SET007 Axioms: SET007+398.ax


%------------------------------------------------------------------------------
% File     : SET007+398 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Free Many Sorted 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    : msafree [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   78 (   4 unit)
%            Number of atoms       :  606 (  63 equality)
%            Maximal formula depth :   25 (   9 average)
%            Number of connectives :  673 ( 145 ~  ;   0  |; 308  &)
%                                         (  27 <=>; 193 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   40 (   1 propositional; 0-4 arity)
%            Number of functors    :   69 (   3 constant; 0-5 arity)
%            Number of variables   :  257 (   0 singleton; 240 !;  17 ?)
%            Maximal term depth    :    6 (   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_msafree,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A) )
     => ( v1_relat_1(k2_card_3(B))
        & v2_relat_1(k2_card_3(B))
        & v1_funct_1(k2_card_3(B)) ) ) )).

fof(fc2_msafree,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A) )
     => ~ v1_xboole_0(k3_card_3(B)) ) )).

fof(fc3_msafree,axiom,(
    ! [A] :
      ( ( ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ~ v1_xboole_0(u1_msualg_1(A)) ) )).

fof(fc4_msafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k5_msafree(A,B))
        & v1_lang1(k5_msafree(A,B)) ) ) )).

fof(fc5_msafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k5_msafree(A,B))
        & v1_lang1(k5_msafree(A,B))
        & v1_dtconstr(k5_msafree(A,B))
        & v2_dtconstr(k5_msafree(A,B))
        & v3_dtconstr(k5_msafree(A,B)) ) ) )).

fof(fc6_msafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( ~ v1_xboole_0(k7_msafree(A,B,C))
        & v3_trees_3(k7_msafree(A,B,C)) ) ) )).

fof(fc7_msafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( v1_relat_1(k8_msafree(A,B))
        & v2_relat_1(k8_msafree(A,B))
        & ~ v3_relat_1(k8_msafree(A,B))
        & v1_funct_1(k8_msafree(A,B)) ) ) )).

fof(fc8_msafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( v4_msualg_1(k11_msafree(A,B),A)
        & v5_msualg_1(k11_msafree(A,B),A) ) ) )).

fof(fc9_msafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ~ v1_xboole_0(k12_msafree(A,B,C)) ) )).

fof(rc1_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ? [B] :
          ( l3_msualg_1(B,A)
          & v4_msualg_1(B,A)
          & v5_msualg_1(B,A)
          & v2_msafree(B,A) ) ) )).

fof(rc2_msafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_msafree(B,A)
        & l3_msualg_1(B,A) )
     => ? [C] :
          ( m1_msafree(C,A,B)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_msafree(C,A,B) ) ) )).

fof(t1_msafree,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k3_finseq_2(B))
            & m2_relset_1(C,A,k3_finseq_2(B)) )
         => ! [D] :
              ( m1_pboole(D,B)
             => ! [E] :
                  ( m2_finseq_2(E,B,k3_finseq_2(B))
                 => ! [F] :
                      ( ( r2_hidden(F,A)
                        & E = k1_funct_1(C,F) )
                     => k1_funct_1(k7_pboole(A,k3_finseq_2(B),C,k6_pboole(B,D)),F) = k4_card_3(k5_relat_1(E,D)) ) ) ) ) ) )).

fof(d1_msafree,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m4_pboole(D,A,B)
             => ! [E] :
                  ( m3_pboole(E,A,B,C)
                 => ! [F] :
                      ( m3_pboole(F,A,D,C)
                     => ( F = k1_msafree(A,B,C,D,E)
                      <=> ! [G] :
                            ( r2_hidden(G,A)
                           => ! [H] :
                                ( ( v1_funct_1(H)
                                  & v1_funct_2(H,k1_funct_1(B,G),k1_funct_1(C,G))
                                  & m2_relset_1(H,k1_funct_1(B,G),k1_funct_1(C,G)) )
                               => ( H = k1_funct_1(E,G)
                                 => k1_funct_1(F,G) = k8_relset_1(k1_funct_1(B,G),k1_funct_1(C,G),H,k1_funct_1(D,G)) ) ) ) ) ) ) ) ) ) )).

fof(d2_msafree,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( r2_hidden(C,A)
         => ! [D] :
              ( D = k2_msafree(A,B,C)
            <=> ! [E] :
                  ( r2_hidden(E,D)
                <=> ? [F] :
                      ( r2_hidden(F,k1_funct_1(B,C))
                      & E = k4_tarski(F,C) ) ) ) ) ) )).

