SET007 Axioms: SET007+735.ax


%------------------------------------------------------------------------------
% File     : SET007+735 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Order Sorted Algebras
% 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_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  124 (   5 unit)
%            Number of atoms       : 1115 (  65 equality)
%            Maximal formula depth :   24 (   9 average)
%            Number of connectives : 1213 ( 222 ~  ;   1  |; 669  &)
%                                         (  31 <=>; 290 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   59 (   1 propositional; 0-4 arity)
%            Number of functors    :   42 (   1 constant; 0-6 arity)
%            Number of variables   :  345 (   0 singleton; 326 !;  19 ?)
%            Maximal term depth    :    4 (   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(fc1_osalg_1,axiom,(
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_finseq_1(C,A) )
     => ( v1_relat_1(k5_relat_1(C,B))
        & v1_funct_1(k5_relat_1(C,B))
        & v1_finseq_1(k5_relat_1(C,B)) ) ) )).

fof(rc1_osalg_1,axiom,(
    ? [A] :
      ( l1_osalg_1(A)
      & v1_osalg_1(A) ) )).

fof(rc2_osalg_1,axiom,(
    ? [A] :
      ( l2_osalg_1(A)
      & v2_osalg_1(A) ) )).

fof(rc3_osalg_1,axiom,(
    ? [A] :
      ( l3_osalg_1(A)
      & v3_osalg_1(A) ) )).

fof(fc2_osalg_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_2(B)
        & v4_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A)
        & ~ v1_xboole_0(C)
        & v3_relat_2(D)
        & v8_relat_2(D)
        & v1_partfun1(D,C,C)
        & m1_relset_1(D,C,C)
        & v1_funct_1(E)
        & v1_funct_2(E,C,k3_finseq_2(A))
        & m1_relset_1(E,C,k3_finseq_2(A))
        & v1_funct_1(F)
        & v1_funct_2(F,C,A)
        & m1_relset_1(F,C,A) )
     => ( ~ v3_struct_0(g3_osalg_1(A,B,C,D,E,F))
        & v2_orders_2(g3_osalg_1(A,B,C,D,E,F))
        & v3_orders_2(g3_osalg_1(A,B,C,D,E,F))
        & v4_orders_2(g3_osalg_1(A,B,C,D,E,F))
        & v3_osalg_1(g3_osalg_1(A,B,C,D,E,F)) ) ) )).

fof(cc1_osalg_1,axiom,(
    ! [A] :
      ( l3_osalg_1(A)
     => ( v4_osalg_1(A)
       => ( v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A) ) ) ) )).

fof(rc4_osalg_1,axiom,(
    ? [A] :
      ( l3_osalg_1(A)
      & ~ v3_struct_0(A)
      & ~ v2_msualg_1(A)
      & v3_osalg_1(A)
      & v4_osalg_1(A) ) )).

fof(rc5_osalg_1,axiom,(
    ? [A] :
      ( l1_osalg_1(A)
      & ~ v3_struct_0(A)
      & ~ v2_msualg_1(A) ) )).

fof(rc6_osalg_1,axiom,(
    ? [A] :
      ( l3_osalg_1(A)
      & ~ v3_struct_0(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_orders_3(A)
      & ~ v2_msualg_1(A)
      & v3_osalg_1(A)
      & v4_osalg_1(A)
      & v5_osalg_1(A)
      & v6_osalg_1(A) ) )).

fof(cc2_osalg_1,axiom,(
    ! [A] :
      ( l3_osalg_1(A)
     => ( ( ~ v3_struct_0(A)
          & ~ v2_msualg_1(A)
          & v6_osalg_1(A) )
       => ( ~ v3_struct_0(A)
          & ~ v2_msualg_1(A)
          & v5_osalg_1(A) ) ) ) )).

fof(fc3_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ( ~ v3_struct_0(k2_osalg_1(A))
        & v2_orders_2(k2_osalg_1(A))
        & v3_orders_2(k2_osalg_1(A))
        & v4_orders_2(k2_osalg_1(A))
        & v1_orders_3(k2_osalg_1(A))
        & ~ v2_msualg_1(k2_osalg_1(A))
        & v3_osalg_1(k2_osalg_1(A))
        & v4_osalg_1(k2_osalg_1(A))
        & v5_osalg_1(k2_osalg_1(A))
        & v6_osalg_1(k2_osalg_1(A)) ) ) )).

fof(rc7_osalg_1,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)
      & v8_osalg_1(A) ) )).

fof(rc8_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & l3_osalg_1(A) )
     => ? [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
          & v7_osalg_1(B,A) ) ) )).

