SET007 Axioms: SET007+738.ax


%------------------------------------------------------------------------------
% File     : SET007+738 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Order Sorted Quotient 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    : osalg_4 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  103 (   4 unit)
%            Number of atoms       : 1354 (  49 equality)
%            Maximal formula depth :   24 (  12 average)
%            Number of connectives : 1433 ( 182 ~  ;   0  |; 915  &)
%                                         (  28 <=>; 308 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   56 (   1 propositional; 0-4 arity)
%            Number of functors    :   66 (   5 constant; 0-6 arity)
%            Number of variables   :  388 (   0 singleton; 373 !;  15 ?)
%            Maximal term depth    :    6 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_pboole(B,u1_struct_0(A))
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v11_osalg_1(B,A)
          & v1_msualg_4(B) ) ) )).

fof(rc2_osalg_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & m1_pboole(B,u1_struct_0(A))
        & m1_pboole(C,u1_struct_0(A)) )
     => ? [D] :
          ( m1_msualg_4(D,u1_struct_0(A),B,C)
          & v1_relat_1(D)
          & v1_funct_1(D)
          & v1_msualg_4(D)
          & v1_osalg_4(D,A,B,C) ) ) )).

fof(cc1_osalg_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & m1_pboole(B,u1_struct_0(A))
        & m1_pboole(C,u1_struct_0(A)) )
     => ! [D] :
          ( m1_msualg_4(D,u1_struct_0(A),B,C)
         => ( v1_osalg_4(D,A,B,C)
           => ( v11_osalg_1(D,A)
              & v1_msualg_4(D) ) ) ) ) )).

fof(rc3_osalg_4,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_osalg_4(C,A,B)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_msualg_4(C)
          & v3_msualg_4(C,A,B) ) ) )).

fof(rc4_osalg_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v5_msualg_1(B,A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A) )
     => ? [C] :
          ( m1_osalg_4(C,A,B)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_msualg_4(C)
          & v3_msualg_4(C,A,B)
          & v4_msualg_4(C,A,B) ) ) )).

fof(cc2_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_osalg_4(A))
         => ~ v1_xboole_0(B) ) ) )).

fof(rc5_osalg_4,axiom,(
    ? [A] :
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v2_osalg_4(A) ) )).

fof(rc6_osalg_4,axiom,(
    ? [A] :
      ( l3_osalg_1(A)
      & ~ v3_struct_0(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & ~ v2_msualg_1(A)
      & v4_osalg_1(A)
      & v5_osalg_1(A)
      & v2_osalg_4(A) ) )).

fof(cc3_osalg_4,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_orders_3(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v2_osalg_4(A) ) ) ) )).

fof(cc4_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_osalg_4(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k2_osalg_4(A))
         => ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,A) ) ) ) )).

fof(fc1_osalg_4,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)
        & v5_msualg_1(B,A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & m1_osalg_4(C,A,B)
        & m1_subset_1(D,u1_struct_0(A)) )
     => ~ v1_xboole_0(k6_osalg_4(A,B,C,D)) ) )).

fof(fc2_osalg_4,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)
        & v5_msualg_1(B,A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & m1_osalg_4(C,A,B) )
     => ( v1_relat_1(k7_osalg_4(A,B,C))
        & v2_relat_1(k7_osalg_4(A,B,C))
        & ~ v3_relat_1(k7_osalg_4(A,B,C))
        & v1_funct_1(k7_osalg_4(A,B,C))
        & v11_osalg_1(k7_osalg_4(A,B,C),A) ) ) )).

fof(fc3_osalg_4,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)
        & v5_msualg_1(B,A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & v4_msualg_4(C,A,B)
        & m1_osalg_4(C,A,B) )
     => ( v4_msualg_1(k16_osalg_4(A,B,C),A)
        & v5_msualg_1(k16_osalg_4(A,B,C),A)
        & v12_osalg_1(k16_osalg_4(A,B,C),A) ) ) )).

fof(rc7_osalg_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v5_msualg_1(B,A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A) )
     => ? [C] :
          ( m1_osalg_4(C,A,B)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_msualg_4(C)
          & v3_msualg_4(C,A,B)
          & v4_msualg_4(C,A,B)
          & v3_osalg_4(C,A,B) ) ) )).

fof(rc8_osalg_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v5_msualg_1(B,A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A) )
     => ? [C] :
          ( m1_osalg_4(C,A,B)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_msualg_4(C)
          & v3_msualg_4(C,A,B)
          & v3_osalg_4(C,A,B) ) ) )).

fof(cc5_osalg_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v5_msualg_1(B,A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A) )
     => ! [C] :
          ( m1_osalg_4(C,A,B)
         => ( ( v3_msualg_4(C,A,B)
              & v3_osalg_4(C,A,B) )
           => ( v1_msualg_4(C)
              & v3_msualg_4(C,A,B)
              & v4_msualg_4(C,A,B) ) ) ) ) )).

fof(cc6_osalg_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v5_msualg_1(B,A)
        & v12_osalg_1(B,A)
        & v13_osalg_1(B,A)
        & l3_msualg_1(B,A) )
     => ! [C] :
          ( m1_osalg_4(C,A,B)
         => ( ( v3_msualg_4(C,A,B)
              & v4_msualg_4(C,A,B) )
           => ( v1_msualg_4(C)
              & v3_msualg_4(C,A,B)
              & v4_msualg_4(C,A,B)
              & v3_osalg_4(C,A,B) ) ) ) ) )).

