SET007 Axioms: SET007+736.ax


%------------------------------------------------------------------------------
% File     : SET007+736 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Subalgebras of an Order Sorted Algebra. Lattice of Subalgebras
% 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_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  115 (  11 unit)
%            Number of atoms       : 1125 (  45 equality)
%            Maximal formula depth :   18 (   9 average)
%            Number of connectives : 1215 ( 205 ~  ;   0  |; 713  &)
%                                         (  23 <=>; 274 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   55 (   1 propositional; 0-3 arity)
%            Number of functors    :   59 (   0 constant; 1-6 arity)
%            Number of variables   :  335 (   0 singleton; 320 !;  15 ?)
%            Maximal term depth    :    7 (   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_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & v2_relat_1(B)
        & v11_osalg_1(B,A)
        & m1_pboole(B,u1_struct_0(A)) )
     => ? [C] :
          ( m1_osalg_2(C,A,B)
          & v1_relat_1(C)
          & v2_relat_1(C)
          & v1_funct_1(C) ) ) )).

fof(rc2_osalg_2,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(rc3_osalg_2,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] :
          ( m2_osalg_2(C,A,B)
          & v1_relat_1(C)
          & v2_relat_1(C)
          & v1_funct_1(C) ) ) )).

fof(rc4_osalg_2,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)
      & v3_osalg_1(A)
      & v4_osalg_1(A)
      & v5_osalg_1(A)
      & v2_msualg_2(A) ) )).

fof(rc5_osalg_2,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_msualg_2(C,A,B)
          & v12_osalg_1(C,A) ) ) )).

fof(rc6_osalg_2,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_msualg_2(C,A,B)
          & v4_msualg_1(C,A)
          & v12_osalg_1(C,A) ) ) )).

fof(rc7_osalg_2,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_msualg_2(C,A,B)
          & v4_msualg_1(C,A)
          & v5_msualg_1(C,A)
          & v12_osalg_1(C,A) ) ) )).

fof(fc1_osalg_2,axiom,(
    ! [A,B,C] :
      ( ( ~ 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)
        & m2_osalg_2(C,A,B) )
     => ~ v1_xboole_0(k5_osalg_2(A,B,C)) ) )).

fof(fc2_osalg_2,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) )
     => ~ v1_xboole_0(k6_osalg_2(A,B)) ) )).

fof(fc3_osalg_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & m2_osalg_2(C,A,B)
        & m1_subset_1(D,u1_struct_0(A)) )
     => ~ v1_xboole_0(k8_osalg_2(A,B,C,D)) ) )).

fof(rc8_osalg_2,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] :
          ( m2_osalg_2(C,A,B)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v3_msualg_2(C,A,B) ) ) )).

fof(fc4_osalg_2,axiom,(
    ! [A,B,C] :
      ( ( ~ 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)
        & m2_osalg_2(C,A,B) )
     => ( v1_relat_1(k9_osalg_2(A,B,C))
        & v1_funct_1(k9_osalg_2(A,B,C))
        & v3_msualg_2(k9_osalg_2(A,B,C),A,B) ) ) )).

fof(fc5_osalg_2,axiom,(
    ! [A,B,C] :
      ( ( ~ 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)
        & v3_msualg_2(C,A,B)
        & m2_osalg_2(C,A,B) )
     => ( v4_msualg_1(k10_msualg_2(A,B,C),A)
        & v12_osalg_1(k10_msualg_2(A,B,C),A) ) ) )).

fof(fc6_osalg_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & v12_osalg_1(C,A)
        & m1_msualg_2(C,A,B)
        & v12_osalg_1(D,A)
        & m1_msualg_2(D,A,B) )
     => ( v4_msualg_1(k11_msualg_2(A,B,C,D),A)
        & v12_osalg_1(k11_msualg_2(A,B,C,D),A) ) ) )).

fof(fc7_osalg_2,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) )
     => ~ v1_xboole_0(k12_osalg_2(A,B)) ) )).