fof(cc3_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => v7_osalg_1(B,A) ) ) )).

fof(cc4_osalg_1,axiom,(
    ! [A] :
      ( l3_osalg_1(A)
     => ( ( ~ v3_struct_0(A)
          & ~ v2_msualg_1(A)
          & v4_osalg_1(A)
          & v5_osalg_1(A)
          & v6_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)
          & v8_osalg_1(A) ) ) ) )).

fof(rc9_osalg_1,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)
      & v8_osalg_1(A)
      & v10_osalg_1(A) ) )).

fof(cc5_osalg_1,axiom,(
    ! [A] :
      ( l3_osalg_1(A)
     => ( ( ~ v3_struct_0(A)
          & ~ v2_msualg_1(A)
          & v4_osalg_1(A)
          & v5_osalg_1(A)
          & v6_osalg_1(A)
          & v8_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)
          & v8_osalg_1(A)
          & v10_osalg_1(A) ) ) ) )).

fof(cc6_osalg_1,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)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ( v7_osalg_1(B,A)
            & v9_osalg_1(B,A) ) ) ) )).

fof(rc10_osalg_1,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) ) ) )).

fof(rc11_osalg_1,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)
          & v2_relat_1(B)
          & v1_funct_1(B)
          & v11_osalg_1(B,A) ) ) )).

fof(rc12_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(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) ) ) )).

fof(fc4_osalg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & ~ v1_xboole_0(B)
        & m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osalg_1(A,B))),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osalg_1(A,B))) )
     => ( v4_msualg_1(k6_osalg_1(A,B,C),A)
        & v5_msualg_1(k6_osalg_1(A,B,C),A)
        & v12_osalg_1(k6_osalg_1(A,B,C),A) ) ) )).

fof(cc7_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_orders_3(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => v12_osalg_1(B,A) ) ) )).

fof(rc13_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(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) ) ) )).

fof(fc5_osalg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,B) )
     => ( v4_msualg_1(k8_osalg_1(A,B,C),A)
        & v5_msualg_1(k8_osalg_1(A,B,C),A)
        & v12_osalg_1(k8_osalg_1(A,B,C),A)
        & v13_osalg_1(k8_osalg_1(A,B,C),A) ) ) )).

fof(cc8_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k9_osalg_1(A))
         => ~ v1_xboole_0(B) ) ) )).

fof(t1_osalg_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_relat_2(C)
                & v4_relat_2(C)
                & v8_relat_2(C)
                & v1_partfun1(C,A,A)
                & m2_relset_1(C,A,A) )
             => ! [D] :
                  ( ( v3_relat_2(D)
                    & v8_relat_2(D)
                    & v1_partfun1(D,B,B)
                    & m2_relset_1(D,B,B) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,k3_finseq_2(A))
                        & m2_relset_1(E,B,k3_finseq_2(A)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,B,A)
                            & m2_relset_1(F,B,A) )
                         => ( ~ v3_struct_0(g3_osalg_1(A,C,B,D,E,F))
                            & ~ v2_msualg_1(g3_osalg_1(A,C,B,D,E,F))
                            & v2_orders_2(g3_osalg_1(A,C,B,D,E,F))
                            & v3_orders_2(g3_osalg_1(A,C,B,D,E,F))
                            & v4_orders_2(g3_osalg_1(A,C,B,D,E,F)) ) ) ) ) ) ) ) )).

fof(d1_osalg_1,axiom,(
    $true )).

fof(d2_osalg_1,axiom,(
    ! [A] :
      ( l3_osalg_1(A)
     => ( v4_osalg_1(A)
      <=> ( v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A) ) ) ) )).

fof(d3_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ( r1_osalg_1(A,B,C)
              <=> r2_hidden(k4_tarski(B,C),u1_osalg_1(A)) ) ) ) ) )).

fof(t2_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_msualg_1(A))
                 => ( ( r1_osalg_1(A,B,C)
                      & r1_osalg_1(A,C,D) )
                   => r1_osalg_1(A,B,D) ) ) ) ) ) )).

fof(d4_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_osalg_1(A) )
     => ( v5_osalg_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_msualg_1(A))
           => ! [C] :
                ( m1_subset_1(C,u1_msualg_1(A))
               => ( ( r1_osalg_1(A,B,C)
                    & k1_msualg_1(A,B) = k1_msualg_1(A,C)
                    & k1_osalg_1(A,B) = k1_osalg_1(A,C) )
                 => B = C ) ) ) ) ) )).