fof(fc4_osalg_4,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)
        & v5_msualg_1(B,A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & v4_msualg_4(C,A,B)
        & v3_osalg_4(C,A,B)
        & m1_osalg_4(C,A,B) )
     => ( v4_msualg_1(k16_osalg_4(A,B,C),A)
        & v5_msualg_1(k16_osalg_4(A,B,C),A)
        & v12_osalg_1(k16_osalg_4(A,B,C),A)
        & v13_osalg_1(k16_osalg_4(A,B,C),A) ) ) )).

fof(d1_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_pboole(B,u1_struct_0(A))
         => ! [C] :
              ( m1_pboole(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_msualg_4(D,u1_struct_0(A),B,C)
                 => ( v1_osalg_4(D,A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( r3_orders_2(A,E,F)
                             => ! [G,H] :
                                  ( ( r2_hidden(G,k1_funct_1(B,E))
                                    & r2_hidden(H,k1_funct_1(C,E)) )
                                 => ( r2_hidden(k4_tarski(G,H),k1_msualg_4(u1_struct_0(A),B,C,D,E))
                                  <=> r2_hidden(k4_tarski(G,H),k1_msualg_4(u1_struct_0(A),B,C,D,F)) ) ) ) ) ) ) ) ) ) ) )).

fof(t1_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_pboole(B,u1_struct_0(A))
         => ! [C] :
              ( m1_pboole(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_msualg_4(D,u1_struct_0(A),B,C)
                 => ( v1_osalg_4(D,A,B,C)
                   => ( v11_osalg_1(D,A)
                      & m1_pboole(D,u1_struct_0(A)) ) ) ) ) ) ) )).

fof(d2_osalg_4,axiom,(
    $true )).

fof(d3_osalg_4,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] :
              ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => ( m1_osalg_4(C,A,B)
              <=> v1_osalg_4(C,A,u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ) ) )).

fof(d4_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
            & v3_relat_2(B)
            & v8_relat_2(B)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( B = k1_osalg_4(A)
          <=> ! [C,D] :
                ( r2_hidden(k4_tarski(C,D),B)
              <=> ( r2_hidden(C,u1_struct_0(A))
                  & r2_hidden(D,u1_struct_0(A))
                  & ? [E] :
                      ( m2_finseq_1(E,u1_struct_0(A))
                      & ~ r1_xreal_0(k3_finseq_1(E),np__1)
                      & k1_funct_1(E,np__1) = C
                      & k1_funct_1(E,k3_finseq_1(E)) = D
                      & ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ~ ( r1_xreal_0(np__2,F)
                              & r1_xreal_0(F,k3_finseq_1(E))
                              & ~ r2_hidden(k4_tarski(k1_funct_1(E,F),k1_funct_1(E,k6_xcmplx_0(F,np__1))),u1_orders_2(A))
                              & ~ r2_hidden(k4_tarski(k1_funct_1(E,k6_xcmplx_0(F,np__1)),k1_funct_1(E,F)),u1_orders_2(A)) ) ) ) ) ) ) ) ) )).

fof(t2_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_orders_2(A,B,C)
               => r2_hidden(k4_tarski(B,C),k1_osalg_4(A)) ) ) ) ) )).

fof(d5_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_osalg_4(A,B,C)
              <=> r2_hidden(k4_tarski(B,C),k1_osalg_4(A)) ) ) ) ) )).

fof(t3_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r1_osalg_4(A,B,C)
                      & r1_osalg_4(A,C,D) )
                   => r1_osalg_4(A,B,D) ) ) ) ) ) )).

fof(d6_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => k2_osalg_4(A) = k8_eqrel_1(u1_struct_0(A),k1_osalg_4(A)) ) )).

fof(d7_osalg_4,axiom,(
    $true )).

fof(d8_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k3_osalg_4(A,B) = k6_eqrel_1(u1_struct_0(A),k1_osalg_4(A),B) ) ) )).

fof(t4_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r2_hidden(B,k3_osalg_4(A,B)) ) ) )).

fof(t5_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_orders_2(A,B,C)
               => k3_osalg_4(A,B) = k3_osalg_4(A,C) ) ) ) ) )).

fof(t6_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [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))
                 => r2_hidden(D,k4_osalg_4(A,B,k3_osalg_4(A,C))) ) ) ) ) )).

fof(d10_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v2_osalg_4(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_zfmisc_1(u1_struct_0(A)),k2_osalg_4(A))
           => v1_waybel_0(B,A) ) ) ) )).

fof(t7_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_orders_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(k4_tarski(B,C),k1_osalg_4(A))
               => B = C ) ) ) ) )).

fof(t8_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_orders_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(u1_struct_0(A)),k2_osalg_4(A))
         => ? [C] :
              ( m1_subset_1(C,u1_struct_0(A))
              & B = k1_struct_0(A,C) ) ) ) )).

fof(t9_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_orders_3(A)
        & l1_orders_2(A) )
     => v2_osalg_4(A) ) )).

