SET007 Axioms: SET007+461.ax


%------------------------------------------------------------------------------
% File     : SET007+461 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : More on the Lattice of Congruences in Many Sorted 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    : msualg_8 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   34 (   3 unit)
%            Number of atoms       :  294 (  29 equality)
%            Maximal formula depth :   19 (  10 average)
%            Number of connectives :  305 (  45 ~  ;   2  |; 168  &)
%                                         (   7 <=>;  83 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   43 (   0 propositional; 1-4 arity)
%            Number of functors    :   35 (   4 constant; 0-5 arity)
%            Number of variables   :  112 (   0 singleton; 105 !;   7 ?)
%            Maximal term depth    :    5 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_msualg_8,axiom,(
    ! [A] :
      ( ~ v3_struct_0(k2_msualg_5(A))
      & v3_lattices(k2_msualg_5(A))
      & v4_lattices(k2_msualg_5(A))
      & v5_lattices(k2_msualg_5(A))
      & v6_lattices(k2_msualg_5(A))
      & v7_lattices(k2_msualg_5(A))
      & v8_lattices(k2_msualg_5(A))
      & v9_lattices(k2_msualg_5(A))
      & v10_lattices(k2_msualg_5(A))
      & v13_lattices(k2_msualg_5(A))
      & v14_lattices(k2_msualg_5(A))
      & v15_lattices(k2_msualg_5(A)) ) )).

fof(fc2_msualg_8,axiom,(
    ! [A] :
      ( ~ v3_struct_0(k2_msualg_5(A))
      & v3_lattices(k2_msualg_5(A))
      & v4_lattices(k2_msualg_5(A))
      & v5_lattices(k2_msualg_5(A))
      & v6_lattices(k2_msualg_5(A))
      & v7_lattices(k2_msualg_5(A))
      & v8_lattices(k2_msualg_5(A))
      & v9_lattices(k2_msualg_5(A))
      & v10_lattices(k2_msualg_5(A))
      & v13_lattices(k2_msualg_5(A))
      & v14_lattices(k2_msualg_5(A))
      & v15_lattices(k2_msualg_5(A))
      & v4_lattice3(k2_msualg_5(A)) ) )).

fof(fc3_msualg_8,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A) )
     => ( ~ v3_struct_0(k6_msualg_5(A,B))
        & v3_lattices(k6_msualg_5(A,B))
        & v4_lattices(k6_msualg_5(A,B))
        & v5_lattices(k6_msualg_5(A,B))
        & v6_lattices(k6_msualg_5(A,B))
        & v7_lattices(k6_msualg_5(A,B))
        & v8_lattices(k6_msualg_5(A,B))
        & v9_lattices(k6_msualg_5(A,B))
        & v10_lattices(k6_msualg_5(A,B))
        & v13_lattices(k6_msualg_5(A,B))
        & v14_lattices(k6_msualg_5(A,B))
        & v15_lattices(k6_msualg_5(A,B))
        & v4_lattice3(k6_msualg_5(A,B))
        & v1_msualg_7(k6_msualg_5(A,B),k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B)))
        & v2_msualg_7(k6_msualg_5(A,B),k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B))) ) ) )).

fof(t1_msualg_8,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( ( r1_xreal_0(np__1,A)
             => ( r1_xreal_0(k3_finseq_1(B),A)
                | ( r2_hidden(A,k4_finseq_1(B))
                  & r2_hidden(k1_nat_1(A,np__1),k4_finseq_1(B)) ) ) )
            & ( ( r2_hidden(A,k4_finseq_1(B))
                & r2_hidden(k1_nat_1(A,np__1),k4_finseq_1(B)) )
             => ( r1_xreal_0(np__1,A)
                & ~ r1_xreal_0(k3_finseq_1(B),A) ) ) ) ) ) )).

fof(t2_msualg_8,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,u1_struct_0(k2_msualg_5(A)))
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(k2_msualg_5(A)))
         => ! [D] :
              ( ( v3_relat_2(D)
                & v8_relat_2(D)
                & v1_partfun1(D,A,A)
                & m2_relset_1(D,A,A) )
             => ! [E] :
                  ( ( v3_relat_2(E)
                    & v8_relat_2(E)
                    & v1_partfun1(E,A,A)
                    & m2_relset_1(E,A,A) )
                 => ( ( B = D
                      & C = E )
                   => ( r3_lattices(k2_msualg_5(A),B,C)
                    <=> r1_tarski(D,E) ) ) ) ) ) ) )).

fof(t3_msualg_8,axiom,(
    ! [A] : k5_lattices(k2_msualg_5(A)) = k6_partfun1(A) )).

fof(t4_msualg_8,axiom,(
    ! [A] : k6_lattices(k2_msualg_5(A)) = k1_eqrel_1(A) )).

fof(t5_msualg_8,axiom,(
    ! [A] : v4_lattice3(k2_msualg_5(A)) )).

fof(t6_msualg_8,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_msualg_5(A))))
     => m2_relset_1(k3_tarski(B),A,A) ) )).