fof(d5_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_osalg_1(A) )
     => ( v6_osalg_1(A)
      <=> u1_osalg_1(A) = k6_partfun1(u1_msualg_1(A)) ) ) )).

fof(t3_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_osalg_1(A) )
     => ( v6_osalg_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_msualg_1(A))
           => ! [C] :
                ( m1_subset_1(C,u1_msualg_1(A))
               => ( r1_osalg_1(A,B,C)
                 => B = C ) ) ) ) ) )).

fof(t4_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_osalg_1(A) )
     => ( v6_osalg_1(A)
       => v5_osalg_1(A) ) ) )).

fof(d6_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & v3_osalg_1(B)
            & v4_osalg_1(B)
            & l3_osalg_1(B) )
         => ( B = k2_osalg_1(A)
          <=> ( u1_struct_0(A) = u1_struct_0(B)
              & k6_partfun1(u1_struct_0(A)) = u1_orders_2(B)
              & u1_msualg_1(A) = u1_msualg_1(B)
              & k6_partfun1(u1_msualg_1(A)) = u1_osalg_1(B)
              & u2_msualg_1(A) = u2_msualg_1(B)
              & u3_msualg_1(A) = u3_msualg_1(B) ) ) ) ) )).

fof(t5_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ( v1_orders_3(k2_osalg_1(A))
        & v6_osalg_1(k2_osalg_1(A)) ) ) )).

fof(d7_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
             => ( r2_osalg_1(A,B,C)
              <=> ( k3_finseq_1(B) = k3_finseq_1(C)
                  & ! [D] :
                      ( r2_hidden(D,k4_finseq_1(B))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ( ( E = k1_funct_1(B,D)
                                  & F = k1_funct_1(C,D) )
                               => r3_orders_2(A,E,F) ) ) ) ) ) ) ) ) ) )).

fof(t6_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
             => ( ( r2_osalg_1(A,B,C)
                  & r2_osalg_1(A,C,B) )
               => B = C ) ) ) ) )).

fof(t7_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
             => ( ( v1_orders_3(A)
                  & r2_osalg_1(A,B,C) )
               => B = C ) ) ) ) )).

fof(t8_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ( ( v1_orders_3(A)
                  & r1_osalg_1(A,B,C)
                  & r2_osalg_1(A,k1_msualg_1(A,B),k1_msualg_1(A,C))
                  & r3_orders_2(A,k1_osalg_1(A,B),k1_osalg_1(A,C)) )
               => B = C ) ) ) ) )).

fof(d8_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ( v7_osalg_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_msualg_1(A))
               => ( ( r1_osalg_1(A,B,C)
                    & r2_osalg_1(A,k1_msualg_1(A,B),k1_msualg_1(A,C)) )
                 => r3_orders_2(A,k1_osalg_1(A,B),k1_osalg_1(A,C)) ) ) ) ) ) )).

fof(d9_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ( v8_osalg_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_msualg_1(A))
           => v7_osalg_1(B,A) ) ) ) )).

fof(t9_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ( v6_osalg_1(A)
       => v8_osalg_1(A) ) ) )).

fof(t10_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ( ( v8_osalg_1(A)
                  & k1_msualg_1(A,B) = k1_xboole_0
                  & r1_osalg_1(A,B,C)
                  & k1_msualg_1(A,C) = k1_xboole_0 )
               => B = C ) ) ) ) )).

fof(d10_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
                 => ( r3_osalg_1(A,B,C,D)
                  <=> ( r1_osalg_1(A,B,C)
                      & r2_osalg_1(A,D,k1_msualg_1(A,C))
                      & ! [E] :
                          ( m1_subset_1(E,u1_msualg_1(A))
                         => ( ( r1_osalg_1(A,B,E)
                              & r2_osalg_1(A,D,k1_msualg_1(A,E)) )
                           => r2_osalg_1(A,k1_msualg_1(A,C),k1_msualg_1(A,E)) ) ) ) ) ) ) ) ) )).

fof(d11_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
                 => ( r4_osalg_1(A,B,C,D)
                  <=> ( r1_osalg_1(A,B,C)
                      & r2_osalg_1(A,D,k1_msualg_1(A,C))
                      & ! [E] :
                          ( m1_subset_1(E,u1_msualg_1(A))
                         => ( ( r1_osalg_1(A,B,E)
                              & r2_osalg_1(A,D,k1_msualg_1(A,E)) )
                           => r3_orders_2(A,k1_osalg_1(A,C),k1_osalg_1(A,E)) ) ) ) ) ) ) ) ) )).