fof(t10_osalg_4,axiom,
    ( v1_partfun1(k1_xboole_0,k1_xboole_0,k1_xboole_0)
    & v3_relat_2(k1_xboole_0)
    & v8_relat_2(k1_xboole_0)
    & m2_relset_1(k1_xboole_0,k1_xboole_0,k1_xboole_0) )).

fof(d11_osalg_4,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] :
          ( ( v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,B)
                & m1_osalg_4(C,A,B) )
             => ! [D] :
                  ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k2_osalg_4(A))
                 => ! [E] :
                      ( ( v1_partfun1(E,k4_osalg_4(A,u4_msualg_1(A,B),D),k4_osalg_4(A,u4_msualg_1(A,B),D))
                        & v3_relat_2(E)
                        & v8_relat_2(E)
                        & m2_relset_1(E,k4_osalg_4(A,u4_msualg_1(A,B),D),k4_osalg_4(A,u4_msualg_1(A,B),D)) )
                     => ( E = k5_osalg_4(A,B,C,D)
                      <=> ! [F,G] :
                            ( r2_hidden(k4_tarski(F,G),E)
                          <=> ? [H] :
                                ( m1_subset_1(H,u1_struct_0(A))
                                & r2_hidden(H,D)
                                & r2_hidden(k4_tarski(F,G),k2_msualg_4(A,B,C,H)) ) ) ) ) ) ) ) ) )).

fof(d12_osalg_4,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] :
          ( ( v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,B)
                & m1_osalg_4(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(k8_eqrel_1(k4_osalg_4(A,u4_msualg_1(A,B),k3_osalg_4(A,D)),k5_osalg_4(A,B,C,k3_osalg_4(A,D)))))
                     => ( E = k6_osalg_4(A,B,C,D)
                      <=> ! [F] :
                            ( r2_hidden(F,E)
                          <=> ? [G] :
                                ( r2_hidden(G,k1_funct_1(u4_msualg_1(A,B),D))
                                & F = k6_eqrel_1(k4_osalg_4(A,u4_msualg_1(A,B),k3_osalg_4(A,D)),k5_osalg_4(A,B,C,k3_osalg_4(A,D)),G) ) ) ) ) ) ) ) ) )).

fof(t11_osalg_4,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] :
          ( ( v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,B)
                & m1_osalg_4(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r3_orders_2(A,D,E)
                       => r1_tarski(k6_osalg_4(A,B,C,D),k6_osalg_4(A,B,C,E)) ) ) ) ) ) ) )).

fof(d13_osalg_4,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] :
          ( ( v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,B)
                & m1_osalg_4(C,A,B) )
             => ! [D] :
                  ( ( v11_osalg_1(D,A)
                    & m1_pboole(D,u1_struct_0(A)) )
                 => ( D = k7_osalg_4(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k1_funct_1(D,E) = k6_osalg_4(A,B,C,E) ) ) ) ) ) ) )).

fof(d14_osalg_4,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] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,B)
                & m1_osalg_4(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D))
                     => k8_osalg_4(A,B,C,D,E) = k6_eqrel_1(k4_osalg_4(A,u4_msualg_1(A,B),k3_osalg_4(A,D)),k5_osalg_4(A,B,C,k3_osalg_4(A,D)),E) ) ) ) ) ) )).

fof(t12_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_osalg_4(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( ? [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                      & r3_orders_2(A,D,B)
                      & r3_orders_2(A,D,C) )
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r3_orders_2(A,B,D)
                          & r3_orders_2(A,C,D) ) ) ) ) ) ) )).

fof(t13_osalg_4,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] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,B)
                & m1_osalg_4(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D))
                     => ! [F] :
                          ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D))
                         => ( k8_osalg_4(A,B,C,D,E) = k8_osalg_4(A,B,C,D,F)
                          <=> r2_hidden(k4_tarski(E,F),k2_msualg_4(A,B,C,D)) ) ) ) ) ) ) ) )).

fof(t14_osalg_4,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] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,B)
                & m1_osalg_4(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D))
                         => ( r3_orders_2(A,D,E)
                           => ! [G] :
                                ( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,B),E))
                               => ( G = F
                                 => k8_osalg_4(A,B,C,D,F) = k8_osalg_4(A,B,C,E,G) ) ) ) ) ) ) ) ) ) )).

fof(d15_osalg_4,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] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & v12_osalg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( ( v3_msualg_4(D,A,C)
                    & v4_msualg_4(D,A,C)
                    & m1_osalg_4(D,A,C) )
                 => ! [E] :
                      ( m1_subset_1(E,k3_msualg_1(A,B,C))
                     => ! [F] :
                          ( m1_subset_1(F,k4_card_3(k6_msualg_4(u1_struct_0(A),k1_msualg_1(A,B),k7_osalg_4(A,C,D))))
                         => ( F = k9_osalg_4(A,B,C,D,E)
                          <=> ! [G] :
                                ( m2_subset_1(G,k1_numbers,k5_numbers)
                               => ~ ( r2_hidden(G,k4_finseq_1(k1_msualg_1(A,B)))
                                    & ! [H] :
                                        ( m1_subset_1(H,k1_funct_1(u4_msualg_1(A,C),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),G)))
                                       => ~ ( H = k1_funct_1(E,G)
                                            & k1_funct_1(F,G) = k8_osalg_4(A,C,D,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),G),H) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d16_osalg_4,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] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & v12_osalg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( ( v3_msualg_4(D,A,C)
                    & v4_msualg_4(D,A,C)
                    & m1_osalg_4(D,A,C) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,C,D)),B))
                        & m2_relset_1(E,k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,C,D)),B)) )
                     => ( E = k10_osalg_4(A,B,C,D)
                      <=> ! [F] :
                            ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,C),k1_osalg_1(A,B)))
                           => k1_funct_1(E,F) = k8_osalg_4(A,C,D,k1_osalg_1(A,B),F) ) ) ) ) ) ) ) )).

