------------------------------------------
% File     : SET007+373 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Subalgebras of the Universal Algebra. Lattices of Subalgebras
% 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    : unialg_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   74 (   1 unit)
%            Number of atoms       :  708 (  58 equality)
%            Maximal formula depth :   16 (   9 average)
%            Number of connectives :  751 ( 117 ~  ;   1  |; 439  &)
%                                         (  16 <=>; 178 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   32 (   1 propositional; 0-3 arity)
%            Number of functors    :   39 (   4 constant; 0-6 arity)
%            Number of variables   :  179 (   0 singleton; 171 !;   8 ?)
%            Maximal term depth    :    5 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ? [B] :
          ( m3_unialg_2(B,A)
          & ~ v3_struct_0(B)
          & v3_unialg_1(B)
          & v6_unialg_1(B)
          & v7_unialg_1(B)
          & v8_unialg_1(B) ) ) )).

fof(rc2_unialg_2,axiom,(
    ? [A] :
      ( l1_unialg_1(A)
      & ~ v3_struct_0(A)
      & v3_unialg_1(A)
      & v6_unialg_1(A)
      & v7_unialg_1(A)
      & v8_unialg_1(A)
      & v2_unialg_2(A) ) )).

fof(fc1_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & v2_unialg_2(A)
        & l1_unialg_1(A) )
     => ~ v1_xboole_0(k6_unialg_2(A)) ) )).

fof(fc2_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ~ v1_xboole_0(k9_unialg_2(A)) ) )).

fof(t1_unialg_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(B)) )
             => k3_xboole_0(k4_finseq_2(A,B),k4_finseq_2(A,C)) = k4_finseq_2(A,C) ) ) ) )).

fof(t2_unialg_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_funct_1(B)
            & v1_unialg_1(B,A)
            & v2_unialg_1(B,A)
            & m2_relset_1(B,k3_finseq_2(A),A) )
         => k1_relat_1(B) = k4_finseq_2(k2_unialg_1(A,B),A) ) ) )).

fof(d1_unialg_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ( m1_unialg_2(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,B)
               => ( ~ v1_xboole_0(C)
                  & v1_funct_1(C)
                  & v1_unialg_1(C,A)
                  & v2_unialg_1(C,A)
                  & m2_relset_1(C,k3_finseq_2(A),A) ) ) ) ) ) )).

fof(d2_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( r1_unialg_2(A,B)
          <=> k3_unialg_1(A) = k3_unialg_1(B) ) ) ) )).

fof(t3_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( r1_unialg_2(A,B)
           => k3_finseq_1(u1_unialg_1(A)) = k3_finseq_1(u1_unialg_1(B)) ) ) ) )).

fof(t4_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_unialg_1(C)
                & v7_unialg_1(C)
                & v8_unialg_1(C)
                & l1_unialg_1(C) )
             => ( ( r1_unialg_2(A,B)
                  & r1_unialg_2(B,C) )
               => r1_unialg_2(A,C) ) ) ) ) )).

fof(t5_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ( ~ v1_xboole_0(k2_relat_1(u1_unialg_1(A)))
        & m1_subset_1(k2_relat_1(u1_unialg_1(A)),k1_zfmisc_1(k4_partfun1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)))) ) ) )).

fof(d3_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => k1_unialg_2(A) = k2_relat_1(u1_unialg_1(A)) ) )).

fof(t6_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( r2_hidden(B,k4_finseq_1(u1_unialg_1(A)))
         => m2_unialg_2(k1_funct_1(u1_unialg_1(A),B),u1_struct_0(A),k1_unialg_2(A)) ) ) )).

fof(d4_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
             => ( r2_unialg_2(A,B,C)
              <=> ! [D] :
                    ( m2_finseq_1(D,B)
                   => ( k3_finseq_1(D) = k2_unialg_1(u1_struct_0(A),C)
                     => r2_hidden(k1_funct_1(C,D),B) ) ) ) ) ) ) )).

fof(d5_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_unialg_2(B,A)
          <=> ! [C] :
                ( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
               => r2_unialg_2(A,B,C) ) ) ) ) )).

fof(d6_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
             => ( r2_unialg_2(A,B,C)
               => k2_unialg_2(A,B,C) = k2_partfun1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),C,k4_finseq_2(k2_unialg_1(u1_struct_0(A),C),B)) ) ) ) ) )).

