SET007 Axioms: SET007+434.ax


%------------------------------------------------------------------------------
% File     : SET007+434 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On the Lattice of Subalgebras of a Universal Algebra
% 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_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   53 (   1 unit)
%            Number of atoms       :  518 (  47 equality)
%            Maximal formula depth :   19 (   9 average)
%            Number of connectives :  535 (  70 ~  ;   0  |; 333  &)
%                                         (  13 <=>; 119 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   38 (   1 propositional; 0-3 arity)
%            Number of functors    :   34 (   2 constant; 0-4 arity)
%            Number of variables   :  124 (   0 singleton; 118 !;   6 ?)
%            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_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ? [B] :
          ( m1_unialg_3(B,A)
          & ~ v1_xboole_0(B) ) ) )).

fof(cc1_unialg_3,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)
         => v2_unialg_2(B) ) ) )).

fof(fc1_unialg_3,axiom,(
    ! [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)
        & l1_unialg_1(A) )
     => ( ~ v3_struct_0(k12_unialg_2(A))
        & v3_lattices(k12_unialg_2(A))
        & v4_lattices(k12_unialg_2(A))
        & v5_lattices(k12_unialg_2(A))
        & v6_lattices(k12_unialg_2(A))
        & v7_lattices(k12_unialg_2(A))
        & v8_lattices(k12_unialg_2(A))
        & v9_lattices(k12_unialg_2(A))
        & v10_lattices(k12_unialg_2(A))
        & v13_lattices(k12_unialg_2(A))
        & v14_lattices(k12_unialg_2(A))
        & v15_lattices(k12_unialg_2(A)) ) ) )).

fof(d1_unialg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m1_unialg_3(B,A)
        <=> ! [C] :
              ( r2_hidden(C,B)
             => m3_unialg_2(C,A) ) ) ) )).

fof(d2_unialg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m2_unialg_3(B,A,k1_unialg_3(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( C = k4_unialg_3(A,B)
              <=> ? [D] :
                    ( m3_unialg_2(D,A)
                    & B = D
                    & C = u1_struct_0(D) ) ) ) ) ) )).

fof(d3_unialg_3,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,k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A))) )
         => ( B = k5_unialg_3(A)
          <=> ! [C] :
                ( m2_unialg_3(C,A,k1_unialg_3(A))
               => k8_funct_2(k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A)),B,C) = k4_unialg_3(A,C) ) ) ) ) )).

fof(t1_unialg_3,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,k1_unialg_3(A))
        <=> ? [C] :
              ( v3_unialg_1(C)
              & m3_unialg_2(C,A)
              & B = C ) ) ) )).

fof(t2_unialg_3,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))
             => ( k2_unialg_1(u1_struct_0(A),C) = np__0
               => ( r2_unialg_2(A,B,C)
                <=> r2_hidden(k1_funct_1(C,k1_xboole_0),B) ) ) ) ) ) )).

fof(t3_unialg_3,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)
         => r1_tarski(u1_struct_0(B),u1_struct_0(A)) ) ) )).

fof(t4_unialg_3,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(u1_struct_0(A),C) = np__0 )
               => k2_unialg_2(A,B,C) = C ) ) ) ) )).

fof(t6_unialg_3,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)
         => k6_unialg_2(A) = k6_unialg_2(B) ) ) )).

fof(t7_unialg_3,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)
             => k6_unialg_2(B) = k6_unialg_2(C) ) ) ) )).

fof(d4_unialg_3,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,k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A))) )
         => ( B = k6_unialg_3(A)
          <=> ! [C] :
                ( m2_unialg_3(C,A,k1_unialg_3(A))
               => ! [D] :
                    ( m3_unialg_2(D,A)
                   => ( C = D
                     => k8_funct_2(k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A)),B,C) = u1_struct_0(D) ) ) ) ) ) ) )).

fof(t8_unialg_3,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] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,k1_funct_1(k6_unialg_3(A),B))
              <=> r1_rlvect_1(B,C) ) ) ) ) )).

fof(t9_unialg_3,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(k1_unialg_3(A))) )
         => ~ v1_xboole_0(k2_funct_2(k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A)),k6_unialg_3(A),B)) ) ) )).

fof(t10_unialg_3,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) )
         => r1_tarski(k6_unialg_2(A),k1_funct_1(k6_unialg_3(A),B)) ) ) )).

fof(t11_unialg_3,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] :
              ( m1_struct_0(C,A,k6_unialg_2(A))
             => r2_hidden(C,u1_struct_0(B)) ) ) ) )).

fof(t12_unialg_3,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] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_unialg_3(A))) )
         => ( ~ v1_xboole_0(k6_setfam_1(u1_struct_0(A),k2_funct_2(k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A)),k6_unialg_3(A),B)))
            & m1_subset_1(k6_setfam_1(u1_struct_0(A),k2_funct_2(k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A)),k6_unialg_3(A),B)),k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).