fof(d17_osalg_4,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] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & v12_osalg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( ( v3_msualg_4(D,A,C)
                    & v4_msualg_4(D,A,C)
                    & m1_osalg_4(D,A,C) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,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),u4_msualg_1(A,C))),B),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),k7_osalg_4(A,C,D))),B))
                        & m2_relset_1(E,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),u4_msualg_1(A,C))),B),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),k7_osalg_4(A,C,D))),B)) )
                     => ( E = k11_osalg_4(A,B,C,D)
                      <=> ! [F] :
                            ( m1_subset_1(F,k3_msualg_1(A,B,C))
                           => k1_funct_1(E,F) = k9_osalg_4(A,B,C,D,F) ) ) ) ) ) ) ) )).

fof(d18_osalg_4,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] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,B)
                & v4_msualg_4(C,A,B)
                & m1_osalg_4(C,A,B) )
             => ! [D] :
                  ( m3_pboole(D,u1_msualg_1(A),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,B)),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,B,C)))
                 => ( D = k12_osalg_4(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_msualg_1(A))
                       => k5_msualg_4(A,k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,B)),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,B,C)),D,E) = k10_osalg_4(A,E,B,C) ) ) ) ) ) ) )).

fof(d19_osalg_4,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] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,B)
                & v4_msualg_4(C,A,B)
                & m1_osalg_4(C,A,B) )
             => ! [D] :
                  ( m3_pboole(D,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),u4_msualg_1(A,B))),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k7_osalg_4(A,B,C))))
                 => ( D = k13_osalg_4(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,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),u4_msualg_1(A,B))),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k7_osalg_4(A,B,C))),D,E) = k11_osalg_4(A,E,B,C) ) ) ) ) ) ) )).

fof(t15_osalg_4,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] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & v12_osalg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( ( v3_msualg_4(D,A,C)
                    & v4_msualg_4(D,A,C)
                    & m1_osalg_4(D,A,C) )
                 => ! [E] :
                      ~ ( r2_hidden(E,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),k7_osalg_4(A,C,D))),B))
                        & ! [F] :
                            ( m1_subset_1(F,k3_msualg_1(A,B,C))
                           => E != k9_osalg_4(A,B,C,D,F) ) ) ) ) ) ) )).

fof(d20_osalg_4,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] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & v12_osalg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( ( v3_msualg_4(D,A,C)
                    & v4_msualg_4(D,A,C)
                    & m1_osalg_4(D,A,C) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,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),k7_osalg_4(A,C,D))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,C,D)),B))
                        & m2_relset_1(E,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),k7_osalg_4(A,C,D))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,C,D)),B)) )
                     => ( E = k14_osalg_4(A,B,C,D)
                      <=> ! [F] :
                            ( m1_subset_1(F,k3_msualg_1(A,B,C))
                           => ( r2_hidden(k9_osalg_4(A,B,C,D,F),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),k7_osalg_4(A,C,D))),B))
                             => k1_funct_1(E,k9_osalg_4(A,B,C,D,F)) = k1_funct_1(k1_partfun1(k3_msualg_1(A,B,C),k4_msualg_1(A,B,C),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,C,D)),B),k5_msualg_1(A,B,C),k10_osalg_4(A,B,C,D)),F) ) ) ) ) ) ) ) ) )).

fof(d21_osalg_4,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] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,B)
                & v4_msualg_4(C,A,B)
                & m1_osalg_4(C,A,B) )
             => ! [D] :
                  ( m3_pboole(D,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),k7_osalg_4(A,B,C))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,B,C)))
                 => ( D = k15_osalg_4(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,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),k7_osalg_4(A,B,C))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,B,C)),D,E) = k14_osalg_4(A,E,B,C) ) ) ) ) ) ) )).

fof(d22_osalg_4,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] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,B)
                & v4_msualg_4(C,A,B)
                & m1_osalg_4(C,A,B) )
             => k16_osalg_4(A,B,C) = g3_msualg_1(A,k7_osalg_4(A,B,C),k15_osalg_4(A,B,C)) ) ) ) )).

fof(d23_osalg_4,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] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,B)
                & v4_msualg_4(C,A,B)
                & m1_osalg_4(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k1_funct_1(u4_msualg_1(A,B),D),k6_osalg_4(A,B,C,D))
                        & m2_relset_1(E,k1_funct_1(u4_msualg_1(A,B),D),k6_osalg_4(A,B,C,D)) )
                     => ( E = k17_osalg_4(A,B,C,D)
                      <=> ! [F] :
                            ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D))
                           => k8_funct_2(k1_funct_1(u4_msualg_1(A,B),D),k6_osalg_4(A,B,C,D),E,F) = k8_osalg_4(A,B,C,D,F) ) ) ) ) ) ) ) )).

