SET007 Axioms: SET007+739.ax


%------------------------------------------------------------------------------
% File     : SET007+739 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Free Order 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    : osafree [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  135 (   1 unit)
%            Number of atoms       : 1675 ( 108 equality)
%            Maximal formula depth :   30 (  12 average)
%            Number of connectives : 1827 ( 287 ~  ;   1  |;1059  &)
%                                         (  52 <=>; 428 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   66 (   1 propositional; 0-4 arity)
%            Number of functors    :   99 (   3 constant; 0-5 arity)
%            Number of variables   :  525 (   0 singleton; 494 !;  31 ?)
%            Maximal term depth    :    8 (   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_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k2_osafree(A,B))
        & v1_lang1(k2_osafree(A,B)) ) ) )).

fof(fc2_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k2_osafree(A,B))
        & v1_lang1(k2_osafree(A,B))
        & v1_dtconstr(k2_osafree(A,B))
        & v2_dtconstr(k2_osafree(A,B))
        & v3_dtconstr(k2_osafree(A,B)) ) ) )).

fof(fc3_osafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( ~ v1_xboole_0(k4_osafree(A,B,C))
        & v3_trees_3(k4_osafree(A,B,C)) ) ) )).

fof(fc4_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( v1_relat_1(k5_osafree(A,B))
        & v2_relat_1(k5_osafree(A,B))
        & ~ v3_relat_1(k5_osafree(A,B))
        & v1_funct_1(k5_osafree(A,B))
        & v11_osalg_1(k5_osafree(A,B),A) ) ) )).

fof(fc5_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( v4_msualg_1(k8_osafree(A,B),A)
        & v5_msualg_1(k8_osafree(A,B),A)
        & v12_osalg_1(k8_osafree(A,B),A) ) ) )).

fof(fc6_osafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_msualg_1(A)) )
     => ~ v1_xboole_0(k3_msualg_1(A,C,k8_osafree(A,B))) ) )).

fof(rc1_osafree,axiom,(
    ? [A] :
      ( l3_osalg_1(A)
      & ~ v3_struct_0(A)
      & ~ v2_msualg_1(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v4_osalg_1(A)
      & v5_osalg_1(A)
      & v8_osalg_1(A)
      & v10_osalg_1(A)
      & v2_osalg_4(A) ) )).

fof(fc7_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( v1_relat_1(k20_osafree(A,B))
        & v1_funct_1(k20_osafree(A,B))
        & v1_msualg_4(k20_osafree(A,B))
        & v3_msualg_4(k20_osafree(A,B),A,k8_osafree(A,B))
        & v4_msualg_4(k20_osafree(A,B),A,k8_osafree(A,B))
        & v3_osalg_4(k20_osafree(A,B),A,k8_osafree(A,B)) ) ) )).

fof(fc8_osafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ~ v1_xboole_0(k21_osafree(A,B,C)) ) )).

fof(fc9_osafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ~ v1_xboole_0(k23_osafree(A,B,C)) ) )).

fof(fc10_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( v1_relat_1(k24_osafree(A,B))
        & v2_relat_1(k24_osafree(A,B))
        & ~ v3_relat_1(k24_osafree(A,B))
        & v1_funct_1(k24_osafree(A,B)) ) ) )).

fof(rc2_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ? [B] :
          ( l3_msualg_1(B,A)
          & v4_msualg_1(B,A)
          & v5_msualg_1(B,A)
          & v12_osalg_1(B,A)
          & v13_osalg_1(B,A)
          & v2_osafree(B,A) ) ) )).

fof(d1_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ( m1_osafree(C,A,B)
              <=> ! [D] :
                    ( m2_osalg_2(D,A,B)
                   => ( r6_pboole(u1_struct_0(A),D,k2_osalg_2(A,C))
                     => r6_pboole(u1_struct_0(A),u4_msualg_1(A,k10_osalg_2(A,B,D)),u4_msualg_1(A,B)) ) ) ) ) ) ) )).

fof(t1_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v4_msualg_1(B,A)
            & v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ( m1_osafree(C,A,B)
              <=> ! [D] :
                    ( m2_osalg_2(D,A,B)
                   => ( r6_pboole(u1_struct_0(A),D,k2_osalg_2(A,C))
                     => k10_osalg_2(A,B,D) = B ) ) ) ) ) ) )).

fof(d2_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v12_osalg_1(B,A)
            & v13_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m1_osafree(C,A,B)
             => ( v1_osafree(C,A,B)
              <=> ! [D] :
                    ( ( v5_msualg_1(D,A)
                      & v12_osalg_1(D,A)
                      & v13_osalg_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)
                            & v1_osalg_3(F,A)
                            & 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(d3_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v12_osalg_1(B,A)
            & v13_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ( v2_osafree(B,A)
          <=> ? [C] :
                ( m1_osafree(C,A,B)
                & v1_osafree(C,A,B) ) ) ) ) )).

fof(d4_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_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 = k1_osafree(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)
                                                 => r3_orders_2(A,k1_osalg_1(A,H),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,F),G)) ) ) )
                                          & ~ ( r2_hidden(k1_funct_1(E,G),k3_card_3(k3_msafree(u1_struct_0(A),B)))
                                              & ! [H] :
                                                  ( m1_subset_1(H,u1_struct_0(A))
                                                 => ~ ( r3_orders_2(A,H,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,F),G))
                                                      & r2_hidden(k1_funct_1(E,G),k2_msafree(u1_struct_0(A),B,H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t2_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_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),k1_osafree(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)
                                   => r3_orders_2(A,k1_osalg_1(A,F),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),E)) ) ) )
                            & ~ ( r2_hidden(k1_funct_1(D,E),k3_card_3(k3_msafree(u1_struct_0(A),B)))
                                & ! [F] :
                                    ( m1_subset_1(F,u1_struct_0(A))
                                   => ~ ( r3_orders_2(A,F,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),E))
                                        & r2_hidden(k1_funct_1(D,E),k2_msafree(u1_struct_0(A),B,F)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d5_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_pboole(B,u1_struct_0(A))
         => k2_osafree(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))),k1_osafree(A,B)) ) ) )).