fof(d3_msafree,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m1_pboole(C,A)
         => ( C = k3_msafree(A,B)
          <=> ! [D] :
                ( r2_hidden(D,A)
               => k1_funct_1(C,D) = k2_msafree(A,B,D) ) ) ) ) )).

fof(t2_msafree,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( r2_hidden(C,A)
         => ( ~ ( k1_funct_1(B,C) != k1_xboole_0
                & k1_funct_1(k3_msafree(A,B),C) = k1_xboole_0 )
            & ~ ( k1_funct_1(k3_msafree(A,B),C) != k1_xboole_0
                & k1_funct_1(B,C) = k1_xboole_0 ) ) ) ) )).

fof(d4_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ( m1_msafree(C,A,B)
              <=> r6_pboole(u1_struct_0(A),u4_msualg_1(A,k12_msualg_2(A,B,C)),u4_msualg_1(A,B)) ) ) ) ) )).

fof(t3_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v4_msualg_1(B,A)
            & v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ( m1_msafree(C,A,B)
              <=> k12_msualg_2(A,B,C) = B ) ) ) ) )).

fof(d5_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m1_msafree(C,A,B)
             => ( v1_msafree(C,A,B)
              <=> ! [D] :
                    ( ( v5_msualg_1(D,A)
                      & l3_msualg_1(D,A) )
                   => ! [E] :
                        ( m3_pboole(E,u1_struct_0(A),C,u4_msualg_1(A,D))
                       => ? [F] :
                            ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,D))
                            & r1_msualg_3(A,B,D,F)
                            & r6_pboole(u1_struct_0(A),k1_msafree(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,D),C,F),E) ) ) ) ) ) ) ) )).

fof(d6_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ( v2_msafree(B,A)
          <=> ? [C] :
                ( m1_msafree(C,A,B)
                & v1_msafree(C,A,B) ) ) ) ) )).

fof(t4_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_pboole(B,u1_struct_0(A))
         => r1_xboole_0(k3_card_3(k3_msafree(u1_struct_0(A),B)),k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A)))) ) ) )).

fof(d7_msafree,axiom,(
    $true )).

fof(d8_msafree,axiom,(
    $true )).

fof(d9_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_pboole(B,u1_struct_0(A))
         => ! [C] :
              ( m2_relset_1(C,k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))),k3_finseq_2(k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B)))))
             => ( C = k4_msafree(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))))
                   => ! [E] :
                        ( m2_finseq_2(E,k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))),k3_finseq_2(k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B)))))
                       => ( r2_hidden(k4_tarski(D,E),C)
                        <=> ( r2_hidden(D,k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))))
                            & ! [F] :
                                ( m1_subset_1(F,u1_msualg_1(A))
                               => ( k4_tarski(F,u1_struct_0(A)) = D
                                 => ( k3_finseq_1(E) = k3_finseq_1(k1_msualg_1(A,F))
                                    & ! [G] :
                                        ( r2_hidden(G,k4_finseq_1(E))
                                       => ( ( r2_hidden(k1_funct_1(E,G),k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))))
                                           => ! [H] :
                                                ( m1_subset_1(H,u1_msualg_1(A))
                                               => ( k4_tarski(H,u1_struct_0(A)) = k1_funct_1(E,G)
                                                 => k2_msualg_1(A,H) = k1_funct_1(k1_msualg_1(A,F),G) ) ) )
                                          & ( r2_hidden(k1_funct_1(E,G),k3_card_3(k3_msafree(u1_struct_0(A),B)))
                                           => r2_hidden(k1_funct_1(E,G),k2_msafree(u1_struct_0(A),B,k1_funct_1(k1_msualg_1(A,F),G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t5_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_pboole(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( m2_finseq_2(D,k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))),k3_finseq_2(k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B)))))
                 => ( r2_hidden(k4_tarski(k4_tarski(C,u1_struct_0(A)),D),k4_msafree(A,B))
                  <=> ( k3_finseq_1(D) = k3_finseq_1(k1_msualg_1(A,C))
                      & ! [E] :
                          ( r2_hidden(E,k4_finseq_1(D))
                         => ( ( r2_hidden(k1_funct_1(D,E),k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))))
                             => ! [F] :
                                  ( m1_subset_1(F,u1_msualg_1(A))
                                 => ( k4_tarski(F,u1_struct_0(A)) = k1_funct_1(D,E)
                                   => k2_msualg_1(A,F) = k1_funct_1(k1_msualg_1(A,C),E) ) ) )
                            & ( r2_hidden(k1_funct_1(D,E),k3_card_3(k3_msafree(u1_struct_0(A),B)))
                             => r2_hidden(k1_funct_1(D,E),k2_msafree(u1_struct_0(A),B,k1_funct_1(k1_msualg_1(A,C),E))) ) ) ) ) ) ) ) ) ) )).