fof(d24_osalg_4,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] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,B)
                & v4_msualg_4(C,A,B)
                & m1_osalg_4(C,A,B) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k16_osalg_4(A,B,C)))
                 => ( D = k18_osalg_4(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k16_osalg_4(A,B,C)),D,E) = k17_osalg_4(A,B,C,E) ) ) ) ) ) ) )).

fof(t16_osalg_4,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] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,B)
                & v4_msualg_4(C,A,B)
                & m1_osalg_4(C,A,B) )
             => ( r2_msualg_3(A,B,k16_osalg_4(A,B,C),k18_osalg_4(A,B,C))
                & v1_osalg_3(k18_osalg_4(A,B,C),A) ) ) ) ) )).

fof(t17_osalg_4,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] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & v12_osalg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( ( r1_msualg_3(A,B,C,D)
                      & v1_osalg_3(D,A) )
                   => ( v3_msualg_4(k18_msualg_4(A,B,C,D),A,B)
                      & v4_msualg_4(k18_msualg_4(A,B,C,D),A,B)
                      & m1_osalg_4(k18_msualg_4(A,B,C,D),A,B) ) ) ) ) ) ) )).

fof(d25_osalg_4,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] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & v12_osalg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( ( r1_msualg_3(A,B,C,D)
                      & v1_osalg_3(D,A) )
                   => k19_osalg_4(A,B,C,D) = k18_msualg_4(A,B,C,D) ) ) ) ) ) )).

fof(d26_osalg_4,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] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & v12_osalg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r1_msualg_3(A,B,C,D)
                          & v1_osalg_3(D,A) )
                       => ! [F] :
                            ( ( v1_funct_1(F)
                              & v1_funct_2(F,k1_funct_1(u4_msualg_1(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D))),E),k1_funct_1(u4_msualg_1(A,C),E))
                              & m2_relset_1(F,k1_funct_1(u4_msualg_1(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D))),E),k1_funct_1(u4_msualg_1(A,C),E)) )
                           => ( F = k20_osalg_4(A,B,C,D,E)
                            <=> ! [G] :
                                  ( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,B),E))
                                 => k1_funct_1(F,k8_osalg_4(A,B,k19_osalg_4(A,B,C,D),E,G)) = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,C),E),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,E),G) ) ) ) ) ) ) ) ) ) )).

fof(d27_osalg_4,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] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & v12_osalg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ! [E] :
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D))),u4_msualg_1(A,C))
                     => ( E = k21_osalg_4(A,B,C,D)
                      <=> ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D))),u4_msualg_1(A,C),E,F) = k20_osalg_4(A,B,C,D,F) ) ) ) ) ) ) ) )).

fof(t18_osalg_4,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] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & v12_osalg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( ( r1_msualg_3(A,B,C,D)
                      & v1_osalg_3(D,A) )
                   => ( r3_msualg_3(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D)),C,k21_osalg_4(A,B,C,D))
                      & v1_osalg_3(k21_osalg_4(A,B,C,D),A) ) ) ) ) ) ) )).

fof(t19_osalg_4,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] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & v12_osalg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( ( r2_msualg_3(A,B,C,D)
                      & v1_osalg_3(D,A) )
                   => r4_msualg_3(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D)),C,k21_osalg_4(A,B,C,D)) ) ) ) ) ) )).

fof(t20_osalg_4,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] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & v12_osalg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( ( r2_msualg_3(A,B,C,D)
                      & v1_osalg_3(D,A) )
                   => r6_msualg_3(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D)),C) ) ) ) ) ) )).

fof(d28_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,B)
                & m1_osalg_4(C,A,B) )
             => ( v3_osalg_4(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_msualg_1(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_msualg_1(A))
                       => ( r6_osalg_1(A,D,E)
                         => ! [F] :
                              ( m1_subset_1(F,k3_msualg_1(A,D,B))
                             => ! [G] :
                                  ( m1_subset_1(G,k3_msualg_1(A,E,B))
                                 => ( ! [H] :
                                        ( m2_subset_1(H,k1_numbers,k5_numbers)
                                       => ( r2_hidden(H,k1_relat_1(F))
                                         => r2_hidden(k4_tarski(k1_funct_1(F,H),k1_funct_1(G,H)),k2_msualg_4(A,B,C,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,E),H))) ) )
                                   => r2_hidden(k4_tarski(k8_funct_2(k3_msualg_1(A,D,B),k4_msualg_1(A,D,B),k5_msualg_1(A,D,B),F),k8_funct_2(k3_msualg_1(A,E,B),k4_msualg_1(A,E,B),k5_msualg_1(A,E,B),G)),k2_msualg_4(A,B,C,k1_osalg_1(A,E))) ) ) ) ) ) ) ) ) ) ) )).

fof(t21_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ( v3_msualg_4(k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)),A,B)
            & v4_msualg_4(k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)),A,B)
            & m1_osalg_4(k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)),A,B) ) ) ) )).