fof(t13_unialg_3,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) )
     => u1_struct_0(k12_unialg_2(A)) = k1_unialg_3(A) ) )).

fof(t14_unialg_3,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] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_unialg_3(A))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( C = k6_setfam_1(u1_struct_0(A),k2_funct_2(k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A)),k6_unialg_3(A),B))
               => v1_unialg_2(C,A) ) ) ) ) )).

fof(d5_unialg_3,axiom,(
    ! [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)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_unialg_3(A))) )
         => ! [C] :
              ( ( v3_unialg_1(C)
                & m3_unialg_2(C,A) )
             => ( C = k7_unialg_3(A,B)
              <=> u1_struct_0(C) = k6_setfam_1(u1_struct_0(A),k2_funct_2(k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A)),k6_unialg_3(A),B)) ) ) ) ) )).

fof(t15_unialg_3,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] :
          ( m1_subset_1(B,u1_struct_0(k12_unialg_2(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k12_unialg_2(A)))
             => ! [D] :
                  ( ( v3_unialg_1(D)
                    & m3_unialg_2(D,A) )
                 => ! [E] :
                      ( ( v3_unialg_1(E)
                        & m3_unialg_2(E,A) )
                     => ( ( B = D
                          & C = E )
                       => k3_lattices(k12_unialg_2(A),B,C) = k8_unialg_2(A,D,E) ) ) ) ) ) ) )).

fof(t16_unialg_3,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] :
          ( m1_subset_1(B,u1_struct_0(k12_unialg_2(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k12_unialg_2(A)))
             => ! [D] :
                  ( ( v3_unialg_1(D)
                    & m3_unialg_2(D,A) )
                 => ! [E] :
                      ( ( v3_unialg_1(E)
                        & m3_unialg_2(E,A) )
                     => ( ( B = D
                          & C = E )
                       => k4_lattices(k12_unialg_2(A),B,C) = k5_unialg_2(A,D,E) ) ) ) ) ) ) )).

fof(t17_unialg_3,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] :
          ( m1_subset_1(B,u1_struct_0(k12_unialg_2(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k12_unialg_2(A)))
             => ! [D] :
                  ( ( v3_unialg_1(D)
                    & m3_unialg_2(D,A) )
                 => ! [E] :
                      ( ( v3_unialg_1(E)
                        & m3_unialg_2(E,A) )
                     => ( ( B = D
                          & C = E )
                       => ( r3_lattices(k12_unialg_2(A),B,C)
                        <=> r1_tarski(u1_struct_0(D),u1_struct_0(E)) ) ) ) ) ) ) ) )).

fof(t18_unialg_3,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] :
          ( m1_subset_1(B,u1_struct_0(k12_unialg_2(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k12_unialg_2(A)))
             => ! [D] :
                  ( ( v3_unialg_1(D)
                    & m3_unialg_2(D,A) )
                 => ! [E] :
                      ( ( v3_unialg_1(E)
                        & m3_unialg_2(E,A) )
                     => ( ( B = D
                          & C = E )
                       => ( r3_lattices(k12_unialg_2(A),B,C)
                        <=> m3_unialg_2(D,E) ) ) ) ) ) ) ) )).

fof(t19_unialg_3,axiom,(
    ! [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)
        & l1_unialg_1(A) )
     => v15_lattices(k12_unialg_2(A)) ) )).

fof(t20_unialg_3,axiom,(
    ! [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)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( v3_unialg_1(B)
            & m3_unialg_2(B,A) )
         => k5_unialg_2(A,k7_unialg_2(A,k6_unialg_2(A)),B) = k7_unialg_2(A,k6_unialg_2(A)) ) ) )).

fof(t21_unialg_3,axiom,(
    ! [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)
        & l1_unialg_1(A) )
     => k5_lattices(k12_unialg_2(A)) = k7_unialg_2(A,k6_unialg_2(A)) ) )).

fof(t22_unialg_3,axiom,(
    ! [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)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m3_unialg_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( C = u1_struct_0(A)
               => k8_unialg_2(A,k7_unialg_2(A,C),B) = k7_unialg_2(A,C) ) ) ) ) )).

fof(t23_unialg_3,axiom,(
    ! [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)
        & l1_unialg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( B = u1_struct_0(A)
           => k6_lattices(k12_unialg_2(A)) = k7_unialg_2(A,B) ) ) ) )).

fof(t24_unialg_3,axiom,(
    ! [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)
        & l1_unialg_1(A) )
     => k6_lattices(k12_unialg_2(A)) = A ) )).

fof(t25_unialg_3,axiom,(
    ! [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)
        & l1_unialg_1(A) )
     => v4_lattice3(k12_unialg_2(A)) ) )).