fof(d12_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
                 => ( r5_osalg_1(A,B,C,D)
                  <=> ( r3_osalg_1(A,B,C,D)
                      & r4_osalg_1(A,B,C,D) ) ) ) ) ) ) )).

fof(d13_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ( v9_osalg_1(B,A)
          <=> ( v7_osalg_1(B,A)
              & ! [C] :
                  ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
                 => ~ ( r2_osalg_1(A,C,k1_msualg_1(A,B))
                      & ! [D] :
                          ( m1_subset_1(D,u1_msualg_1(A))
                         => ~ r3_osalg_1(A,B,D,C) ) ) ) ) ) ) ) )).

fof(d14_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & l3_osalg_1(A) )
     => ( v10_osalg_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_msualg_1(A))
           => v9_osalg_1(B,A) ) ) ) )).

fof(t11_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & l3_osalg_1(A) )
     => ( v10_osalg_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_msualg_1(A))
           => ! [C] :
                ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
               => ~ ( r2_osalg_1(A,C,k1_msualg_1(A,B))
                    & ! [D] :
                        ( m1_subset_1(D,u1_msualg_1(A))
                       => ~ r5_osalg_1(A,B,D,C) ) ) ) ) ) ) )).

fof(t12_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & l3_osalg_1(A) )
     => ( v6_osalg_1(A)
       => v10_osalg_1(A) ) ) )).

fof(t13_osalg_1,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)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_msualg_1(A))
                 => ! [E] :
                      ( m2_finseq_2(E,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
                     => ( ( r2_osalg_1(A,E,k1_msualg_1(A,B))
                          & r3_osalg_1(A,B,C,E)
                          & r3_osalg_1(A,B,D,E) )
                       => C = D ) ) ) ) ) ) )).

fof(d15_osalg_1,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)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
             => ( r2_osalg_1(A,C,k1_msualg_1(A,B))
               => ! [D] :
                    ( m1_subset_1(D,u1_msualg_1(A))
                   => ( D = k3_osalg_1(A,B,C)
                    <=> r3_osalg_1(A,B,D,C) ) ) ) ) ) ) )).

fof(t14_osalg_1,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)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
             => ( r2_osalg_1(A,C,k1_msualg_1(A,B))
               => r5_osalg_1(A,B,k3_osalg_1(A,B,C),C) ) ) ) ) )).

fof(d16_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => k4_osalg_1(A,B) = k10_pboole(u1_struct_0(A),B) ) ) )).

fof(t15_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ( v2_relat_1(k4_osalg_1(A,B))
            & ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r3_orders_2(A,C,D)
                     => r1_tarski(k1_funct_1(k4_osalg_1(A,B),C),k1_funct_1(k4_osalg_1(A,B),D)) ) ) ) ) ) ) )).

fof(d17_osalg_1,axiom,(
    $true )).

fof(d18_osalg_1,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))
         => ( v11_osalg_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r3_orders_2(A,C,D)
                     => r1_tarski(k1_funct_1(B,C),k1_funct_1(B,D)) ) ) ) ) ) ) )).

fof(t16_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => v11_osalg_1(k4_osalg_1(A,B),A) ) ) )).

fof(d19_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ( v12_osalg_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r3_orders_2(A,C,D)
                     => r1_tarski(k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),D)) ) ) ) ) ) ) )).

fof(t17_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ( v12_osalg_1(B,A)
          <=> ( v11_osalg_1(u4_msualg_1(A,B),A)
              & m1_pboole(u4_msualg_1(A,B),u1_struct_0(A)) ) ) ) ) )).

fof(d20_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osalg_1(A,B))),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osalg_1(A,B)))
             => ! [D] :
                  ( ( v4_msualg_1(D,A)
                    & v5_msualg_1(D,A)
                    & l3_msualg_1(D,A) )
                 => ( D = k6_osalg_1(A,B,C)
                  <=> ( r6_pboole(u1_struct_0(A),u4_msualg_1(A,D),k5_osalg_1(A,B))
                      & r6_pboole(u1_msualg_1(A),u5_msualg_1(A,D),C) ) ) ) ) ) ) )).

fof(t18_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osalg_1(A,B))),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osalg_1(A,B)))
             => v12_osalg_1(k6_osalg_1(A,B,C),A) ) ) ) )).

fof(t19_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_orders_3(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => v12_osalg_1(B,A) ) ) )).

fof(t20_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
             => ! [D] :
                  ( ( v12_osalg_1(D,A)
                    & l3_msualg_1(D,A) )
                 => ( r2_osalg_1(A,B,C)
                   => r1_tarski(k1_funct_1(k6_pboole(u1_struct_0(A),u4_msualg_1(A,D)),B),k1_funct_1(k6_pboole(u1_struct_0(A),u4_msualg_1(A,D)),C)) ) ) ) ) ) )).