fof(t3_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ( k6_lang1(k2_osafree(A,B)) = k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A)))
            & k5_lang1(k2_osafree(A,B)) = k3_card_3(k3_msafree(u1_struct_0(A),B)) ) ) ) )).

fof(t4_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( r2_hidden(C,k6_dtconstr(k2_osafree(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(d6_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => k3_osafree(A,B,C) = k4_tarski(C,u1_struct_0(A)) ) ) ) )).

fof(d8_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( ( v11_osalg_1(C,A)
                & m1_pboole(C,u1_struct_0(A)) )
             => ( C = k5_osafree(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k1_funct_1(C,D) = k4_osafree(A,B,D) ) ) ) ) ) )).

fof(t5_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_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),k5_osafree(A,B))),C))
                 => m1_trees_4(D,k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) ) ) ) ) )).

fof(t6_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_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(k2_osafree(A,B))),k4_dtconstr(k2_osafree(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),k5_osafree(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),k4_osafree(A,B,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),E))) ) ) ) ) ) ) ) ) )).

fof(t7_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_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(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                 => ( r1_lang1(k2_osafree(A,B),k3_osafree(A,B,C),k1_dtconstr(u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(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),k5_osafree(A,B))),C)) ) ) ) ) ) )).

fof(t8_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => k3_tarski(k2_relat_1(k5_osafree(A,B))) = k4_dtconstr(k2_osafree(A,B)) ) ) )).

fof(d9_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_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),k5_osafree(A,B))),C),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osafree(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),k5_osafree(A,B))),C),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osafree(A,B)),C)) )
                 => ( D = k6_osafree(A,B,C)
                  <=> ! [E] :
                        ( m1_trees_4(E,k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                       => ( r1_lang1(k2_osafree(A,B),k3_osafree(A,B,C),k1_dtconstr(u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),E))
                         => k1_funct_1(D,E) = k12_trees_4(u1_struct_0(k2_osafree(A,B)),k3_osafree(A,B,C),E) ) ) ) ) ) ) ) )).

fof(d10_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_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),k5_osafree(A,B))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osafree(A,B)))
             => ( C = k7_osafree(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_msualg_1(A))
                   => k5_msualg_4(A,k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osafree(A,B))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osafree(A,B)),C,D) = k6_osafree(A,B,D) ) ) ) ) ) )).

fof(d11_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => k8_osafree(A,B) = g3_msualg_1(A,k5_osafree(A,B),k7_osafree(A,B)) ) ) )).

fof(t10_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_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))
                 => ! [E] :
                      ( r2_hidden(E,k1_funct_1(B,C))
                     => ( m1_dtconstr(k1_trees_4(k4_tarski(E,C)),u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                        & ! [F] : k4_tarski(F,u1_struct_0(A)) != k1_funct_1(k1_trees_4(k4_tarski(E,C)),k1_xboole_0)
                        & ( r2_hidden(k1_trees_4(k4_tarski(E,C)),k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),D))
                         => r3_orders_2(A,C,D) )
                        & ( r3_orders_2(A,C,D)
                         => r2_hidden(k1_trees_4(k4_tarski(E,C)),k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),D)) ) ) ) ) ) ) ) )).

fof(t11_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_msualg_1(A))
                 => ( k1_funct_1(C,k1_xboole_0) = k4_tarski(D,u1_struct_0(A))
                   => ( ? [E] :
                          ( m2_dtconstr(E,k2_osafree(A,B),k9_osafree(A,B,D))
                          & C = k9_dtconstr(k2_osafree(A,B),k9_osafree(A,B,D),E)
                          & r1_lang1(k2_osafree(A,B),k9_osafree(A,B,D),k1_dtconstr(u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),E))
                          & r2_hidden(E,k3_msualg_1(A,D,k8_osafree(A,B)))
                          & C = k1_funct_1(k5_msualg_1(A,D,k8_osafree(A,B)),E) )
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ! [F] : C != k1_trees_4(k4_tarski(F,E)) )
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( r2_hidden(C,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),E))
                          <=> r3_orders_2(A,k1_osalg_1(A,D),E) ) ) ) ) ) ) ) ) )).

fof(t12_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k2_osafree(A,B)))
             => ! [D] :
                  ( m1_trees_4(D,k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                 => ( r1_lang1(k2_osafree(A,B),C,k1_dtconstr(u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),D))
                   => ( r2_hidden(C,k7_dtconstr(k2_osafree(A,B)))
                      & r2_hidden(k12_trees_4(u1_struct_0(k2_osafree(A,B)),C,D),k4_dtconstr(k2_osafree(A,B)))
                      & ? [E] :
                          ( m1_subset_1(E,u1_msualg_1(A))
                          & C = k4_tarski(E,u1_struct_0(A))
                          & r2_hidden(D,k3_msualg_1(A,E,k8_osafree(A,B)))
                          & k12_trees_4(u1_struct_0(k2_osafree(A,B)),C,D) = k1_funct_1(k5_msualg_1(A,E,k8_osafree(A,B)),D)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ( r2_hidden(k12_trees_4(u1_struct_0(k2_osafree(A,B)),C,D),k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),F))
                              <=> r3_orders_2(A,k1_osalg_1(A,E),F) ) ) ) ) ) ) ) ) ) )).

fof(t13_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_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_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ( r2_hidden(D,k3_msualg_1(A,C,k8_osafree(A,B)))
                  <=> ( m1_trees_4(D,k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                      & r1_lang1(k2_osafree(A,B),k9_osafree(A,B,C),k16_trees_3(D)) ) ) ) ) ) ) )).

fof(t14_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
             => ? [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                  & r2_hidden(C,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),D))
                  & ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r2_hidden(C,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),E))
                       => r3_orders_2(A,D,E) ) ) ) ) ) ) )).