fof(t7_msualg_8,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_msualg_5(A))))
     => r1_tarski(k3_tarski(B),k15_lattice3(k2_msualg_5(A),B)) ) )).

fof(t8_msualg_8,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_msualg_5(A))))
     => ! [C] :
          ( m2_relset_1(C,A,A)
         => ( C = k3_tarski(B)
           => k15_lattice3(k2_msualg_5(A),B) = k1_msualg_5(A,C) ) ) ) )).

fof(t9_msualg_8,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_msualg_5(A))))
     => ! [C] :
          ( v1_relat_1(C)
         => ( C = k3_tarski(B)
           => C = k4_relat_1(C) ) ) ) )).

fof(t10_msualg_8,axiom,(
    ! [A,B,C,D] :
      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k2_msualg_5(C))))
     => ( ( r2_hidden(A,C)
          & r2_hidden(B,C) )
       => ( r2_hidden(k4_tarski(A,B),k15_lattice3(k2_msualg_5(C),D))
        <=> ? [E] :
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & v1_finseq_1(E)
              & r1_xreal_0(np__1,k3_finseq_1(E))
              & A = k1_funct_1(E,np__1)
              & B = k1_funct_1(E,k3_finseq_1(E))
              & ! [F] :
                  ( m2_subset_1(F,k1_numbers,k5_numbers)
                 => ( r1_xreal_0(np__1,F)
                   => ( r1_xreal_0(k3_finseq_1(E),F)
                      | r2_hidden(k4_tarski(k1_funct_1(E,F),k1_funct_1(E,k1_nat_1(F,np__1))),k3_tarski(D)) ) ) ) ) ) ) ) )).

fof(t11_msualg_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_msualg_5(A,B))))
             => ( v3_msualg_4(k16_lattice3(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B)),C),A,B)
                & v4_msualg_4(k16_lattice3(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B)),C),A,B)
                & m1_msualg_4(k16_lattice3(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B)),C),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ) ) )).

fof(t12_msualg_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B))))
             => ( ( v3_msualg_4(C,A,B)
                  & v4_msualg_4(C,A,B)
                  & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
               => k1_msualg_8(A,B,C) = C ) ) ) ) )).

fof(t13_msualg_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B)))))
             => r6_pboole(u1_struct_0(A),k1_msualg_8(A,B,k15_lattice3(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B)),C)),k2_msualg_8(A,B,C)) ) ) ) )).

fof(t14_msualg_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_msualg_5(A,B))))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_msualg_5(A,B))))
                 => ! [E] :
                      ( ( v3_msualg_4(E,A,B)
                        & v4_msualg_4(E,A,B)
                        & m1_msualg_4(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
                     => ! [F] :
                          ( ( v3_msualg_4(F,A,B)
                            & v4_msualg_4(F,A,B)
                            & m1_msualg_4(F,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
                         => ( ( E = k15_lattice3(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B)),C)
                              & F = k15_lattice3(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B)),D) )
                           => k4_msualg_5(u1_struct_0(A),u4_msualg_1(A,B),E,F) = k15_lattice3(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B)),k4_subset_1(u1_struct_0(k6_msualg_5(A,B)),C,D)) ) ) ) ) ) ) ) )).

fof(t16_msualg_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_pboole(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( ( v3_relat_2(D)
                    & v8_relat_2(D)
                    & v1_partfun1(D,k1_funct_1(B,C),k1_funct_1(B,C))
                    & m2_relset_1(D,k1_funct_1(B,C),k1_funct_1(B,C)) )
                 => ? [E] :
                      ( v2_msualg_4(E,A,B)
                      & m1_msualg_4(E,A,B,B)
                      & k1_msualg_4(A,B,B,E,C) = D
                      & ! [F] :
                          ( m1_subset_1(F,A)
                         => ( F != C
                           => k1_msualg_4(A,B,B,E,F) = k1_eqrel_1(k1_funct_1(B,F)) ) ) ) ) ) ) ) )).

fof(d3_msualg_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_pboole(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_msualg_5(A,B))))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k2_msualg_5(k1_funct_1(B,C)))))
                     => ( E = k3_msualg_8(A,B,C,D)
                      <=> ! [F] :
                            ( r2_hidden(F,E)
                          <=> ? [G] :
                                ( v2_msualg_4(G,A,B)
                                & m1_msualg_4(G,A,B,B)
                                & F = k1_msualg_4(A,B,B,G,C)
                                & r2_hidden(G,D) ) ) ) ) ) ) ) ) )).

fof(t17_msualg_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B)))))
                 => ! [E] :
                      ( ( v2_msualg_4(E,u1_struct_0(A),u4_msualg_1(A,B))
                        & m1_msualg_4(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
                     => ( E = k15_lattice3(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B)),D)
                       => k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),E,C) = k15_lattice3(k2_msualg_5(k1_funct_1(u4_msualg_1(A,B),C)),k3_msualg_8(u1_struct_0(A),u4_msualg_1(A,B),C,D)) ) ) ) ) ) ) )).