fof(d21_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( ( v4_msualg_1(C,k2_osalg_1(A))
                & v12_osalg_1(C,k2_osalg_1(A))
                & l3_msualg_1(C,k2_osalg_1(A)) )
             => ( C = k7_osalg_1(A,B)
              <=> ( u4_msualg_1(k2_osalg_1(A),C) = u4_msualg_1(A,B)
                  & u5_msualg_1(k2_osalg_1(A),C) = u5_msualg_1(A,B) ) ) ) ) ) )).

fof(t21_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
                 => ( ( r2_osalg_1(A,B,C)
                      & r2_osalg_1(A,C,D) )
                   => r2_osalg_1(A,B,D) ) ) ) ) ) )).

fof(d22_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ( r6_osalg_1(A,B,C)
              <=> ( r1_osalg_1(A,B,C)
                  & r2_osalg_1(A,k1_msualg_1(A,B),k1_msualg_1(A,C))
                  & r3_orders_2(A,k1_osalg_1(A,B),k1_osalg_1(A,C)) ) ) ) ) ) )).

fof(t22_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ( ( r6_osalg_1(A,B,C)
                  & r6_osalg_1(A,C,B) )
               => B = C ) ) ) ) )).

fof(t23_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_msualg_1(A))
                 => ( ( r6_osalg_1(A,B,C)
                      & r6_osalg_1(A,C,D) )
                   => r6_osalg_1(A,B,D) ) ) ) ) ) )).

fof(t24_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( ( v12_osalg_1(D,A)
                    & l3_msualg_1(D,A) )
                 => ( r3_orders_2(A,k1_osalg_1(A,B),k1_osalg_1(A,C))
                   => r1_tarski(k4_msualg_1(A,B,D),k4_msualg_1(A,C,D)) ) ) ) ) ) )).

fof(t25_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( ( v12_osalg_1(D,A)
                    & l3_msualg_1(D,A) )
                 => ( r2_osalg_1(A,k1_msualg_1(A,B),k1_msualg_1(A,C))
                   => r1_tarski(k3_msualg_1(A,B,D),k3_msualg_1(A,C,D)) ) ) ) ) ) )).

fof(t26_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( ( v12_osalg_1(D,A)
                    & l3_msualg_1(D,A) )
                 => ( r6_osalg_1(A,B,C)
                   => ( r1_tarski(k3_msualg_1(A,B,D),k3_msualg_1(A,C,D))
                      & r1_tarski(k4_msualg_1(A,B,D),k4_msualg_1(A,C,D)) ) ) ) ) ) ) )).

fof(d23_osalg_1,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) )
         => ( v13_osalg_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_msualg_1(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_msualg_1(A))
                   => ( r6_osalg_1(A,C,D)
                     => k2_partfun1(k3_msualg_1(A,D,B),k4_msualg_1(A,D,B),k5_msualg_1(A,D,B),k3_msualg_1(A,C,B)) = k5_msualg_1(A,C,B) ) ) ) ) ) ) )).

fof(t27_osalg_1,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) )
         => ( v13_osalg_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_msualg_1(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_msualg_1(A))
                   => ( r6_osalg_1(A,C,D)
                     => r1_tarski(k5_msualg_1(A,C,B),k5_msualg_1(A,D,B)) ) ) ) ) ) ) )).

fof(t28_osalg_1,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) )
         => ( ( v1_orders_3(A)
              | v6_osalg_1(A) )
           => v13_osalg_1(B,A) ) ) ) )).

fof(d24_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,B)
             => ! [D] :
                  ( ( v4_msualg_1(D,A)
                    & v12_osalg_1(D,A)
                    & l3_msualg_1(D,A) )
                 => ( D = k8_osalg_1(A,B,C)
                  <=> ( r6_pboole(u1_struct_0(A),u4_msualg_1(A,D),k5_osalg_1(A,B))
                      & ! [E] :
                          ( m1_subset_1(E,u1_msualg_1(A))
                         => k5_msualg_1(A,E,D) = k10_pboole(k3_msualg_1(A,E,D),C) ) ) ) ) ) ) ) )).

fof(t29_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,B)
             => ( v5_msualg_1(k8_osalg_1(A,B,C),A)
                & v13_osalg_1(k8_osalg_1(A,B,C),A) ) ) ) ) )).

fof(d25_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => k9_osalg_1(A) = k8_eqrel_1(u1_msualg_1(A),u1_osalg_1(A)) ) )).