fof(fc8_osalg_2,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) )
     => ( ~ v3_struct_0(k16_osalg_2(A,B))
        & v3_lattices(k16_osalg_2(A,B))
        & v4_lattices(k16_osalg_2(A,B))
        & v5_lattices(k16_osalg_2(A,B))
        & v6_lattices(k16_osalg_2(A,B))
        & v7_lattices(k16_osalg_2(A,B))
        & v8_lattices(k16_osalg_2(A,B))
        & v9_lattices(k16_osalg_2(A,B))
        & v10_lattices(k16_osalg_2(A,B))
        & v13_lattices(k16_osalg_2(A,B))
        & v14_lattices(k16_osalg_2(A,B))
        & v15_lattices(k16_osalg_2(A,B)) ) ) )).

fof(t1_osalg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v11_osalg_1(B,A)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( ( v11_osalg_1(C,A)
                & m1_pboole(C,u1_struct_0(A)) )
             => ( v11_osalg_1(k3_pboole(u1_struct_0(A),B,C),A)
                & m1_pboole(k3_pboole(u1_struct_0(A),B,C),u1_struct_0(A)) ) ) ) ) )).

fof(t2_osalg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v11_osalg_1(B,A)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( ( v11_osalg_1(C,A)
                & m1_pboole(C,u1_struct_0(A)) )
             => ( v11_osalg_1(k2_pboole(u1_struct_0(A),B,C),A)
                & m1_pboole(k2_pboole(u1_struct_0(A),B,C),u1_struct_0(A)) ) ) ) ) )).

fof(d1_osalg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v11_osalg_1(B,A)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),B)
             => ( m1_osalg_2(C,A,B)
              <=> ( v11_osalg_1(C,A)
                  & m1_pboole(C,u1_struct_0(A)) ) ) ) ) ) )).

fof(d2_osalg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ( m2_osalg_2(C,A,B)
              <=> ( v11_osalg_1(C,A)
                  & m1_pboole(C,u1_struct_0(A)) ) ) ) ) ) )).

fof(t3_osalg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_msualg_1(A)
        & ~ v2_msualg_1(A)
        & v2_msualg_2(A)
        & l1_msualg_1(A) )
     => v2_msualg_2(k2_osalg_1(A)) ) )).

fof(t4_osalg_2,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) )
         => v12_osalg_1(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A) ) ) )).

fof(t5_osalg_2,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] :
              ( l3_msualg_1(C,A)
             => ( ( v12_osalg_1(C,A)
                  & m1_msualg_2(C,A,B) )
              <=> ( m2_osalg_2(u4_msualg_1(A,C),A,B)
                  & ! [D] :
                      ( m2_osalg_2(D,A,B)
                     => ( r6_pboole(u1_struct_0(A),D,u4_msualg_1(A,C))
                       => ( v3_msualg_2(D,A,B)
                          & r6_pboole(u1_msualg_1(A),u5_msualg_1(A,C),k4_msualg_2(A,B,D)) ) ) ) ) ) ) ) ) )).

fof(t6_osalg_2,axiom,(
    $true )).

fof(t7_osalg_2,axiom,(
    $true )).

fof(t8_osalg_2,axiom,(
    $true )).

fof(t9_osalg_2,axiom,(
    $true )).

fof(t10_osalg_2,axiom,(
    $true )).

fof(t11_osalg_2,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_subset_1(C,u1_struct_0(A))
             => r1_tarski(k1_msualg_2(A,B,C),k1_osalg_2(A,B,C)) ) ) ) )).

fof(t12_osalg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_pboole(B,u1_struct_0(A))
         => r2_pboole(u1_struct_0(A),B,k2_osalg_2(A,B)) ) ) )).

fof(t13_osalg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_pboole(B,u1_struct_0(A))
         => ! [C] :
              ( ( v11_osalg_1(C,A)
                & m1_pboole(C,u1_struct_0(A)) )
             => ( r2_pboole(u1_struct_0(A),B,C)
               => r2_pboole(u1_struct_0(A),k2_osalg_2(A,B),C) ) ) ) ) )).

fof(t14_osalg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v11_osalg_1(B,A)
            & m1_pboole(B,u1_struct_0(A)) )
         => r6_pboole(u1_struct_0(A),k2_osalg_2(A,B),B) ) ) )).

fof(d5_osalg_2,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] :
              ( m2_osalg_2(C,A,B)
             => ( C = k3_osalg_2(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k1_funct_1(C,D) = k1_osalg_2(A,B,D) ) ) ) ) ) )).