fof(t18_msualg_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_msualg_5(A,B))))
             => ( v3_msualg_4(k15_lattice3(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B)),C),A,B)
                & v4_msualg_4(k15_lattice3(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B)),C),A,B)
                & m1_msualg_4(k15_lattice3(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B)),C),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ) ) )).

fof(t19_msualg_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => v1_msualg_7(k6_msualg_5(A,B),k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B))) ) ) )).

fof(t20_msualg_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => v2_msualg_7(k6_msualg_5(A,B),k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B))) ) ) )).

fof(s1_msualg_8,axiom,
    ( ! [A] :
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ~ ( r2_hidden(A,k2_finseq_1(f1_s1_msualg_8))
            & ! [B] : ~ p1_s1_msualg_8(A,B) ) )
   => ? [A] :
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & k4_finseq_1(A) = k2_finseq_1(f1_s1_msualg_8)
        & ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( r2_hidden(B,k2_finseq_1(f1_s1_msualg_8))
             => p1_s1_msualg_8(B,k1_funct_1(A,B)) ) ) ) )).

fof(dt_k1_msualg_8,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A)
        & m1_subset_1(C,u1_struct_0(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B)))) )
     => ( v3_msualg_4(k1_msualg_8(A,B,C),A,B)
        & v4_msualg_4(k1_msualg_8(A,B,C),A,B)
        & m1_msualg_4(k1_msualg_8(A,B,C),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) )).

fof(dt_k2_msualg_8,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B))))) )
     => ( v3_msualg_4(k2_msualg_8(A,B,C),A,B)
        & v4_msualg_4(k2_msualg_8(A,B,C),A,B)
        & m1_msualg_4(k2_msualg_8(A,B,C),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) )).

fof(dt_k3_msualg_8,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A)
        & m1_subset_1(C,A)
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_msualg_5(A,B)))) )
     => m1_subset_1(k3_msualg_8(A,B,C,D),k1_zfmisc_1(u1_struct_0(k2_msualg_5(k1_funct_1(B,C))))) ) )).

fof(redefinition_k3_msualg_8,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A)
        & m1_subset_1(C,A)
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_msualg_5(A,B)))) )
     => k3_msualg_8(A,B,C,D) = k5_card_3(C,D) ) )).

fof(d1_msualg_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B))))
             => k1_msualg_8(A,B,C) = k16_lattice3(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B)),a_3_0_msualg_8(A,B,C)) ) ) ) )).

fof(d2_msualg_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B)))))
             => k2_msualg_8(A,B,C) = k16_lattice3(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B)),a_3_1_msualg_8(A,B,C)) ) ) ) )).

fof(t15_msualg_8,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_msualg_5(A,B))))
             => k15_lattice3(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B)),C) = k15_lattice3(k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B)),a_3_2_msualg_8(A,B,C)) ) ) ) )).

fof(fraenkel_a_3_0_msualg_8,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & v5_msualg_1(C,B)
        & l3_msualg_1(C,B)
        & m1_subset_1(D,u1_struct_0(k5_msualg_5(u1_struct_0(B),u4_msualg_1(B,C)))) )
     => ( r2_hidden(A,a_3_0_msualg_8(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(k5_msualg_5(u1_struct_0(B),u4_msualg_1(B,C))))
            & A = E
            & v3_msualg_4(E,B,C)
            & v4_msualg_4(E,B,C)
            & m1_msualg_4(E,u1_struct_0(B),u4_msualg_1(B,C),u4_msualg_1(B,C))
            & r3_lattices(k5_msualg_5(u1_struct_0(B),u4_msualg_1(B,C)),D,E) ) ) ) )).

fof(fraenkel_a_3_1_msualg_8,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & v5_msualg_1(C,B)
        & l3_msualg_1(C,B)
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_msualg_5(u1_struct_0(B),u4_msualg_1(B,C))))) )
     => ( r2_hidden(A,a_3_1_msualg_8(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(k5_msualg_5(u1_struct_0(B),u4_msualg_1(B,C))))
            & A = E
            & v3_msualg_4(E,B,C)
            & v4_msualg_4(E,B,C)
            & m1_msualg_4(E,u1_struct_0(B),u4_msualg_1(B,C),u4_msualg_1(B,C))
            & r4_lattice3(k5_msualg_5(u1_struct_0(B),u4_msualg_1(B,C)),E,D) ) ) ) )).

fof(fraenkel_a_3_2_msualg_8,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & v5_msualg_1(C,B)
        & l3_msualg_1(C,B)
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_msualg_5(B,C)))) )
     => ( r2_hidden(A,a_3_2_msualg_8(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k5_msualg_5(u1_struct_0(B),u4_msualg_1(B,C)))))
            & A = k15_lattice3(k5_msualg_5(u1_struct_0(B),u4_msualg_1(B,C)),E)
            & v1_finset_1(E)
            & m1_subset_1(E,k1_zfmisc_1(D)) ) ) ) )).
%------------------------------------------------------------------------------