fof(d12_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( D = k10_osafree(A,B,C)
                  <=> ( r2_hidden(C,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),D))
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( r2_hidden(C,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),E))
                           => r3_orders_2(A,D,E) ) ) ) ) ) ) ) ) )).

fof(t15_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,k3_card_3(u4_msualg_1(A,k8_osafree(A,B))))
            <=> m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) ) ) ) )).

fof(t16_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( r2_hidden(D,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),C))
                 => m1_dtconstr(D,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) ) ) ) ) )).

fof(t17_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( r2_hidden(D,k1_funct_1(B,C))
                 => ! [E] :
                      ( m1_dtconstr(E,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                     => ( E = k1_trees_4(k4_tarski(D,C))
                       => k10_osafree(A,B,E) = C ) ) ) ) ) ) )).

fof(t18_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_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_subset_1(D,k3_msualg_1(A,C,k8_osafree(A,B)))
                 => ! [E] :
                      ( m1_dtconstr(E,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                     => ( E = k8_funct_2(k3_msualg_1(A,C,k8_osafree(A,B)),k4_msualg_1(A,C,k8_osafree(A,B)),k5_msualg_1(A,C,k8_osafree(A,B)),D)
                       => k10_osafree(A,B,E) = k1_osalg_1(A,C) ) ) ) ) ) ) )).

fof(d13_osafree,axiom,(
    $true )).

fof(d14_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_trees_4(C,k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
                 => ( D = k11_osafree(A,B,C)
                  <=> ( k4_finseq_1(D) = k4_finseq_1(C)
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ~ ( r2_hidden(E,k4_finseq_1(C))
                              & ! [F] :
                                  ( m1_dtconstr(F,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                                 => ~ ( F = k1_funct_1(C,E)
                                      & k1_funct_1(D,E) = k10_osafree(A,B,F) ) ) ) ) ) ) ) ) ) ) )).

fof(t19_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_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(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                 => ( r2_osalg_1(A,k11_osafree(A,B,D),k1_msualg_1(A,C))
                  <=> r2_hidden(D,k3_msualg_1(A,C,k8_osafree(A,B))) ) ) ) ) ) )).

fof(d15_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & v10_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_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(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                 => ( r1_lang1(k2_osafree(A,B),k9_osafree(A,B,k3_osalg_1(A,C,k11_osafree(A,B,D))),k1_dtconstr(u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),D))
                   => k12_osafree(A,B,C,D) = k12_trees_4(u1_struct_0(k2_osafree(A,B)),k9_osafree(A,B,k3_osalg_1(A,C,k11_osafree(A,B,D))),D) ) ) ) ) ) )).

fof(d16_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k2_osafree(A,B)))
             => ( ? [D] :
                    ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D)
                    & r1_lang1(k2_osafree(A,B),C,D) )
               => ! [D] :
                    ( m1_subset_1(D,u1_msualg_1(A))
                   => ( D = k13_osafree(A,B,C)
                    <=> k4_tarski(D,u1_struct_0(A)) = C ) ) ) ) ) ) )).

fof(d17_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k2_osafree(A,B)))
             => ( r2_hidden(C,k6_dtconstr(k2_osafree(A,B)))
               => k14_osafree(A,B,C) = k2_trees_4(u1_struct_0(k2_osafree(A,B)),C) ) ) ) ) )).

fof(d18_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,k8_osafree(A,B))
                & v4_msualg_4(C,A,k8_osafree(A,B))
                & v3_osalg_4(C,A,k8_osafree(A,B))
                & m1_osalg_4(C,A,k8_osafree(A,B)) )
             => ( C = k15_osafree(A,B)
              <=> ! [D] :
                    ( ( v3_msualg_4(D,A,k8_osafree(A,B))
                      & v4_msualg_4(D,A,k8_osafree(A,B))
                      & v3_osalg_4(D,A,k8_osafree(A,B))
                      & m1_osalg_4(D,A,k8_osafree(A,B)) )
                   => r2_pboole(u1_struct_0(A),C,D) ) ) ) ) ) )).

fof(d19_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => k16_osafree(A,B) = k16_osalg_4(A,k8_osafree(A,B),k15_osafree(A,B)) ) ) )).

fof(d22_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))))
                & m2_relset_1(C,k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A)))) )
             => ( C = k19_osafree(A,B)
              <=> ( ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k2_osafree(A,B)))
                     => ( r2_hidden(D,k6_dtconstr(k2_osafree(A,B)))
                       => k1_funct_1(C,k2_trees_4(u1_struct_0(k2_osafree(A,B)),D)) = k17_osafree(A,B,D) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k2_osafree(A,B)))
                     => ! [E] :
                          ( m1_trees_4(E,k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                         => ( r1_lang1(k2_osafree(A,B),D,k1_dtconstr(u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),E))
                           => k1_funct_1(C,k12_trees_4(u1_struct_0(k2_osafree(A,B)),D,E)) = k18_osafree(A,B,D,k15_lang1(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),E,C)) ) ) ) ) ) ) ) ) )).

fof(t20_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
             => ( ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(C,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),D))
                    <=> r2_hidden(k4_tarski(C,D),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),C)) ) )
                & ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_dtconstr(E,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                       => ( r2_hidden(k4_tarski(E,D),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),C))
                         => r2_hidden(k4_tarski(C,D),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),E)) ) ) ) ) ) ) ) )).

fof(t21_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ? [E] :
                        ( m1_dtconstr(E,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                        & r2_hidden(k4_tarski(E,D),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),C)) )
                   => r2_hidden(k4_tarski(C,D),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),C)) ) ) ) ) ) )).

fof(t22_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
             => ! [D] :
                  ( m1_dtconstr(D,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r3_orders_2(A,E,F)
                              & r2_hidden(C,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),E))
                              & r2_hidden(D,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),E)) )
                           => ( r2_hidden(k4_tarski(D,E),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),C))
                            <=> r2_hidden(k4_tarski(D,F),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),C)) ) ) ) ) ) ) ) ) )).