fof(d10_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( m1_pboole(B,u1_struct_0(A))
         => k5_msafree(A,B) = g1_lang1(k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))),k4_msafree(A,B)) ) ) )).

fof(t6_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ( k6_lang1(k5_msafree(A,B)) = k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A)))
            & k5_lang1(k5_msafree(A,B)) = k3_card_3(k3_msafree(u1_struct_0(A),B)) ) ) ) )).

fof(t7_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( r2_hidden(C,k6_dtconstr(k5_msafree(A,B)))
            <=> ? [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                  & ? [E] :
                      ( r2_hidden(E,k1_funct_1(B,D))
                      & C = k4_tarski(E,D) ) ) ) ) ) )).

fof(d11_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => k6_msafree(A,B,C) = k4_tarski(C,u1_struct_0(A)) ) ) ) )).

fof(d13_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_pboole(C,u1_struct_0(A))
             => ( C = k8_msafree(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k1_funct_1(C,D) = k7_msafree(A,B,D) ) ) ) ) ) )).

fof(t8_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( r2_hidden(D,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k8_msafree(A,B))),C))
                 => m1_trees_4(D,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k4_dtconstr(k5_msafree(A,B))) ) ) ) ) )).

fof(t9_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( m1_trees_4(D,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k4_dtconstr(k5_msafree(A,B)))
                 => ( r2_hidden(D,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k8_msafree(A,B))),C))
                  <=> ( k4_finseq_1(D) = k4_finseq_1(k1_msualg_1(A,C))
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( r2_hidden(E,k4_finseq_1(D))
                           => r2_hidden(k1_funct_1(D,E),k7_msafree(A,B,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),E))) ) ) ) ) ) ) ) ) )).

fof(t10_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( m1_trees_4(D,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k4_dtconstr(k5_msafree(A,B)))
                 => ( r1_lang1(k5_msafree(A,B),k6_msafree(A,B,C),k1_dtconstr(u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),D))
                  <=> r2_hidden(D,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k8_msafree(A,B))),C)) ) ) ) ) ) )).

fof(t11_msafree,axiom,(
    $true )).

fof(t12_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => k3_tarski(k2_relat_1(k8_msafree(A,B))) = k4_dtconstr(k5_msafree(A,B)) ) ) )).

fof(t13_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( C != D
                   => r1_subset_1(k1_funct_1(k8_msafree(A,B),C),k1_funct_1(k8_msafree(A,B),D)) ) ) ) ) ) )).

fof(d14_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k8_msafree(A,B))),C),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k8_msafree(A,B)),C))
                    & m2_relset_1(D,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k8_msafree(A,B))),C),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k8_msafree(A,B)),C)) )
                 => ( D = k9_msafree(A,B,C)
                  <=> ! [E] :
                        ( m1_trees_4(E,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k4_dtconstr(k5_msafree(A,B)))
                       => ( r1_lang1(k5_msafree(A,B),k6_msafree(A,B,C),k1_dtconstr(u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),E))
                         => k1_funct_1(D,E) = k12_trees_4(u1_struct_0(k5_msafree(A,B)),k6_msafree(A,B,C),E) ) ) ) ) ) ) ) )).

fof(d15_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m3_pboole(C,u1_msualg_1(A),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k8_msafree(A,B))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k8_msafree(A,B)))
             => ( C = k10_msafree(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_msualg_1(A))
                   => k1_msualg_3(u1_msualg_1(A),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k8_msafree(A,B))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k8_msafree(A,B)),C,D) = k9_msafree(A,B,D) ) ) ) ) ) )).

fof(d16_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => k11_msafree(A,B) = g3_msualg_1(A,k8_msafree(A,B),k10_msafree(A,B)) ) ) )).

fof(d17_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(k1_funct_1(k8_msafree(A,B),C)))
                 => ( D = k12_msafree(A,B,C)
                  <=> ! [E] :
                        ( r2_hidden(E,D)
                      <=> ? [F] :
                            ( r2_hidden(F,k1_funct_1(B,C))
                            & E = k1_trees_4(k4_tarski(F,C)) ) ) ) ) ) ) ) )).

fof(d18_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_msafree(C,A,k11_msafree(A,B))
             => ( C = k13_msafree(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k1_funct_1(C,D) = k12_msafree(A,B,D) ) ) ) ) ) )).

fof(t15_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => v2_relat_1(k13_msafree(A,B)) ) ) )).