fof(d7_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m2_finseq_1(C,k4_partfun1(k13_finseq_1(B),B))
             => ( C = k3_unialg_2(A,B)
              <=> ( k4_finseq_1(C) = k4_finseq_1(u1_unialg_1(A))
                  & ! [D,E] :
                      ( m2_unialg_2(E,u1_struct_0(A),k1_unialg_2(A))
                     => ( ( r2_hidden(D,k4_finseq_1(C))
                          & E = k1_funct_1(u1_unialg_1(A),D) )
                       => k1_funct_1(C,D) = k2_unialg_2(A,B,E) ) ) ) ) ) ) ) )).

fof(t7_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( B = u1_struct_0(A)
           => ( v1_unialg_2(B,A)
              & ! [C] :
                  ( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
                 => k2_unialg_2(A,B,C) = C ) ) ) ) ) )).

fof(t8_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
             => ( r2_unialg_2(A,B,C)
               => k2_unialg_1(B,k2_unialg_2(A,B,C)) = k2_unialg_1(u1_struct_0(A),C) ) ) ) ) )).

fof(d8_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( m3_unialg_2(B,A)
          <=> ( m1_subset_1(u1_struct_0(B),k1_zfmisc_1(u1_struct_0(A)))
              & ! [C] :
                  ( ( ~ v1_xboole_0(C)
                    & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
                 => ( C = u1_struct_0(B)
                   => ( u1_unialg_1(B) = k3_unialg_2(A,C)
                      & v1_unialg_2(C,A) ) ) ) ) ) ) ) )).

fof(t9_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] :
              ( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
             => ! [D] :
                  ( m2_unialg_2(D,u1_struct_0(B),k1_unialg_2(B))
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( m3_unialg_2(A,B)
                          & r2_hidden(E,k4_finseq_1(u1_unialg_1(A)))
                          & C = k1_funct_1(u1_unialg_1(A),E)
                          & D = k1_funct_1(u1_unialg_1(B),E) )
                       => k2_unialg_1(u1_struct_0(A),C) = k2_unialg_1(u1_struct_0(B),D) ) ) ) ) ) ) )).

fof(t10_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( m3_unialg_2(A,B)
           => k4_finseq_1(u1_unialg_1(A)) = k4_finseq_1(u1_unialg_1(B)) ) ) ) )).

fof(t11_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => m3_unialg_2(A,A) ) )).

fof(t12_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v6_unialg_1(C)
                & v7_unialg_1(C)
                & v8_unialg_1(C)
                & l1_unialg_1(C) )
             => ( ( m3_unialg_2(A,B)
                  & m3_unialg_2(B,C) )
               => m3_unialg_2(A,C) ) ) ) ) )).

fof(t13_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( ( v3_unialg_1(A)
              & m3_unialg_2(A,B)
              & v3_unialg_1(B)
              & m3_unialg_2(B,A) )
           => A = B ) ) ) )).

fof(t14_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m3_unialg_2(B,A)
         => ! [C] :
              ( m3_unialg_2(C,A)
             => ( r1_tarski(u1_struct_0(B),u1_struct_0(C))
               => m3_unialg_2(B,C) ) ) ) ) )).

fof(t15_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( v3_unialg_1(B)
            & m3_unialg_2(B,A) )
         => ! [C] :
              ( ( v3_unialg_1(C)
                & m3_unialg_2(C,A) )
             => ( u1_struct_0(B) = u1_struct_0(C)
               => B = C ) ) ) ) )).

fof(t16_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( m3_unialg_2(A,B)
           => r1_unialg_2(A,B) ) ) ) )).

fof(t17_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( ~ v3_struct_0(g1_unialg_1(B,k3_unialg_2(A,B)))
            & v3_unialg_1(g1_unialg_1(B,k3_unialg_2(A,B)))
            & v6_unialg_1(g1_unialg_1(B,k3_unialg_2(A,B)))
            & v7_unialg_1(g1_unialg_1(B,k3_unialg_2(A,B)))
            & v8_unialg_1(g1_unialg_1(B,k3_unialg_2(A,B)))
            & l1_unialg_1(g1_unialg_1(B,k3_unialg_2(A,B))) ) ) ) )).

fof(d9_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( v1_unialg_2(B,A)
           => k4_unialg_2(A,B) = g1_unialg_1(B,k3_unialg_2(A,B)) ) ) ) )).