fof(t23_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
             => ! [D] :
                  ( m1_dtconstr(D,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                 => ! [E] :
                      ( m1_dtconstr(E,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r2_hidden(k4_tarski(D,F),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),C))
                              & r2_hidden(k4_tarski(E,F),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),D)) )
                           => r2_hidden(k4_tarski(C,F),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),E)) ) ) ) ) ) ) ) )).

fof(t24_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C,D,E] :
              ( r2_hidden(k4_tarski(C,E),k1_funct_1(k19_osafree(A,B),D))
             => ( r2_hidden(C,k4_dtconstr(k2_osafree(A,B)))
                & r2_hidden(D,k4_dtconstr(k2_osafree(A,B)))
                & r2_hidden(E,u1_struct_0(A)) ) ) ) ) )).

fof(t25_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k2_osalg_4(A))
             => ! [D,E] :
                  ( r2_hidden(k4_tarski(D,E),k5_osalg_4(A,k8_osafree(A,B),k20_osafree(A,B),C))
                <=> ? [F] :
                      ( m1_subset_1(F,u1_struct_0(A))
                      & r2_hidden(F,C)
                      & r2_hidden(k4_tarski(D,F),k1_funct_1(k19_osafree(A,B),E)) ) ) ) ) ) )).

fof(t26_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_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_funct_1(u4_msualg_1(A,k8_osafree(A,B)),C))
                 => k8_osalg_4(A,k8_osafree(A,B),k20_osafree(A,B),C,D) = k1_funct_5(k1_funct_1(k19_osafree(A,B),D)) ) ) ) ) )).

fof(t27_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)))
             => ( r6_pboole(u1_struct_0(A),C,k20_osafree(A,B))
              <=> ( ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ! [F] :
                              ( r2_hidden(F,k1_funct_1(B,D))
                             => ( ( r3_orders_2(A,D,E)
                                 => r2_hidden(k4_tarski(k1_trees_4(k4_tarski(F,D)),k1_trees_4(k4_tarski(F,D))),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)),C,E)) )
                                & ! [G] :
                                    ( ( r2_hidden(k4_tarski(k1_trees_4(k4_tarski(F,D)),G),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)),C,E))
                                      | r2_hidden(k4_tarski(G,k1_trees_4(k4_tarski(F,D))),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)),C,E)) )
                                   => ( r3_orders_2(A,D,E)
                                      & G = k1_trees_4(k4_tarski(F,D)) ) ) ) ) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u1_msualg_1(A))
                     => ! [E] :
                          ( m1_subset_1(E,u1_msualg_1(A))
                         => ! [F] :
                              ( m1_subset_1(F,k3_msualg_1(A,D,k8_osafree(A,B)))
                             => ! [G] :
                                  ( m1_subset_1(G,k3_msualg_1(A,E,k8_osafree(A,B)))
                                 => ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(A))
                                     => ( r2_hidden(k4_tarski(k8_funct_2(k3_msualg_1(A,D,k8_osafree(A,B)),k4_msualg_1(A,D,k8_osafree(A,B)),k5_msualg_1(A,D,k8_osafree(A,B)),F),k8_funct_2(k3_msualg_1(A,E,k8_osafree(A,B)),k4_msualg_1(A,E,k8_osafree(A,B)),k5_msualg_1(A,E,k8_osafree(A,B)),G)),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)),C,H))
                                      <=> ( r1_osalg_1(A,D,E)
                                          & k3_finseq_1(k1_msualg_1(A,D)) = k3_finseq_1(k1_msualg_1(A,E))
                                          & r3_orders_2(A,k1_osalg_1(A,D),H)
                                          & r3_orders_2(A,k1_osalg_1(A,E),H)
                                          & ? [I] :
                                              ( m2_finseq_2(I,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
                                              & k4_finseq_1(I) = k4_finseq_1(F)
                                              & ! [J] :
                                                  ( m2_subset_1(J,k1_numbers,k5_numbers)
                                                 => ( r2_hidden(J,k4_finseq_1(I))
                                                   => r2_hidden(k4_tarski(k1_funct_1(F,J),k1_funct_1(G,J)),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)),C,k4_finseq_4(k5_numbers,u1_struct_0(A),I,J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t28_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => v3_osalg_4(k20_osafree(A,B),A,k8_osafree(A,B)) ) ) )).

fof(d24_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_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(u4_msualg_1(A,k8_osafree(A,B)),C)))
                 => ( D = k21_osafree(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(d25_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)))
             => ( C = k22_osafree(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k1_funct_1(C,D) = k21_osafree(A,B,D) ) ) ) ) ) )).

fof(t30_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => v2_relat_1(k22_osafree(A,B)) ) ) )).

fof(d26_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_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(u4_msualg_1(A,k16_osafree(A,B)),C)))
                 => ( D = k23_osafree(A,B,C)
                  <=> ! [E] :
                        ( r2_hidden(E,D)
                      <=> ? [F] :
                            ( r2_hidden(F,k1_funct_1(B,C))
                            & E = k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k16_osalg_4(A,k8_osafree(A,B),k15_osafree(A,B))),k18_osalg_4(A,k8_osafree(A,B),k15_osafree(A,B)),C),k1_trees_4(k4_tarski(F,C))) ) ) ) ) ) ) ) )).

fof(d27_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_osafree(C,A,k16_osafree(A,B))
             => ( C = k24_osafree(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k1_funct_1(C,D) = k23_osafree(A,B,D) ) ) ) ) ) )).

fof(t32_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => v2_relat_1(k24_osafree(A,B)) ) ) )).

fof(d28_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,k8_osafree(A,B))
                & v4_msualg_4(C,A,k8_osafree(A,B))
                & m1_osalg_4(C,A,k8_osafree(A,B)) )
             => ! [D] :
                  ( m1_dtconstr(D,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                 => ! [E] :
                      ( m1_subset_1(E,k6_osalg_4(A,k8_osafree(A,B),C,k10_osafree(A,B,D)))
                     => ( E = k25_osafree(A,B,C,D)
                      <=> ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),F))
                               => ( D = G
                                 => E = k8_osalg_4(A,k8_osafree(A,B),C,F,G) ) ) ) ) ) ) ) ) ) )).