fof(t22_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,B)
                & v4_msualg_4(C,A,B)
                & m1_osalg_4(C,A,B) )
             => ( r6_pboole(u1_struct_0(A),C,k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)))
               => v3_osalg_4(C,A,B) ) ) ) ) )).

fof(t23_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,B)
                & v3_osalg_4(C,A,B)
                & m1_osalg_4(C,A,B) )
             => v4_msualg_4(C,A,B) ) ) ) )).

fof(t24_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & v13_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v3_msualg_4(C,A,B)
                & v4_msualg_4(C,A,B)
                & m1_osalg_4(C,A,B) )
             => v3_osalg_4(C,A,B) ) ) ) )).

fof(t25_osalg_4,axiom,(
    $true )).

fof(t26_osalg_4,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] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,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),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( ( r1_msualg_3(A,B,C,D)
                      & v1_osalg_3(D,A) )
                   => v3_osalg_4(k19_osalg_4(A,B,C,D),A,B) ) ) ) ) ) )).

fof(d29_osalg_4,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] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & v12_osalg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ! [E] :
                      ( ( v3_msualg_4(E,A,B)
                        & v4_msualg_4(E,A,B)
                        & m1_osalg_4(E,A,B) )
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r1_msualg_3(A,B,C,D)
                              & v1_osalg_3(D,A)
                              & r2_pboole(u1_struct_0(A),E,k19_osalg_4(A,B,C,D)) )
                           => ! [G] :
                                ( ( v1_funct_1(G)
                                  & v1_funct_2(G,k1_funct_1(u4_msualg_1(A,k16_osalg_4(A,B,E)),F),k1_funct_1(u4_msualg_1(A,C),F))
                                  & m2_relset_1(G,k1_funct_1(u4_msualg_1(A,k16_osalg_4(A,B,E)),F),k1_funct_1(u4_msualg_1(A,C),F)) )
                               => ( G = k22_osalg_4(A,B,C,D,E,F)
                                <=> ! [H] :
                                      ( m1_subset_1(H,k1_funct_1(u4_msualg_1(A,B),F))
                                     => k1_funct_1(G,k8_osalg_4(A,B,E,F,H)) = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),F),k1_funct_1(u4_msualg_1(A,C),F),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,F),H) ) ) ) ) ) ) ) ) ) ) )).

fof(d30_osalg_4,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] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & v12_osalg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ! [E] :
                      ( ( v3_msualg_4(E,A,B)
                        & v4_msualg_4(E,A,B)
                        & m1_osalg_4(E,A,B) )
                     => ! [F] :
                          ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,k16_osalg_4(A,B,E)),u4_msualg_1(A,C))
                         => ( F = k23_osalg_4(A,B,C,D,E)
                          <=> ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k16_osalg_4(A,B,E)),u4_msualg_1(A,C),F,G) = k22_osalg_4(A,B,C,D,E,G) ) ) ) ) ) ) ) ) )).

fof(t27_osalg_4,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] :
          ( ( v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( ( v5_msualg_1(C,A)
                & v12_osalg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] :
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ! [E] :
                      ( ( v3_msualg_4(E,A,B)
                        & v4_msualg_4(E,A,B)
                        & m1_osalg_4(E,A,B) )
                     => ( ( r1_msualg_3(A,B,C,D)
                          & v1_osalg_3(D,A)
                          & r2_pboole(u1_struct_0(A),E,k19_osalg_4(A,B,C,D)) )
                       => ( r1_msualg_3(A,k16_osalg_4(A,B,E),C,k23_osalg_4(A,B,C,D,E))
                          & v1_osalg_3(k23_osalg_4(A,B,C,D,E),A) ) ) ) ) ) ) ) )).

fof(dt_m1_osalg_4,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_osalg_4(C,A,B)
         => m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) )).

fof(existence_m1_osalg_4,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_osalg_4(C,A,B) ) )).

fof(symmetry_r1_osalg_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r1_osalg_4(A,B,C)
       => r1_osalg_4(A,C,B) ) ) )).

fof(reflexivity_r1_osalg_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => r1_osalg_4(A,B,B) ) )).

fof(dt_k1_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_partfun1(k1_osalg_4(A),u1_struct_0(A),u1_struct_0(A))
        & v3_relat_2(k1_osalg_4(A))
        & v8_relat_2(k1_osalg_4(A))
        & m2_relset_1(k1_osalg_4(A),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(dt_k2_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( ~ v1_xboole_0(k2_osalg_4(A))
        & m1_subset_1(k2_osalg_4(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) )).

fof(dt_k3_osalg_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m2_subset_1(k3_osalg_4(A,B),k1_zfmisc_1(u1_struct_0(A)),k2_osalg_4(A)) ) )).

fof(dt_k4_osalg_4,axiom,(
    $true )).