fof(d10_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m3_unialg_2(B,A)
         => ! [C] :
              ( m3_unialg_2(C,A)
             => ( ~ r2_subset_1(u1_struct_0(B),u1_struct_0(C))
               => ! [D] :
                    ( ( v3_unialg_1(D)
                      & m3_unialg_2(D,A) )
                   => ( D = k5_unialg_2(A,B,C)
                    <=> ( u1_struct_0(D) = k3_xboole_0(u1_struct_0(B),u1_struct_0(C))
                        & ! [E] :
                            ( ( ~ v1_xboole_0(E)
                              & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) )
                           => ( E = u1_struct_0(D)
                             => ( u1_unialg_1(D) = k3_unialg_2(A,E)
                                & v1_unialg_2(E,A) ) ) ) ) ) ) ) ) ) ) )).

fof(d12_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ( v2_unialg_2(A)
      <=> ? [B] :
            ( m2_unialg_2(B,u1_struct_0(A),k1_unialg_2(A))
            & k2_unialg_1(u1_struct_0(A),B) = np__0 ) ) ) )).

fof(t18_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m3_unialg_2(B,A)
         => m1_subset_1(k6_unialg_2(A),k1_zfmisc_1(u1_struct_0(B))) ) ) )).

fof(t19_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & v2_unialg_2(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m3_unialg_2(B,A)
         => ( ~ v1_xboole_0(k6_unialg_2(A))
            & m1_subset_1(k6_unialg_2(A),k1_zfmisc_1(u1_struct_0(B))) ) ) ) )).

fof(t20_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & v2_unialg_2(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m3_unialg_2(B,A)
         => ! [C] :
              ( m3_unialg_2(C,A)
             => ~ r2_subset_1(u1_struct_0(B),u1_struct_0(C)) ) ) ) )).

fof(d13_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ~ ( k6_unialg_2(A) = k1_xboole_0
                & B = k1_xboole_0 )
           => ! [C] :
                ( ( v3_unialg_1(C)
                  & m3_unialg_2(C,A) )
               => ( C = k7_unialg_2(A,B)
                <=> ( r1_tarski(B,u1_struct_0(C))
                    & ! [D] :
                        ( m3_unialg_2(D,A)
                       => ( r1_tarski(B,u1_struct_0(D))
                         => m3_unialg_2(C,D) ) ) ) ) ) ) ) ) )).

fof(t21_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_unialg_1(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => k7_unialg_2(A,k2_subset_1(u1_struct_0(A))) = A ) )).

fof(t22_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( v3_unialg_1(B)
            & m3_unialg_2(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( C = u1_struct_0(B)
               => k7_unialg_2(A,C) = B ) ) ) ) )).

fof(d14_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m3_unialg_2(B,A)
         => ! [C] :
              ( m3_unialg_2(C,A)
             => ! [D] :
                  ( ( v3_unialg_1(D)
                    & m3_unialg_2(D,A) )
                 => ( D = k8_unialg_2(A,B,C)
                  <=> ! [E] :
                        ( ( ~ v1_xboole_0(E)
                          & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) )
                       => ( E = k2_xboole_0(u1_struct_0(B),u1_struct_0(C))
                         => D = k7_unialg_2(A,E) ) ) ) ) ) ) ) )).

fof(t23_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m3_unialg_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( D = k2_xboole_0(C,u1_struct_0(B))
                   => ( ( C = k1_xboole_0
                        & k6_unialg_2(A) = k1_xboole_0 )
                      | k8_unialg_2(A,k7_unialg_2(A,C),B) = k7_unialg_2(A,D) ) ) ) ) ) ) )).

fof(t24_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m3_unialg_2(B,A)
         => ! [C] :
              ( m3_unialg_2(C,A)
             => k8_unialg_2(A,B,C) = k8_unialg_2(A,C,B) ) ) ) )).

fof(t25_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & v2_unialg_2(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( v3_unialg_1(B)
            & m3_unialg_2(B,A) )
         => ! [C] :
              ( ( v3_unialg_1(C)
                & m3_unialg_2(C,A) )
             => k5_unialg_2(A,B,k8_unialg_2(A,B,C)) = B ) ) ) )).