fof(t33_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,k8_osafree(A,B))
                & v4_msualg_4(C,A,k8_osafree(A,B))
                & m1_osalg_4(C,A,k8_osafree(A,B)) )
             => ! [D] :
                  ( m1_dtconstr(D,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                 => r2_hidden(D,k25_osafree(A,B,C,D)) ) ) ) ) )).

fof(t34_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_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_dtconstr(D,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                 => ! [E,F] :
                      ( ( r2_hidden(E,k1_funct_1(B,C))
                        & D = k1_trees_4(k4_tarski(E,C)) )
                     => ( r2_hidden(F,k25_osafree(A,B,k20_osafree(A,B),D))
                      <=> F = D ) ) ) ) ) ) )).

fof(t35_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,k8_osafree(A,B))
                & v4_msualg_4(C,A,k8_osafree(A,B))
                & m1_osalg_4(C,A,k8_osafree(A,B)) )
             => ! [D] :
                  ( m1_dtconstr(D,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                 => ! [E] :
                      ( m1_dtconstr(E,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                     => ( r2_hidden(E,k25_osafree(A,B,C,D))
                      <=> k25_osafree(A,B,C,D) = k25_osafree(A,B,C,E) ) ) ) ) ) ) )).

fof(t36_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,k8_osafree(A,B))
                & v4_msualg_4(C,A,k8_osafree(A,B))
                & m1_osalg_4(C,A,k8_osafree(A,B)) )
             => ! [D] :
                  ( ( v3_msualg_4(D,A,k8_osafree(A,B))
                    & v4_msualg_4(D,A,k8_osafree(A,B))
                    & m1_osalg_4(D,A,k8_osafree(A,B)) )
                 => ! [E] :
                      ( m1_dtconstr(E,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                     => ( r2_pboole(u1_struct_0(A),C,D)
                       => r1_tarski(k25_osafree(A,B,C,E),k25_osafree(A,B,D,E)) ) ) ) ) ) ) )).

fof(t37_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_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_dtconstr(D,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                 => ! [E,F] :
                      ( ( r2_hidden(E,k1_funct_1(B,C))
                        & D = k1_trees_4(k4_tarski(E,C)) )
                     => ( r2_hidden(F,k25_osafree(A,B,k15_osafree(A,B),D))
                      <=> F = D ) ) ) ) ) ) )).

fof(d29_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_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),k22_osafree(A,B),C)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k2_osafree(A,B)))
                     => ( r2_hidden(E,k6_dtconstr(k2_osafree(A,B)))
                       => ! [F] :
                            ( m1_subset_1(F,k3_card_3(C))
                           => ( F = k26_osafree(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(k2_osafree(A,B)),E)) ) ) ) ) ) ) ) ) ) ) )).

fof(t38_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & v12_osalg_1(C,A)
                & v13_osalg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),k22_osafree(A,B),u4_msualg_1(A,C))
                 => ? [E] :
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,C))
                      & r1_msualg_3(A,k8_osafree(A,B),C,E)
                      & v1_osalg_3(E,A)
                      & r6_pboole(u1_struct_0(A),k1_msafree(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,C),k22_osafree(A,B),E),D) ) ) ) ) ) )).

fof(d30_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_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,k23_osafree(A,B,C),k21_osafree(A,B,C))
                    & m2_relset_1(D,k23_osafree(A,B,C),k21_osafree(A,B,C)) )
                 => ( D = k27_osafree(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(k2_osafree(A,B)))
                       => ( r2_hidden(k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k16_osalg_4(A,k8_osafree(A,B),k15_osafree(A,B))),k18_osalg_4(A,k8_osafree(A,B),k15_osafree(A,B)),C),k2_trees_4(u1_struct_0(k2_osafree(A,B)),E)),k23_osafree(A,B,C))
                         => k1_funct_1(D,k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k16_osalg_4(A,k8_osafree(A,B),k15_osafree(A,B))),k18_osalg_4(A,k8_osafree(A,B),k15_osafree(A,B)),C),k2_trees_4(u1_struct_0(k2_osafree(A,B)),E))) = k2_trees_4(u1_struct_0(k2_osafree(A,B)),E) ) ) ) ) ) ) ) )).

fof(d31_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m3_pboole(C,u1_struct_0(A),k24_osafree(A,B),k22_osafree(A,B))
             => ( C = k28_osafree(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k1_msualg_3(u1_struct_0(A),k24_osafree(A,B),k22_osafree(A,B),C,D) = k27_osafree(A,B,D) ) ) ) ) ) )).

fof(t39_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => v1_osafree(k24_osafree(A,B),A,k16_osafree(A,B)) ) ) )).

fof(t40_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => v2_osafree(k16_osafree(A,B),A) ) ) )).

fof(d32_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & v10_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)))
                & m2_relset_1(C,k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B))) )
             => ( C = k29_osafree(A,B)
              <=> ( ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k2_osafree(A,B)))
                     => ( r2_hidden(D,k6_dtconstr(k2_osafree(A,B)))
                       => k1_funct_1(C,k2_trees_4(u1_struct_0(k2_osafree(A,B)),D)) = k14_osafree(A,B,D) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k2_osafree(A,B)))
                     => ! [E] :
                          ( m1_trees_4(E,k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                         => ( r1_lang1(k2_osafree(A,B),D,k1_dtconstr(u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),E))
                           => k1_funct_1(C,k12_trees_4(u1_struct_0(k2_osafree(A,B)),D,E)) = k12_osafree(A,B,k13_osafree(A,B,D),k15_lang1(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),E,C)) ) ) ) ) ) ) ) ) )).