fof(t15_osalg_2,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) )
         => r2_pboole(u1_struct_0(A),k2_msualg_2(A,B),k3_osalg_2(A,B)) ) ) )).

fof(t16_osalg_2,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] :
              ( m2_osalg_2(C,A,B)
             => ( r2_pboole(u1_struct_0(A),k2_msualg_2(A,B),C)
               => r2_pboole(u1_struct_0(A),k3_osalg_2(A,B),C) ) ) ) ) )).

fof(t17_osalg_2,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] :
              ( m2_osalg_2(C,A,B)
             => r6_pboole(u1_struct_0(A),k3_osalg_2(A,B),k2_osalg_2(A,k2_msualg_2(A,B))) ) ) ) )).

fof(t18_osalg_2,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] :
              ( ( v12_osalg_1(C,A)
                & m1_msualg_2(C,A,B) )
             => m2_osalg_2(k3_osalg_2(A,B),A,C) ) ) ) )).

fof(t19_osalg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & v2_msualg_2(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)
                & m1_msualg_2(C,A,B) )
             => ( v2_relat_1(k3_osalg_2(A,B))
                & m2_osalg_2(k3_osalg_2(A,B),A,C) ) ) ) ) )).

fof(t20_osalg_2,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( m4_pboole(C,A,B)
        <=> r2_hidden(C,k4_card_3(k1_mboolean(A,B))) ) ) )).

fof(d6_osalg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v11_osalg_1(B,A)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] :
              ( C = k4_osalg_2(A,B)
            <=> ! [D] :
                  ( r2_hidden(D,C)
                <=> m1_osalg_2(D,A,B) ) ) ) ) )).

fof(t21_osalg_2,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] :
              ( m2_osalg_2(C,A,B)
             => r1_tarski(k5_osalg_2(A,B,C),k5_msualg_2(A,B,C)) ) ) ) )).

fof(t22_osalg_2,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] :
              ( m2_osalg_2(C,A,B)
             => r2_hidden(u4_msualg_1(A,B),k5_osalg_2(A,B,C)) ) ) ) )).

fof(t23_osalg_2,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] :
              ( m2_osalg_2(C,A,B)
             => r1_tarski(k5_osalg_2(A,B,C),k6_osalg_2(A,B)) ) ) ) )).

fof(d9_osalg_2,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_subset_1(C,k6_osalg_2(A,B))
             => k7_osalg_2(A,B,C) = C ) ) ) )).

fof(t24_osalg_2,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] :
              ( m2_osalg_2(C,A,B)
             => ! [D] :
                  ( m2_osalg_2(D,A,B)
                 => ( r2_hidden(D,k5_osalg_2(A,B,C))
                  <=> ( v3_msualg_2(D,A,B)
                      & r2_pboole(u1_struct_0(A),k3_osalg_2(A,B),D)
                      & r2_pboole(u1_struct_0(A),C,D) ) ) ) ) ) ) )).

fof(t25_osalg_2,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] :
              ( m2_osalg_2(C,A,B)
             => ( r2_hidden(C,k6_osalg_2(A,B))
              <=> v3_msualg_2(C,A,B) ) ) ) ) )).

fof(d10_osalg_2,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] :
              ( m2_osalg_2(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( E = k8_osalg_2(A,B,C,D)
                    <=> ! [F] :
                          ( r2_hidden(F,E)
                        <=> ? [G] :
                              ( m2_osalg_2(G,A,B)
                              & r2_hidden(G,k5_osalg_2(A,B,C))
                              & F = k1_funct_1(G,D) ) ) ) ) ) ) ) )).

fof(t26_osalg_2,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] :
              ( m2_osalg_2(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)
                       => r2_setfam_1(k8_osalg_2(A,B,C,D),k8_osalg_2(A,B,C,E)) ) ) ) ) ) ) )).

fof(t27_osalg_2,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] :
              ( m2_osalg_2(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => r1_tarski(k8_osalg_2(A,B,C,D),k8_msualg_2(A,B,C,D)) ) ) ) ) )).