fof(t26_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & v2_unialg_2(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( v3_unialg_1(B)
            & m3_unialg_2(B,A) )
         => ! [C] :
              ( ( v3_unialg_1(C)
                & m3_unialg_2(C,A) )
             => k8_unialg_2(A,k5_unialg_2(A,B,C),C) = C ) ) ) )).

fof(d15_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( B = k9_unialg_2(A)
        <=> ! [C] :
              ( r2_hidden(C,B)
            <=> ( v3_unialg_1(C)
                & m3_unialg_2(C,A) ) ) ) ) )).

fof(d16_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(k9_unialg_2(A),k9_unialg_2(A)),k9_unialg_2(A))
            & m2_relset_1(B,k2_zfmisc_1(k9_unialg_2(A),k9_unialg_2(A)),k9_unialg_2(A)) )
         => ( B = k10_unialg_2(A)
          <=> ! [C] :
                ( m1_subset_1(C,k9_unialg_2(A))
               => ! [D] :
                    ( m1_subset_1(D,k9_unialg_2(A))
                   => ! [E] :
                        ( ( v3_unialg_1(E)
                          & m3_unialg_2(E,A) )
                       => ! [F] :
                            ( ( v3_unialg_1(F)
                              & m3_unialg_2(F,A) )
                           => ( ( C = E
                                & D = F )
                             => k2_binop_1(k9_unialg_2(A),k9_unialg_2(A),k9_unialg_2(A),B,C,D) = k8_unialg_2(A,E,F) ) ) ) ) ) ) ) ) )).

fof(d17_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(k9_unialg_2(A),k9_unialg_2(A)),k9_unialg_2(A))
            & m2_relset_1(B,k2_zfmisc_1(k9_unialg_2(A),k9_unialg_2(A)),k9_unialg_2(A)) )
         => ( B = k11_unialg_2(A)
          <=> ! [C] :
                ( m1_subset_1(C,k9_unialg_2(A))
               => ! [D] :
                    ( m1_subset_1(D,k9_unialg_2(A))
                   => ! [E] :
                        ( ( v3_unialg_1(E)
                          & m3_unialg_2(E,A) )
                       => ! [F] :
                            ( ( v3_unialg_1(F)
                              & m3_unialg_2(F,A) )
                           => ( ( C = E
                                & D = F )
                             => k2_binop_1(k9_unialg_2(A),k9_unialg_2(A),k9_unialg_2(A),B,C,D) = k5_unialg_2(A,E,F) ) ) ) ) ) ) ) ) )).

fof(t27_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => v1_binop_1(k10_unialg_2(A),k9_unialg_2(A)) ) )).

fof(t28_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => v2_binop_1(k10_unialg_2(A),k9_unialg_2(A)) ) )).

fof(t29_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & v2_unialg_2(A)
        & l1_unialg_1(A) )
     => v1_binop_1(k11_unialg_2(A),k9_unialg_2(A)) ) )).

fof(t30_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & v2_unialg_2(A)
        & l1_unialg_1(A) )
     => v2_binop_1(k11_unialg_2(A),k9_unialg_2(A)) ) )).

fof(d18_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & v2_unialg_2(A)
        & l1_unialg_1(A) )
     => k12_unialg_2(A) = g3_lattices(k9_unialg_2(A),k10_unialg_2(A),k11_unialg_2(A)) ) )).

fof(dt_m1_unialg_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_unialg_2(B,A)
         => ~ v1_xboole_0(B) ) ) )).

fof(existence_m1_unialg_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] : m1_unialg_2(B,A) ) )).

fof(dt_m2_unialg_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_unialg_2(B,A) )
     => ! [C] :
          ( m2_unialg_2(C,A,B)
         => ( ~ v1_xboole_0(C)
            & v1_funct_1(C)
            & v1_unialg_1(C,A)
            & v2_unialg_1(C,A)
            & m2_relset_1(C,k3_finseq_2(A),A) ) ) ) )).

fof(existence_m2_unialg_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_unialg_2(B,A) )
     => ? [C] : m2_unialg_2(C,A,B) ) )).

fof(redefinition_m2_unialg_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_unialg_2(B,A) )
     => ! [C] :
          ( m2_unialg_2(C,A,B)
        <=> m1_subset_1(C,B) ) ) )).

fof(dt_m3_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m3_unialg_2(B,A)
         => ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) ) ) ) )).