fof(t41_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & v10_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
             => ( r2_hidden(k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),C),k25_osafree(A,B,k20_osafree(A,B),C))
                & r3_orders_2(A,k10_osafree(A,B,k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),C)),k10_osafree(A,B,C))
                & ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( ( r2_hidden(E,k1_funct_1(B,D))
                          & C = k1_trees_4(k4_tarski(E,D)) )
                       => k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),C) = C ) )
                & ! [D] :
                    ( m1_subset_1(D,u1_msualg_1(A))
                   => ! [E] :
                        ( m1_trees_4(E,k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                       => ( ( r1_lang1(k2_osafree(A,B),k9_osafree(A,B,D),k1_dtconstr(u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),E))
                            & C = k12_trees_4(u1_struct_0(k2_osafree(A,B)),k9_osafree(A,B,D),E) )
                         => ( r2_osalg_1(A,k11_osafree(A,B,k15_lang1(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),E,k29_osafree(A,B))),k1_msualg_1(A,D))
                            & r1_lang1(k2_osafree(A,B),k9_osafree(A,B,D),k16_trees_3(k15_lang1(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),E,k29_osafree(A,B))))
                            & r1_lang1(k2_osafree(A,B),k9_osafree(A,B,k3_osalg_1(A,D,k11_osafree(A,B,k15_lang1(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),E,k29_osafree(A,B))))),k16_trees_3(k15_lang1(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),E,k29_osafree(A,B))))
                            & k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),C) = k4_trees_4(k9_osafree(A,B,k3_osalg_1(A,D,k11_osafree(A,B,k15_lang1(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),E,k29_osafree(A,B))))),k15_lang1(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),E,k29_osafree(A,B))) ) ) ) ) ) ) ) ) )).

fof(t42_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & v10_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
             => ! [D] :
                  ( m1_dtconstr(D,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                 => ( r2_hidden(D,k25_osafree(A,B,k20_osafree(A,B),C))
                   => k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),D) = k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),C) ) ) ) ) ) )).

fof(t43_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & v10_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
             => ! [D] :
                  ( m1_dtconstr(D,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                 => ( r2_hidden(D,k25_osafree(A,B,k20_osafree(A,B),C))
                  <=> k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),D) = k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),C) ) ) ) ) ) )).

fof(t44_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & v10_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
             => k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),C)) = k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),C) ) ) ) )).

fof(t45_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & v10_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,k8_osafree(A,B))
                & v3_osalg_4(C,A,k8_osafree(A,B))
                & m1_osalg_4(C,A,k8_osafree(A,B)) )
             => ! [D] :
                  ( m1_dtconstr(D,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
                 => r2_hidden(k4_tarski(D,k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),D)),k2_msualg_4(A,k8_osafree(A,B),C,k10_osafree(A,B,D))) ) ) ) ) )).

fof(t46_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & v10_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,k8_osafree(A,B))
                & v3_osalg_4(C,A,k8_osafree(A,B))
                & m1_osalg_4(C,A,k8_osafree(A,B)) )
             => r2_pboole(u1_struct_0(A),k20_osafree(A,B),C) ) ) ) )).

fof(t47_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & v10_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => r6_pboole(u1_struct_0(A),k15_osafree(A,B),k20_osafree(A,B)) ) ) )).

fof(d33_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & v10_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B)))
             => ( m2_osafree(C,A,B)
              <=> k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)),k29_osafree(A,B),C) = C ) ) ) ) )).

fof(d34_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & v10_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => k30_osafree(A,B) = k2_relat_1(k29_osafree(A,B)) ) ) )).

fof(t48_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & v10_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m2_osafree(C,A,B)
            <=> r2_hidden(C,k30_osafree(A,B)) ) ) ) )).

fof(dt_m1_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A) )
     => ! [C] :
          ( m1_osafree(C,A,B)
         => m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) ) ) )).

fof(existence_m1_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A) )
     => ? [C] : m1_osafree(C,A,B) ) )).

fof(dt_m2_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & v10_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ! [C] :
          ( m2_osafree(C,A,B)
         => m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) ) ) )).

fof(existence_m2_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & v10_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ? [C] : m2_osafree(C,A,B) ) )).

fof(dt_k1_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & m1_pboole(B,u1_struct_0(A)) )
     => m2_relset_1(k1_osafree(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_k2_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & m1_pboole(B,u1_struct_0(A)) )
     => l1_lang1(k2_osafree(A,B)) ) )).

fof(dt_k3_osafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_msualg_1(A)) )
     => m1_subset_1(k3_osafree(A,B,C),u1_struct_0(k2_osafree(A,B))) ) )).

fof(dt_k4_osafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k4_osafree(A,B,C),k1_zfmisc_1(k4_dtconstr(k2_osafree(A,B)))) ) )).

fof(dt_k5_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( v11_osalg_1(k5_osafree(A,B),A)
        & m1_pboole(k5_osafree(A,B),u1_struct_0(A)) ) ) )).

fof(dt_k6_osafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_msualg_1(A)) )
     => ( v1_funct_1(k6_osafree(A,B,C))
        & v1_funct_2(k6_osafree(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),k5_osafree(A,B))),C),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osafree(A,B)),C))
        & m2_relset_1(k6_osafree(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),k5_osafree(A,B))),C),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osafree(A,B)),C)) ) ) )).

fof(dt_k7_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => m3_pboole(k7_osafree(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),k5_osafree(A,B))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osafree(A,B))) ) )).

fof(dt_k8_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( v12_osalg_1(k8_osafree(A,B),A)
        & l3_msualg_1(k8_osafree(A,B),A) ) ) )).

fof(dt_k9_osafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_msualg_1(A)) )
     => m1_struct_0(k9_osafree(A,B,C),k2_osafree(A,B),k7_dtconstr(k2_osafree(A,B))) ) )).

fof(redefinition_k9_osafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_msualg_1(A)) )
     => k9_osafree(A,B,C) = k3_osafree(A,B,C) ) )).