fof(d19_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k12_msafree(A,B,C),k1_funct_1(B,C))
                    & m2_relset_1(D,k12_msafree(A,B,C),k1_funct_1(B,C)) )
                 => ( D = k14_msafree(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(k5_msafree(A,B)))
                       => ( r2_hidden(k2_trees_4(u1_struct_0(k5_msafree(A,B)),E),k12_msafree(A,B,C))
                         => k1_funct_1(D,k2_trees_4(u1_struct_0(k5_msafree(A,B)),E)) = k1_mcart_1(E) ) ) ) ) ) ) ) )).

fof(d20_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m3_pboole(C,u1_struct_0(A),k13_msafree(A,B),B)
             => ( C = k15_msafree(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k1_msualg_3(u1_struct_0(A),k13_msafree(A,B),B,C,D) = k14_msafree(A,B,D) ) ) ) ) ) )).

fof(d21_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( ( v2_relat_1(C)
                & m1_pboole(C,u1_struct_0(A)) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),k13_msafree(A,B),C)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k5_msafree(A,B)))
                     => ( r2_hidden(E,k6_dtconstr(k5_msafree(A,B)))
                       => ! [F] :
                            ( m1_subset_1(F,k3_card_3(C))
                           => ( F = k16_msafree(A,B,C,D,E)
                            <=> ! [G] :
                                  ( ( v1_relat_1(G)
                                    & v1_funct_1(G) )
                                 => ( G = k1_funct_1(D,k2_mcart_1(E))
                                   => F = k1_funct_1(G,k2_trees_4(u1_struct_0(k5_msafree(A,B)),E)) ) ) ) ) ) ) ) ) ) ) )).

fof(d22_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k5_msafree(A,B)))
             => ( ? [D] :
                    ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D)
                    & r1_lang1(k5_msafree(A,B),C,D) )
               => ! [D] :
                    ( m1_subset_1(D,u1_msualg_1(A))
                   => ( D = k17_msafree(A,B,C)
                    <=> k4_tarski(D,u1_struct_0(A)) = C ) ) ) ) ) ) )).

fof(d23_msafree,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_msualg_1(A))
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ( r2_hidden(D,k3_msualg_1(A,C,B))
                   => k18_msafree(A,B,C,D) = k1_funct_1(k5_msualg_1(A,C,B),D) ) ) ) ) ) )).

fof(t17_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => v1_msafree(k13_msafree(A,B),A,k11_msafree(A,B)) ) ) )).

fof(t18_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => v2_msafree(k11_msafree(A,B),A) ) ) )).

fof(t19_msafree,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] :
              ( v4_msualg_1(C,A)
              & v5_msualg_1(C,A)
              & v2_msafree(C,A)
              & l3_msualg_1(C,A)
              & ? [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,B))
                  & r2_msualg_3(A,C,B,D) ) ) ) ) )).

fof(t20_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v4_msualg_1(B,A)
            & v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ? [C] :
              ( v4_msualg_1(C,A)
              & v5_msualg_1(C,A)
              & v2_msafree(C,A)
              & l3_msualg_1(C,A)
              & ? [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,B))
                  & r2_msualg_3(A,C,B,D)
                  & k7_msualg_3(A,C,B,D) = B ) ) ) ) )).

fof(dt_m1_msafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A) )
     => ! [C] :
          ( m1_msafree(C,A,B)
         => m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) ) ) )).

fof(existence_m1_msafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A) )
     => ? [C] : m1_msafree(C,A,B) ) )).

fof(dt_k1_msafree,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A)
        & m4_pboole(D,A,B)
        & m3_pboole(E,A,B,C) )
     => m3_pboole(k1_msafree(A,B,C,D,E),A,D,C) ) )).

fof(dt_k2_msafree,axiom,(
    $true )).

fof(dt_k3_msafree,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => m1_pboole(k3_msafree(A,B),A) ) )).

fof(redefinition_k3_msafree,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => k3_msafree(A,B) = k2_card_3(B) ) )).

fof(dt_k4_msafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_pboole(B,u1_struct_0(A)) )
     => m2_relset_1(k4_msafree(A,B),k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))),k3_finseq_2(k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))))) ) )).

fof(dt_k5_msafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_pboole(B,u1_struct_0(A)) )
     => l1_lang1(k5_msafree(A,B)) ) )).

fof(dt_k6_msafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_msualg_1(A)) )
     => m1_subset_1(k6_msafree(A,B,C),u1_struct_0(k5_msafree(A,B))) ) )).

fof(dt_k7_msafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k7_msafree(A,B,C),k1_zfmisc_1(k4_dtconstr(k5_msafree(A,B)))) ) )).