fof(d26_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => k10_osalg_1(A,B) = k6_eqrel_1(u1_msualg_1(A),u1_osalg_1(A),B) ) ) )).

fof(t30_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ( r1_osalg_1(A,B,C)
              <=> r2_hidden(C,k6_eqrel_1(u1_msualg_1(A),u1_osalg_1(A),B)) ) ) ) ) )).

fof(t31_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ( r1_osalg_1(A,B,C)
              <=> k10_osalg_1(A,B) = k10_osalg_1(A,C) ) ) ) ) )).

fof(t32_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(u1_msualg_1(A)),k9_osalg_1(A))
        <=> ? [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
              & B = k10_osalg_1(A,C) ) ) ) )).

fof(t33_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(u1_msualg_1(A)),k9_osalg_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ( m1_osalg_1(C,A,B)
              <=> k10_osalg_1(A,C) = B ) ) ) ) )).

fof(t34_osalg_1,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)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( m2_finseq_2(D,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
                 => ( ( r1_osalg_1(A,B,C)
                      & k3_finseq_1(k1_msualg_1(A,B)) = k3_finseq_1(k1_msualg_1(A,C))
                      & r2_osalg_1(A,D,k1_msualg_1(A,B))
                      & r2_osalg_1(A,D,k1_msualg_1(A,C)) )
                   => k3_osalg_1(A,B,D) = k3_osalg_1(A,C,D) ) ) ) ) ) )).

fof(d27_osalg_1,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)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(u1_msualg_1(A)),k9_osalg_1(A))
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
             => ( ? [D] :
                    ( m1_osalg_1(D,A,B)
                    & r2_osalg_1(A,C,k1_msualg_1(A,D)) )
               => ! [D] :
                    ( m1_osalg_1(D,A,B)
                   => ( D = k11_osalg_1(A,B,C)
                    <=> ! [E] :
                          ( m1_osalg_1(E,A,B)
                         => ( r2_osalg_1(A,C,k1_msualg_1(A,E))
                           => D = k3_osalg_1(A,E,C) ) ) ) ) ) ) ) ) )).

fof(t35_osalg_1,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)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] :
              ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
             => ( r2_osalg_1(A,C,k1_msualg_1(A,B))
               => r6_osalg_1(A,k3_osalg_1(A,B,C),B) ) ) ) ) )).

fof(dt_m1_osalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & m1_subset_1(B,k9_osalg_1(A)) )
     => ! [C] :
          ( m1_osalg_1(C,A,B)
         => m1_subset_1(C,u1_msualg_1(A)) ) ) )).

fof(existence_m1_osalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & m1_subset_1(B,k9_osalg_1(A)) )
     => ? [C] : m1_osalg_1(C,A,B) ) )).

fof(redefinition_m1_osalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & m1_subset_1(B,k9_osalg_1(A)) )
     => ! [C] :
          ( m1_osalg_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) )).

fof(dt_l1_osalg_1,axiom,(
    ! [A] :
      ( l1_osalg_1(A)
     => l1_msualg_1(A) ) )).

fof(existence_l1_osalg_1,axiom,(
    ? [A] : l1_osalg_1(A) )).

fof(dt_l2_osalg_1,axiom,(
    ! [A] :
      ( l2_osalg_1(A)
     => ( l1_msualg_1(A)
        & l1_orders_2(A) ) ) )).

fof(existence_l2_osalg_1,axiom,(
    ? [A] : l2_osalg_1(A) )).

fof(dt_l3_osalg_1,axiom,(
    ! [A] :
      ( l3_osalg_1(A)
     => ( l1_osalg_1(A)
        & l2_osalg_1(A) ) ) )).

fof(existence_l3_osalg_1,axiom,(
    ? [A] : l3_osalg_1(A) )).

fof(abstractness_v1_osalg_1,axiom,(
    ! [A] :
      ( l1_osalg_1(A)
     => ( v1_osalg_1(A)
       => A = g1_osalg_1(u1_struct_0(A),u1_msualg_1(A),u1_osalg_1(A),u2_msualg_1(A),u3_msualg_1(A)) ) ) )).

fof(abstractness_v2_osalg_1,axiom,(
    ! [A] :
      ( l2_osalg_1(A)
     => ( v2_osalg_1(A)
       => A = g2_osalg_1(u1_struct_0(A),u1_orders_2(A),u1_msualg_1(A),u2_msualg_1(A),u3_msualg_1(A)) ) ) )).