fof(dt_k10_osafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,k4_dtconstr(k2_osafree(A,B))) )
     => m1_subset_1(k10_osafree(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k11_osafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_finseq_1(C,k4_dtconstr(k2_osafree(A,B))) )
     => m2_finseq_2(k11_osafree(A,B,C),u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) ) )).

fof(dt_k12_osafree,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & v10_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_msualg_1(A))
        & m1_finseq_1(D,k4_dtconstr(k2_osafree(A,B))) )
     => m1_dtconstr(k12_osafree(A,B,C,D),u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) ) )).

fof(dt_k13_osafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(k2_osafree(A,B))) )
     => m1_subset_1(k13_osafree(A,B,C),u1_msualg_1(A)) ) )).

fof(dt_k14_osafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(k2_osafree(A,B))) )
     => m1_dtconstr(k14_osafree(A,B,C),u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) ) )).

fof(dt_k15_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( v3_msualg_4(k15_osafree(A,B),A,k8_osafree(A,B))
        & v4_msualg_4(k15_osafree(A,B),A,k8_osafree(A,B))
        & v3_osalg_4(k15_osafree(A,B),A,k8_osafree(A,B))
        & m1_osalg_4(k15_osafree(A,B),A,k8_osafree(A,B)) ) ) )).

fof(dt_k16_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( v4_msualg_1(k16_osafree(A,B),A)
        & v5_msualg_1(k16_osafree(A,B),A)
        & v12_osalg_1(k16_osafree(A,B),A)
        & v13_osalg_1(k16_osafree(A,B),A)
        & l3_msualg_1(k16_osafree(A,B),A) ) ) )).

fof(dt_k17_osafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(k2_osafree(A,B))) )
     => m1_subset_1(k17_osafree(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A)))) ) )).

fof(dt_k18_osafree,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(k2_osafree(A,B)))
        & m1_finseq_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A)))) )
     => m1_subset_1(k18_osafree(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A)))) ) )).

fof(dt_k19_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( v1_funct_1(k19_osafree(A,B))
        & v1_funct_2(k19_osafree(A,B),k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))))
        & m2_relset_1(k19_osafree(A,B),k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A)))) ) ) )).

fof(dt_k20_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( v3_msualg_4(k20_osafree(A,B),A,k8_osafree(A,B))
        & m1_osalg_4(k20_osafree(A,B),A,k8_osafree(A,B)) ) ) )).

fof(dt_k21_osafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k21_osafree(A,B,C),k1_zfmisc_1(k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),C))) ) )).

fof(dt_k22_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => m4_pboole(k22_osafree(A,B),u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B))) ) )).

fof(dt_k23_osafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k23_osafree(A,B,C),k1_zfmisc_1(k1_funct_1(u4_msualg_1(A,k16_osafree(A,B)),C))) ) )).

fof(dt_k24_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => m1_osafree(k24_osafree(A,B),A,k16_osafree(A,B)) ) )).

fof(dt_k25_osafree,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & v3_msualg_4(C,A,k8_osafree(A,B))
        & v4_msualg_4(C,A,k8_osafree(A,B))
        & m1_osalg_4(C,A,k8_osafree(A,B))
        & m1_subset_1(D,k4_dtconstr(k2_osafree(A,B))) )
     => m1_subset_1(k25_osafree(A,B,C,D),k6_osalg_4(A,k8_osafree(A,B),C,k10_osafree(A,B,D))) ) )).

fof(dt_k26_osafree,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_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),k22_osafree(A,B),C)
        & m1_subset_1(E,u1_struct_0(k2_osafree(A,B))) )
     => m1_subset_1(k26_osafree(A,B,C,D,E),k3_card_3(C)) ) )).

fof(dt_k27_osafree,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( v1_funct_1(k27_osafree(A,B,C))
        & v1_funct_2(k27_osafree(A,B,C),k23_osafree(A,B,C),k21_osafree(A,B,C))
        & m2_relset_1(k27_osafree(A,B,C),k23_osafree(A,B,C),k21_osafree(A,B,C)) ) ) )).

fof(dt_k28_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => m3_pboole(k28_osafree(A,B),u1_struct_0(A),k24_osafree(A,B),k22_osafree(A,B)) ) )).

fof(dt_k29_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & v10_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( v1_funct_1(k29_osafree(A,B))
        & v1_funct_2(k29_osafree(A,B),k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B)))
        & m2_relset_1(k29_osafree(A,B),k4_dtconstr(k2_osafree(A,B)),k4_dtconstr(k2_osafree(A,B))) ) ) )).

fof(dt_k30_osafree,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & v10_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => m1_subset_1(k30_osafree(A,B),k1_zfmisc_1(k4_dtconstr(k2_osafree(A,B)))) ) )).

fof(d7_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k4_osafree(A,B,C) = a_3_0_osafree(A,B,C) ) ) ) )).

fof(t9_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),C) = a_3_0_osafree(A,B,C) ) ) ) )).

fof(d20_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k2_osafree(A,B)))
             => k17_osafree(A,B,C) = a_3_1_osafree(A,B,C) ) ) ) )).

fof(d21_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k2_osafree(A,B)))
             => ! [D] :
                  ( m2_finseq_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))))
                 => k18_osafree(A,B,C,D) = a_4_0_osafree(A,B,C,D) ) ) ) ) )).

fof(d23_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,k8_osafree(A,B))
                & m1_osalg_4(C,A,k8_osafree(A,B)) )
             => ( C = k20_osafree(A,B)
              <=> ! [D] :
                    ( r2_hidden(D,u1_struct_0(A))
                   => k1_funct_1(C,D) = a_3_2_osafree(A,B,D) ) ) ) ) ) )).

fof(t29_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k21_osafree(A,B,C) = a_3_3_osafree(A,B,C) ) ) ) )).

fof(t31_osafree,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k23_osafree(A,B,C) = a_3_4_osafree(A,B,C) ) ) ) )).