fof(d6_unialg_3,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_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & v2_unialg_2(B)
            & l1_unialg_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(k12_unialg_2(A)),u1_struct_0(k12_unialg_2(B)))
                    & m2_relset_1(D,u1_struct_0(k12_unialg_2(A)),u1_struct_0(k12_unialg_2(B))) )
                 => ( D = k8_unialg_3(A,B,C)
                  <=> ! [E] :
                        ( ( v3_unialg_1(E)
                          & m3_unialg_2(E,A) )
                       => ! [F] :
                            ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
                           => ( F = k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(E))
                             => k1_funct_1(D,E) = k7_unialg_2(B,F) ) ) ) ) ) ) ) ) )).

fof(t26_unialg_3,axiom,(
    ! [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)
        & l1_unialg_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( B = k6_relat_1(u1_struct_0(A))
           => k8_unialg_3(A,A,B) = k6_relat_1(u1_struct_0(k12_unialg_2(A))) ) ) ) )).

fof(dt_m1_unialg_3,axiom,(
    $true )).

fof(existence_m1_unialg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ? [B] : m1_unialg_3(B,A) ) )).

fof(dt_m2_unialg_3,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_unialg_3(B,A) )
     => ! [C] :
          ( m2_unialg_3(C,A,B)
         => m3_unialg_2(C,A) ) ) )).

fof(existence_m2_unialg_3,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_unialg_3(B,A) )
     => ? [C] : m2_unialg_3(C,A,B) ) )).

fof(redefinition_m2_unialg_3,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_unialg_3(B,A) )
     => ! [C] :
          ( m2_unialg_3(C,A,B)
        <=> m1_subset_1(C,B) ) ) )).

fof(dt_k1_unialg_3,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(k1_unialg_3(A))
        & m1_unialg_3(k1_unialg_3(A),A) ) ) )).

fof(redefinition_k1_unialg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => k1_unialg_3(A) = k9_unialg_2(A) ) )).

fof(dt_k2_unialg_3,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(k2_unialg_3(A))
        & v1_funct_2(k2_unialg_3(A),k2_zfmisc_1(k1_unialg_3(A),k1_unialg_3(A)),k1_unialg_3(A))
        & m2_relset_1(k2_unialg_3(A),k2_zfmisc_1(k1_unialg_3(A),k1_unialg_3(A)),k1_unialg_3(A)) ) ) )).

fof(redefinition_k2_unialg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => k2_unialg_3(A) = k10_unialg_2(A) ) )).

fof(dt_k3_unialg_3,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(k3_unialg_3(A))
        & v1_funct_2(k3_unialg_3(A),k2_zfmisc_1(k1_unialg_3(A),k1_unialg_3(A)),k1_unialg_3(A))
        & m2_relset_1(k3_unialg_3(A),k2_zfmisc_1(k1_unialg_3(A),k1_unialg_3(A)),k1_unialg_3(A)) ) ) )).

fof(redefinition_k3_unialg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => k3_unialg_3(A) = k11_unialg_2(A) ) )).

fof(dt_k4_unialg_3,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_unialg_3(A)) )
     => m1_subset_1(k4_unialg_3(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k5_unialg_3,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(k5_unialg_3(A))
        & v1_funct_2(k5_unialg_3(A),k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A)))
        & m2_relset_1(k5_unialg_3(A),k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(dt_k6_unialg_3,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(k6_unialg_3(A))
        & v1_funct_2(k6_unialg_3(A),k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A)))
        & m2_relset_1(k6_unialg_3(A),k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(redefinition_k6_unialg_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => k6_unialg_3(A) = k5_unialg_3(A) ) )).

fof(dt_k7_unialg_3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_unialg_1(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & v2_unialg_2(A)
        & l1_unialg_1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_unialg_3(A))) )
     => ( v3_unialg_1(k7_unialg_3(A,B))
        & m3_unialg_2(k7_unialg_3(A,B),A) ) ) )).

fof(dt_k8_unialg_3,axiom,(
    ! [A,B,C] :
      ( ( ~ 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(B)
        & v6_unialg_1(B)
        & v7_unialg_1(B)
        & v8_unialg_1(B)
        & v2_unialg_2(B)
        & l1_unialg_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => ( v1_funct_1(k8_unialg_3(A,B,C))
        & v1_funct_2(k8_unialg_3(A,B,C),u1_struct_0(k12_unialg_2(A)),u1_struct_0(k12_unialg_2(B)))
        & m2_relset_1(k8_unialg_3(A,B,C),u1_struct_0(k12_unialg_2(A)),u1_struct_0(k12_unialg_2(B))) ) ) )).

fof(t5_unialg_3,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_3(A) ) )).

fof(fraenkel_a_1_0_unialg_3,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_3(B))
      <=> ? [C] :
            ( m2_unialg_2(C,u1_struct_0(B),k1_unialg_2(B))
            & A = k1_funct_1(C,k1_xboole_0)
            & k2_unialg_1(u1_struct_0(B),C) = np__0 ) ) ) )).
%------------------------------------------------------------------------------