fof(abstractness_v3_osalg_1,axiom,(
    ! [A] :
      ( l3_osalg_1(A)
     => ( v3_osalg_1(A)
       => A = g3_osalg_1(u1_struct_0(A),u1_orders_2(A),u1_msualg_1(A),u1_osalg_1(A),u2_msualg_1(A),u3_msualg_1(A)) ) ) )).

fof(symmetry_r1_osalg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_osalg_1(A)
        & m1_subset_1(B,u1_msualg_1(A))
        & m1_subset_1(C,u1_msualg_1(A)) )
     => ( r1_osalg_1(A,B,C)
       => r1_osalg_1(A,C,B) ) ) )).

fof(reflexivity_r1_osalg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_osalg_1(A)
        & m1_subset_1(B,u1_msualg_1(A))
        & m1_subset_1(C,u1_msualg_1(A)) )
     => r1_osalg_1(A,B,B) ) )).

fof(reflexivity_r2_osalg_1,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,k3_finseq_2(u1_struct_0(A)))
        & m1_subset_1(C,k3_finseq_2(u1_struct_0(A))) )
     => r2_osalg_1(A,B,B) ) )).

fof(reflexivity_r6_osalg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & m1_subset_1(B,u1_msualg_1(A))
        & m1_subset_1(C,u1_msualg_1(A)) )
     => r6_osalg_1(A,B,B) ) )).

fof(dt_k1_osalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_msualg_1(A)) )
     => m1_subset_1(k1_osalg_1(A,B),u1_struct_0(A)) ) )).

fof(redefinition_k1_osalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_msualg_1(A)) )
     => k1_osalg_1(A,B) = k2_msualg_1(A,B) ) )).

fof(dt_k2_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ( ~ v3_struct_0(k2_osalg_1(A))
        & ~ v2_msualg_1(k2_osalg_1(A))
        & v3_osalg_1(k2_osalg_1(A))
        & v4_osalg_1(k2_osalg_1(A))
        & l3_osalg_1(k2_osalg_1(A)) ) ) )).

fof(dt_k3_osalg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & v10_osalg_1(A)
        & l3_osalg_1(A)
        & m1_subset_1(B,u1_msualg_1(A))
        & m1_subset_1(C,k3_finseq_2(u1_struct_0(A))) )
     => m1_subset_1(k3_osalg_1(A,B,C),u1_msualg_1(A)) ) )).

fof(dt_k4_osalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B) )
     => m1_pboole(k4_osalg_1(A,B),u1_struct_0(A)) ) )).

fof(dt_k5_osalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B) )
     => ( v11_osalg_1(k5_osalg_1(A,B),A)
        & m1_pboole(k5_osalg_1(A,B),u1_struct_0(A)) ) ) )).

fof(redefinition_k5_osalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B) )
     => k5_osalg_1(A,B) = k4_osalg_1(A,B) ) )).

fof(dt_k6_osalg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & ~ v1_xboole_0(B)
        & m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osalg_1(A,B))),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osalg_1(A,B))) )
     => ( v4_msualg_1(k6_osalg_1(A,B,C),A)
        & v5_msualg_1(k6_osalg_1(A,B,C),A)
        & l3_msualg_1(k6_osalg_1(A,B,C),A) ) ) )).

fof(dt_k7_osalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A) )
     => ( v4_msualg_1(k7_osalg_1(A,B),k2_osalg_1(A))
        & v12_osalg_1(k7_osalg_1(A,B),k2_osalg_1(A))
        & l3_msualg_1(k7_osalg_1(A,B),k2_osalg_1(A)) ) ) )).

fof(dt_k8_osalg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,B) )
     => ( v4_msualg_1(k8_osalg_1(A,B,C),A)
        & v12_osalg_1(k8_osalg_1(A,B,C),A)
        & l3_msualg_1(k8_osalg_1(A,B,C),A) ) ) )).

fof(dt_k9_osalg_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ( ~ v1_xboole_0(k9_osalg_1(A))
        & m1_subset_1(k9_osalg_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_msualg_1(A)))) ) ) )).

fof(dt_k10_osalg_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & m1_subset_1(B,u1_msualg_1(A)) )
     => m2_subset_1(k10_osalg_1(A,B),k1_zfmisc_1(u1_msualg_1(A)),k9_osalg_1(A)) ) )).

fof(dt_k11_osalg_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v8_osalg_1(A)
        & v10_osalg_1(A)
        & l3_osalg_1(A)
        & m1_subset_1(B,k9_osalg_1(A))
        & m1_subset_1(C,k3_finseq_2(u1_struct_0(A))) )
     => m1_osalg_1(k11_osalg_1(A,B,C),A,B) ) )).