fof(dt_k5_osalg_4,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)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & m1_osalg_4(C,A,B)
        & m1_subset_1(D,k2_osalg_4(A)) )
     => ( v1_partfun1(k5_osalg_4(A,B,C,D),k4_osalg_4(A,u4_msualg_1(A,B),D),k4_osalg_4(A,u4_msualg_1(A,B),D))
        & v3_relat_2(k5_osalg_4(A,B,C,D))
        & v8_relat_2(k5_osalg_4(A,B,C,D))
        & m2_relset_1(k5_osalg_4(A,B,C,D),k4_osalg_4(A,u4_msualg_1(A,B),D),k4_osalg_4(A,u4_msualg_1(A,B),D)) ) ) )).

fof(dt_k6_osalg_4,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)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & m1_osalg_4(C,A,B)
        & m1_subset_1(D,u1_struct_0(A)) )
     => m1_subset_1(k6_osalg_4(A,B,C,D),k1_zfmisc_1(k8_eqrel_1(k4_osalg_4(A,u4_msualg_1(A,B),k3_osalg_4(A,D)),k5_osalg_4(A,B,C,k3_osalg_4(A,D))))) ) )).

fof(dt_k7_osalg_4,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)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & m1_osalg_4(C,A,B) )
     => ( v11_osalg_1(k7_osalg_4(A,B,C),A)
        & m1_pboole(k7_osalg_4(A,B,C),u1_struct_0(A)) ) ) )).

fof(dt_k8_osalg_4,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)
        & v5_msualg_1(B,A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & m1_osalg_4(C,A,B)
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D)) )
     => m1_subset_1(k8_osalg_4(A,B,C,D,E),k6_osalg_4(A,B,C,D)) ) )).

fof(dt_k9_osalg_4,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)
        & m1_subset_1(B,u1_msualg_1(A))
        & v5_msualg_1(C,A)
        & v12_osalg_1(C,A)
        & l3_msualg_1(C,A)
        & v3_msualg_4(D,A,C)
        & v4_msualg_4(D,A,C)
        & m1_osalg_4(D,A,C)
        & m1_subset_1(E,k3_msualg_1(A,B,C)) )
     => m1_subset_1(k9_osalg_4(A,B,C,D,E),k4_card_3(k6_msualg_4(u1_struct_0(A),k1_msualg_1(A,B),k7_osalg_4(A,C,D)))) ) )).

fof(dt_k10_osalg_4,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)
        & m1_subset_1(B,u1_msualg_1(A))
        & v5_msualg_1(C,A)
        & v12_osalg_1(C,A)
        & l3_msualg_1(C,A)
        & v3_msualg_4(D,A,C)
        & v4_msualg_4(D,A,C)
        & m1_osalg_4(D,A,C) )
     => ( v1_funct_1(k10_osalg_4(A,B,C,D))
        & v1_funct_2(k10_osalg_4(A,B,C,D),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,C,D)),B))
        & m2_relset_1(k10_osalg_4(A,B,C,D),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,C,D)),B)) ) ) )).

fof(dt_k11_osalg_4,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)
        & m1_subset_1(B,u1_msualg_1(A))
        & v5_msualg_1(C,A)
        & v12_osalg_1(C,A)
        & l3_msualg_1(C,A)
        & v3_msualg_4(D,A,C)
        & v4_msualg_4(D,A,C)
        & m1_osalg_4(D,A,C) )
     => ( v1_funct_1(k11_osalg_4(A,B,C,D))
        & v1_funct_2(k11_osalg_4(A,B,C,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),u4_msualg_1(A,C))),B),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),k7_osalg_4(A,C,D))),B))
        & m2_relset_1(k11_osalg_4(A,B,C,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),u4_msualg_1(A,C))),B),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),k7_osalg_4(A,C,D))),B)) ) ) )).

fof(dt_k12_osalg_4,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)
        & v5_msualg_1(B,A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & v4_msualg_4(C,A,B)
        & m1_osalg_4(C,A,B) )
     => m3_pboole(k12_osalg_4(A,B,C),u1_msualg_1(A),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,B)),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,B,C))) ) )).

fof(dt_k13_osalg_4,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)
        & v5_msualg_1(B,A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & v4_msualg_4(C,A,B)
        & m1_osalg_4(C,A,B) )
     => m3_pboole(k13_osalg_4(A,B,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),u4_msualg_1(A,B))),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k7_osalg_4(A,B,C)))) ) )).

fof(dt_k14_osalg_4,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)
        & m1_subset_1(B,u1_msualg_1(A))
        & v5_msualg_1(C,A)
        & v12_osalg_1(C,A)
        & l3_msualg_1(C,A)
        & v3_msualg_4(D,A,C)
        & v4_msualg_4(D,A,C)
        & m1_osalg_4(D,A,C) )
     => ( v1_funct_1(k14_osalg_4(A,B,C,D))
        & v1_funct_2(k14_osalg_4(A,B,C,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),k7_osalg_4(A,C,D))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,C,D)),B))
        & m2_relset_1(k14_osalg_4(A,B,C,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),k7_osalg_4(A,C,D))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,C,D)),B)) ) ) )).

fof(dt_k15_osalg_4,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)
        & v5_msualg_1(B,A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & v4_msualg_4(C,A,B)
        & m1_osalg_4(C,A,B) )
     => m3_pboole(k15_osalg_4(A,B,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),k7_osalg_4(A,B,C))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,B,C))) ) )).