fof(dt_k8_msafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => m1_pboole(k8_msafree(A,B),u1_struct_0(A)) ) )).

fof(dt_k9_msafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_msualg_1(A)) )
     => ( v1_funct_1(k9_msafree(A,B,C))
        & v1_funct_2(k9_msafree(A,B,C),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k8_msafree(A,B))),C),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k8_msafree(A,B)),C))
        & m2_relset_1(k9_msafree(A,B,C),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k8_msafree(A,B))),C),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k8_msafree(A,B)),C)) ) ) )).

fof(dt_k10_msafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => m3_pboole(k10_msafree(A,B),u1_msualg_1(A),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k8_msafree(A,B))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k8_msafree(A,B))) ) )).

fof(dt_k11_msafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => l3_msualg_1(k11_msafree(A,B),A) ) )).

fof(dt_k12_msafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k12_msafree(A,B,C),k1_zfmisc_1(k1_funct_1(k8_msafree(A,B),C))) ) )).

fof(dt_k13_msafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => m1_msafree(k13_msafree(A,B),A,k11_msafree(A,B)) ) )).

fof(dt_k14_msafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( v1_funct_1(k14_msafree(A,B,C))
        & v1_funct_2(k14_msafree(A,B,C),k12_msafree(A,B,C),k1_funct_1(B,C))
        & m2_relset_1(k14_msafree(A,B,C),k12_msafree(A,B,C),k1_funct_1(B,C)) ) ) )).

fof(dt_k15_msafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => m3_pboole(k15_msafree(A,B),u1_struct_0(A),k13_msafree(A,B),B) ) )).

fof(dt_k16_msafree,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & v2_relat_1(C)
        & m1_pboole(C,u1_struct_0(A))
        & m3_pboole(D,u1_struct_0(A),k13_msafree(A,B),C)
        & m1_subset_1(E,u1_struct_0(k5_msafree(A,B))) )
     => m1_subset_1(k16_msafree(A,B,C,D,E),k3_card_3(C)) ) )).

fof(dt_k17_msafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(k5_msafree(A,B))) )
     => m1_subset_1(k17_msafree(A,B,C),u1_msualg_1(A)) ) )).

fof(dt_k18_msafree,axiom,(
    ! [A,B,C,D] :
      ( ( ~ 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_msualg_1(A))
        & v1_relat_1(D)
        & v1_funct_1(D)
        & v1_finseq_1(D) )
     => m1_subset_1(k18_msafree(A,B,C,D),k3_card_3(u4_msualg_1(A,B))) ) )).

fof(d12_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k7_msafree(A,B,C) = a_3_0_msafree(A,B,C) ) ) ) )).

fof(t14_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k12_msafree(A,B,C) = a_3_1_msafree(A,B,C) ) ) ) )).

fof(t16_msafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => k3_tarski(k2_relat_1(k13_msafree(A,B))) = a_2_0_msafree(A,B) ) ) )).

fof(fraenkel_a_3_0_msafree,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & v2_relat_1(C)
        & m1_pboole(C,u1_struct_0(B))
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_0_msafree(B,C,D))
      <=> ? [E] :
            ( m1_dtconstr(E,u1_struct_0(k5_msafree(B,C)),k5_trees_3(u1_struct_0(k5_msafree(B,C))),k4_dtconstr(k5_msafree(B,C)))
            & A = E
            & ~ ( ! [F] :
                    ~ ( r2_hidden(F,k1_funct_1(C,D))
                      & E = k1_trees_4(k4_tarski(F,D)) )
                & ! [F] :
                    ( m1_subset_1(F,u1_msualg_1(B))
                   => ~ ( k4_tarski(F,u1_struct_0(B)) = k1_funct_1(E,k1_xboole_0)
                        & k2_msualg_1(B,F) = D ) ) ) ) ) ) )).

fof(fraenkel_a_3_1_msafree,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & v2_relat_1(C)
        & m1_pboole(C,u1_struct_0(B))
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_1_msafree(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(k5_msafree(B,C)))
            & A = k2_trees_4(u1_struct_0(k5_msafree(B,C)),E)
            & r2_hidden(E,k6_dtconstr(k5_msafree(B,C)))
            & k2_mcart_1(E) = D ) ) ) )).

fof(fraenkel_a_2_0_msafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & v2_relat_1(C)
        & m1_pboole(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_0_msafree(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(k5_msafree(B,C)))
            & A = k2_trees_4(u1_struct_0(k5_msafree(B,C)),D)
            & r2_hidden(D,k6_dtconstr(k5_msafree(B,C))) ) ) ) )).
%------------------------------------------------------------------------------