fof(dt_u1_osalg_1,axiom,(
    ! [A] :
      ( l1_osalg_1(A)
     => ( v3_relat_2(u1_osalg_1(A))
        & v8_relat_2(u1_osalg_1(A))
        & v1_partfun1(u1_osalg_1(A),u1_msualg_1(A),u1_msualg_1(A))
        & m2_relset_1(u1_osalg_1(A),u1_msualg_1(A),u1_msualg_1(A)) ) ) )).

fof(dt_g1_osalg_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( v3_relat_2(C)
        & v8_relat_2(C)
        & v1_partfun1(C,B,B)
        & m1_relset_1(C,B,B)
        & v1_funct_1(D)
        & v1_funct_2(D,B,k3_finseq_2(A))
        & m1_relset_1(D,B,k3_finseq_2(A))
        & v1_funct_1(E)
        & v1_funct_2(E,B,A)
        & m1_relset_1(E,B,A) )
     => ( v1_osalg_1(g1_osalg_1(A,B,C,D,E))
        & l1_osalg_1(g1_osalg_1(A,B,C,D,E)) ) ) )).

fof(free_g1_osalg_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( v3_relat_2(C)
        & v8_relat_2(C)
        & v1_partfun1(C,B,B)
        & m1_relset_1(C,B,B)
        & v1_funct_1(D)
        & v1_funct_2(D,B,k3_finseq_2(A))
        & m1_relset_1(D,B,k3_finseq_2(A))
        & v1_funct_1(E)
        & v1_funct_2(E,B,A)
        & m1_relset_1(E,B,A) )
     => ! [F,G,H,I,J] :
          ( g1_osalg_1(A,B,C,D,E) = g1_osalg_1(F,G,H,I,J)
         => ( A = F
            & B = G
            & C = H
            & D = I
            & E = J ) ) ) )).

fof(dt_g2_osalg_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_relset_1(B,A,A)
        & v1_funct_1(D)
        & v1_funct_2(D,C,k3_finseq_2(A))
        & m1_relset_1(D,C,k3_finseq_2(A))
        & v1_funct_1(E)
        & v1_funct_2(E,C,A)
        & m1_relset_1(E,C,A) )
     => ( v2_osalg_1(g2_osalg_1(A,B,C,D,E))
        & l2_osalg_1(g2_osalg_1(A,B,C,D,E)) ) ) )).

fof(free_g2_osalg_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_relset_1(B,A,A)
        & v1_funct_1(D)
        & v1_funct_2(D,C,k3_finseq_2(A))
        & m1_relset_1(D,C,k3_finseq_2(A))
        & v1_funct_1(E)
        & v1_funct_2(E,C,A)
        & m1_relset_1(E,C,A) )
     => ! [F,G,H,I,J] :
          ( g2_osalg_1(A,B,C,D,E) = g2_osalg_1(F,G,H,I,J)
         => ( A = F
            & B = G
            & C = H
            & D = I
            & E = J ) ) ) )).

fof(dt_g3_osalg_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( m1_relset_1(B,A,A)
        & v3_relat_2(D)
        & v8_relat_2(D)
        & v1_partfun1(D,C,C)
        & m1_relset_1(D,C,C)
        & v1_funct_1(E)
        & v1_funct_2(E,C,k3_finseq_2(A))
        & m1_relset_1(E,C,k3_finseq_2(A))
        & v1_funct_1(F)
        & v1_funct_2(F,C,A)
        & m1_relset_1(F,C,A) )
     => ( v3_osalg_1(g3_osalg_1(A,B,C,D,E,F))
        & l3_osalg_1(g3_osalg_1(A,B,C,D,E,F)) ) ) )).

fof(free_g3_osalg_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( m1_relset_1(B,A,A)
        & v3_relat_2(D)
        & v8_relat_2(D)
        & v1_partfun1(D,C,C)
        & m1_relset_1(D,C,C)
        & v1_funct_1(E)
        & v1_funct_2(E,C,k3_finseq_2(A))
        & m1_relset_1(E,C,k3_finseq_2(A))
        & v1_funct_1(F)
        & v1_funct_2(F,C,A)
        & m1_relset_1(F,C,A) )
     => ! [G,H,I,J,K,L] :
          ( g3_osalg_1(A,B,C,D,E,F) = g3_osalg_1(G,H,I,J,K,L)
         => ( A = G
            & B = H
            & C = I
            & D = J
            & E = K
            & F = L ) ) ) )).
%------------------------------------------------------------------------------