fof(dt_k16_osalg_4,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)
        & v5_msualg_1(B,A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & v4_msualg_4(C,A,B)
        & m1_osalg_4(C,A,B) )
     => ( v12_osalg_1(k16_osalg_4(A,B,C),A)
        & l3_msualg_1(k16_osalg_4(A,B,C),A) ) ) )).

fof(dt_k17_osalg_4,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)
        & v5_msualg_1(B,A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & v4_msualg_4(C,A,B)
        & m1_osalg_4(C,A,B)
        & m1_subset_1(D,u1_struct_0(A)) )
     => ( v1_funct_1(k17_osalg_4(A,B,C,D))
        & v1_funct_2(k17_osalg_4(A,B,C,D),k1_funct_1(u4_msualg_1(A,B),D),k6_osalg_4(A,B,C,D))
        & m2_relset_1(k17_osalg_4(A,B,C,D),k1_funct_1(u4_msualg_1(A,B),D),k6_osalg_4(A,B,C,D)) ) ) )).

fof(dt_k18_osalg_4,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)
        & v5_msualg_1(B,A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & v3_msualg_4(C,A,B)
        & v4_msualg_4(C,A,B)
        & m1_osalg_4(C,A,B) )
     => m3_pboole(k18_osalg_4(A,B,C),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k16_osalg_4(A,B,C))) ) )).

fof(dt_k19_osalg_4,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)
        & v5_msualg_1(B,A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & v5_msualg_1(C,A)
        & v12_osalg_1(C,A)
        & l3_msualg_1(C,A)
        & m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) )
     => ( v3_msualg_4(k19_osalg_4(A,B,C,D),A,B)
        & v4_msualg_4(k19_osalg_4(A,B,C,D),A,B)
        & m1_osalg_4(k19_osalg_4(A,B,C,D),A,B) ) ) )).

fof(dt_k20_osalg_4,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)
        & v5_msualg_1(B,A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & v5_msualg_1(C,A)
        & v12_osalg_1(C,A)
        & l3_msualg_1(C,A)
        & m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
        & m1_subset_1(E,u1_struct_0(A)) )
     => ( v1_funct_1(k20_osalg_4(A,B,C,D,E))
        & v1_funct_2(k20_osalg_4(A,B,C,D,E),k1_funct_1(u4_msualg_1(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D))),E),k1_funct_1(u4_msualg_1(A,C),E))
        & m2_relset_1(k20_osalg_4(A,B,C,D,E),k1_funct_1(u4_msualg_1(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D))),E),k1_funct_1(u4_msualg_1(A,C),E)) ) ) )).

fof(dt_k21_osalg_4,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)
        & v5_msualg_1(B,A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & v5_msualg_1(C,A)
        & v12_osalg_1(C,A)
        & l3_msualg_1(C,A)
        & m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) )
     => m3_pboole(k21_osalg_4(A,B,C,D),u1_struct_0(A),u4_msualg_1(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D))),u4_msualg_1(A,C)) ) )).

fof(dt_k22_osalg_4,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_osalg_4(A)
        & l3_osalg_1(A)
        & v5_msualg_1(B,A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & v5_msualg_1(C,A)
        & v12_osalg_1(C,A)
        & l3_msualg_1(C,A)
        & m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
        & v3_msualg_4(E,A,B)
        & v4_msualg_4(E,A,B)
        & m1_osalg_4(E,A,B)
        & m1_subset_1(F,u1_struct_0(A)) )
     => ( v1_funct_1(k22_osalg_4(A,B,C,D,E,F))
        & v1_funct_2(k22_osalg_4(A,B,C,D,E,F),k1_funct_1(u4_msualg_1(A,k16_osalg_4(A,B,E)),F),k1_funct_1(u4_msualg_1(A,C),F))
        & m2_relset_1(k22_osalg_4(A,B,C,D,E,F),k1_funct_1(u4_msualg_1(A,k16_osalg_4(A,B,E)),F),k1_funct_1(u4_msualg_1(A,C),F)) ) ) )).

fof(dt_k23_osalg_4,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)
        & v5_msualg_1(B,A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & v5_msualg_1(C,A)
        & v12_osalg_1(C,A)
        & l3_msualg_1(C,A)
        & m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
        & v3_msualg_4(E,A,B)
        & v4_msualg_4(E,A,B)
        & m1_osalg_4(E,A,B) )
     => m3_pboole(k23_osalg_4(A,B,C,D,E),u1_struct_0(A),u4_msualg_1(A,k16_osalg_4(A,B,E)),u4_msualg_1(A,C)) ) )).

fof(d9_osalg_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_pboole(B,u1_struct_0(A))
         => ! [C] :
              ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k2_osalg_4(A))
             => k4_osalg_4(A,B,C) = k3_tarski(a_3_0_osalg_4(A,B,C)) ) ) ) )).

fof(fraenkel_a_3_0_osalg_4,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & l1_orders_2(B)
        & m1_pboole(C,u1_struct_0(B))
        & m2_subset_1(D,k1_zfmisc_1(u1_struct_0(B)),k2_osalg_4(B)) )
     => ( r2_hidden(A,a_3_0_osalg_4(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = k1_funct_1(C,E)
            & r2_hidden(E,D) ) ) ) )).
%------------------------------------------------------------------------------