fof(existence_m3_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ? [B] : m3_unialg_2(B,A) ) )).

fof(symmetry_r1_unialg_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & ~ v3_struct_0(B)
        & v6_unialg_1(B)
        & v7_unialg_1(B)
        & v8_unialg_1(B)
        & l1_unialg_1(B) )
     => ( r1_unialg_2(A,B)
       => r1_unialg_2(B,A) ) ) )).

fof(reflexivity_r1_unialg_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & ~ v3_struct_0(B)
        & v6_unialg_1(B)
        & v7_unialg_1(B)
        & v8_unialg_1(B)
        & l1_unialg_1(B) )
     => r1_unialg_2(A,A) ) )).

fof(dt_k1_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => m1_unialg_2(k1_unialg_2(A),u1_struct_0(A)) ) )).

fof(dt_k2_unialg_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_unialg_2(A)) )
     => ( ~ v1_xboole_0(k2_unialg_2(A,B,C))
        & v1_funct_1(k2_unialg_2(A,B,C))
        & v1_unialg_1(k2_unialg_2(A,B,C),B)
        & v2_unialg_1(k2_unialg_2(A,B,C),B)
        & m2_relset_1(k2_unialg_2(A,B,C),k3_finseq_2(B),B) ) ) )).

fof(dt_k3_unialg_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m2_finseq_1(k3_unialg_2(A,B),k4_partfun1(k13_finseq_1(B),B)) ) )).

fof(dt_k4_unialg_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v3_unialg_1(k4_unialg_2(A,B))
        & m3_unialg_2(k4_unialg_2(A,B),A) ) ) )).

fof(dt_k5_unialg_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & m3_unialg_2(B,A)
        & m3_unialg_2(C,A) )
     => ( v3_unialg_1(k5_unialg_2(A,B,C))
        & m3_unialg_2(k5_unialg_2(A,B,C),A) ) ) )).

fof(dt_k6_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => m1_subset_1(k6_unialg_2(A),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k7_unialg_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v3_unialg_1(k7_unialg_2(A,B))
        & m3_unialg_2(k7_unialg_2(A,B),A) ) ) )).

fof(dt_k8_unialg_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & m3_unialg_2(B,A)
        & m3_unialg_2(C,A) )
     => ( v3_unialg_1(k8_unialg_2(A,B,C))
        & m3_unialg_2(k8_unialg_2(A,B,C),A) ) ) )).

fof(dt_k9_unialg_2,axiom,(
    $true )).

fof(dt_k10_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ( v1_funct_1(k10_unialg_2(A))
        & v1_funct_2(k10_unialg_2(A),k2_zfmisc_1(k9_unialg_2(A),k9_unialg_2(A)),k9_unialg_2(A))
        & m2_relset_1(k10_unialg_2(A),k2_zfmisc_1(k9_unialg_2(A),k9_unialg_2(A)),k9_unialg_2(A)) ) ) )).

fof(dt_k11_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ( v1_funct_1(k11_unialg_2(A))
        & v1_funct_2(k11_unialg_2(A),k2_zfmisc_1(k9_unialg_2(A),k9_unialg_2(A)),k9_unialg_2(A))
        & m2_relset_1(k11_unialg_2(A),k2_zfmisc_1(k9_unialg_2(A),k9_unialg_2(A)),k9_unialg_2(A)) ) ) )).

fof(dt_k12_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & v2_unialg_2(A)
        & l1_unialg_1(A) )
     => ( ~ v3_struct_0(k12_unialg_2(A))
        & v3_lattices(k12_unialg_2(A))
        & v10_lattices(k12_unialg_2(A))
        & l3_lattices(k12_unialg_2(A)) ) ) )).

fof(d11_unialg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => k6_unialg_2(A) = a_1_0_unialg_2(A) ) )).

fof(fraenkel_a_1_0_unialg_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v6_unialg_1(B)
        & v7_unialg_1(B)
        & v8_unialg_1(B)
        & l1_unialg_1(B) )
     => ( r2_hidden(A,a_1_0_unialg_2(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(B))
            & A = C
            & ? [D] :
                ( m2_unialg_2(D,u1_struct_0(B),k1_unialg_2(B))
                & k2_unialg_1(u1_struct_0(B),D) = np__0
                & r2_hidden(C,k2_relat_1(D)) ) ) ) ) )).
%------------------------------------------------------------------------------