fof(fraenkel_a_3_0_osafree,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & v4_osalg_1(B)
        & v5_osalg_1(B)
        & l3_osalg_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_osafree(B,C,D))
      <=> ? [E] :
            ( m1_dtconstr(E,u1_struct_0(k2_osafree(B,C)),k5_trees_3(u1_struct_0(k2_osafree(B,C))),k4_dtconstr(k2_osafree(B,C)))
            & A = E
            & ~ ( ! [F] :
                    ( m1_subset_1(F,u1_struct_0(B))
                   => ! [G] :
                        ~ ( r3_orders_2(B,F,D)
                          & r2_hidden(G,k1_funct_1(C,F))
                          & E = k1_trees_4(k4_tarski(G,F)) ) )
                & ! [F] :
                    ( m1_subset_1(F,u1_msualg_1(B))
                   => ~ ( k4_tarski(F,u1_struct_0(B)) = k1_funct_1(E,k1_xboole_0)
                        & r3_orders_2(B,k1_osalg_1(B,F),D) ) ) ) ) ) ) )).

fof(fraenkel_a_3_1_osafree,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & v4_osalg_1(B)
        & v5_osalg_1(B)
        & l3_osalg_1(B)
        & v2_relat_1(C)
        & m1_pboole(C,u1_struct_0(B))
        & m1_subset_1(D,u1_struct_0(k2_osafree(B,C))) )
     => ( r2_hidden(A,a_3_1_osafree(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = k4_tarski(k2_trees_4(u1_struct_0(k2_osafree(B,C)),D),E)
            & ? [F] :
                ( m1_subset_1(F,u1_struct_0(B))
                & ? [G] :
                    ( r2_hidden(G,k1_funct_1(C,F))
                    & D = k4_tarski(G,F)
                    & r3_orders_2(B,F,E) ) ) ) ) ) )).

fof(fraenkel_a_4_0_osafree,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & v4_osalg_1(B)
        & v5_osalg_1(B)
        & l3_osalg_1(B)
        & v2_relat_1(C)
        & m1_pboole(C,u1_struct_0(B))
        & m1_subset_1(D,u1_struct_0(k2_osafree(B,C)))
        & m2_finseq_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(B,C)),u1_struct_0(B)))) )
     => ( r2_hidden(A,a_4_0_osafree(B,C,D,E))
      <=> ? [F,G,H] :
            ( m1_subset_1(F,u1_msualg_1(B))
            & m1_subset_1(G,k3_msualg_1(B,F,k8_osafree(B,C)))
            & m1_subset_1(H,u1_struct_0(B))
            & A = k4_tarski(k8_funct_2(k3_msualg_1(B,F,k8_osafree(B,C)),k4_msualg_1(B,F,k8_osafree(B,C)),k5_msualg_1(B,F,k8_osafree(B,C)),G),H)
            & ? [I] :
                ( m1_subset_1(I,u1_msualg_1(B))
                & D = k4_tarski(I,u1_struct_0(B))
                & r1_osalg_1(B,I,F)
                & k3_finseq_1(k1_msualg_1(B,I)) = k3_finseq_1(k1_msualg_1(B,F))
                & r3_orders_2(B,k1_osalg_1(B,I),H)
                & r3_orders_2(B,k1_osalg_1(B,F),H) )
            & ? [I] :
                ( m2_finseq_2(I,u1_struct_0(B),k3_finseq_2(u1_struct_0(B)))
                & k4_finseq_1(I) = k4_finseq_1(E)
                & ! [J] :
                    ( m2_subset_1(J,k1_numbers,k5_numbers)
                   => ( r2_hidden(J,k4_finseq_1(E))
                     => r2_hidden(k4_tarski(k1_funct_1(G,J),k4_finseq_4(k5_numbers,u1_struct_0(B),I,J)),k1_funct_1(E,J)) ) ) ) ) ) ) )).

fof(fraenkel_a_3_2_osafree,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & v4_osalg_1(B)
        & v5_osalg_1(B)
        & v2_osalg_4(B)
        & l3_osalg_1(B)
        & v2_relat_1(C)
        & m1_pboole(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_2_osafree(B,C,D))
      <=> ? [E,F] :
            ( m1_dtconstr(E,u1_struct_0(k2_osafree(B,C)),k5_trees_3(u1_struct_0(k2_osafree(B,C))),k4_dtconstr(k2_osafree(B,C)))
            & m1_dtconstr(F,u1_struct_0(k2_osafree(B,C)),k5_trees_3(u1_struct_0(k2_osafree(B,C))),k4_dtconstr(k2_osafree(B,C)))
            & A = k4_tarski(E,F)
            & r2_hidden(k4_tarski(E,D),k8_funct_2(k4_dtconstr(k2_osafree(B,C)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(B,C)),u1_struct_0(B))),k19_osafree(B,C),F)) ) ) ) )).

fof(fraenkel_a_3_3_osafree,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & v4_osalg_1(B)
        & v5_osalg_1(B)
        & v2_osalg_4(B)
        & l3_osalg_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_3_osafree(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(k2_osafree(B,C)))
            & A = k2_trees_4(u1_struct_0(k2_osafree(B,C)),E)
            & r2_hidden(E,k6_dtconstr(k2_osafree(B,C)))
            & k2_mcart_1(E) = D ) ) ) )).

fof(fraenkel_a_3_4_osafree,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & v4_osalg_1(B)
        & v5_osalg_1(B)
        & v2_osalg_4(B)
        & l3_osalg_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_4_osafree(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(k2_osafree(B,C)))
            & A = k1_funct_1(k1_msualg_3(u1_struct_0(B),u4_msualg_1(B,k8_osafree(B,C)),u4_msualg_1(B,k16_osalg_4(B,k8_osafree(B,C),k15_osafree(B,C))),k18_osalg_4(B,k8_osafree(B,C),k15_osafree(B,C)),D),k2_trees_4(u1_struct_0(k2_osafree(B,C)),E))
            & r2_hidden(E,k6_dtconstr(k2_osafree(B,C)))
            & k2_mcart_1(E) = D ) ) ) )).
%------------------------------------------------------------------------------