fof(t28_osalg_2,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] :
              ( m2_osalg_2(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => r2_hidden(k1_funct_1(u4_msualg_1(A,B),D),k8_osalg_2(A,B,C,D)) ) ) ) ) )).

fof(d11_osalg_2,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] :
              ( m2_osalg_2(C,A,B)
             => ! [D] :
                  ( m2_osalg_2(D,A,B)
                 => ( D = k9_osalg_2(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k1_funct_1(D,E) = k1_setfam_1(k8_osalg_2(A,B,C,E)) ) ) ) ) ) ) )).

fof(t29_osalg_2,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] :
              ( m2_osalg_2(C,A,B)
             => r2_pboole(u1_struct_0(A),k2_pboole(u1_struct_0(A),k3_osalg_2(A,B),C),k9_osalg_2(A,B,C)) ) ) ) )).

fof(t30_osalg_2,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] :
              ( m2_osalg_2(C,A,B)
             => ( v2_relat_1(k2_pboole(u1_struct_0(A),k3_osalg_2(A,B),C))
               => v2_relat_1(k9_osalg_2(A,B,C)) ) ) ) ) )).

fof(t31_osalg_2,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_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( m2_osalg_2(D,A,B)
                 => ! [E] :
                      ( m2_osalg_2(E,A,B)
                     => ( r2_hidden(E,k5_osalg_2(A,B,D))
                       => r1_tarski(k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k9_osalg_2(A,B,D))),C),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),E)),C)) ) ) ) ) ) ) )).

fof(t32_osalg_2,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_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( m2_osalg_2(D,A,B)
                 => ! [E] :
                      ( m2_osalg_2(E,A,B)
                     => ( r2_hidden(E,k5_osalg_2(A,B,D))
                       => r1_tarski(k2_relat_1(k7_relat_1(k5_msualg_1(A,C,B),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k9_osalg_2(A,B,D))),C))),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),E),C)) ) ) ) ) ) ) )).

fof(t33_osalg_2,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_subset_1(C,u1_msualg_1(A))
             => ! [D] :
                  ( m2_osalg_2(D,A,B)
                 => r1_tarski(k2_relat_1(k7_relat_1(k5_msualg_1(A,C,B),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k9_osalg_2(A,B,D))),C))),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k9_osalg_2(A,B,D)),C)) ) ) ) ) )).

fof(t34_osalg_2,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] :
              ( m2_osalg_2(C,A,B)
             => ( v3_msualg_2(k9_osalg_2(A,B,C),A,B)
                & r2_pboole(u1_struct_0(A),C,k9_osalg_2(A,B,C)) ) ) ) ) )).

fof(d12_osalg_2,axiom,(
    $true )).

fof(d13_osalg_2,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] :
              ( m2_osalg_2(C,A,B)
             => ! [D] :
                  ( ( v4_msualg_1(D,A)
                    & v12_osalg_1(D,A)
                    & m1_msualg_2(D,A,B) )
                 => ( D = k10_osalg_2(A,B,C)
                  <=> ( m2_osalg_2(C,A,D)
                      & ! [E] :
                          ( ( v12_osalg_1(E,A)
                            & m1_msualg_2(E,A,B) )
                         => ( m2_osalg_2(C,A,E)
                           => ( v12_osalg_1(D,A)
                              & m1_msualg_2(D,A,E) ) ) ) ) ) ) ) ) ) )).

fof(t35_osalg_2,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] :
              ( m2_osalg_2(C,A,B)
             => ( k10_osalg_2(A,B,C) = k10_msualg_2(A,B,k9_osalg_2(A,B,C))
                & r6_pboole(u1_struct_0(A),u4_msualg_1(A,k10_osalg_2(A,B,C)),k9_osalg_2(A,B,C)) ) ) ) ) )).

fof(t36_osalg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] :
          ( l3_msualg_1(B,A)
         => ! [C] :
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ( k12_msualg_2(A,B,C) = k10_msualg_2(A,B,k9_msualg_2(A,B,C))
                & r6_pboole(u1_struct_0(A),u4_msualg_1(A,k12_msualg_2(A,B,C)),k9_msualg_2(A,B,C)) ) ) ) ) )).

fof(t37_osalg_2,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] :
              ( m2_osalg_2(C,A,B)
             => r2_pboole(u1_struct_0(A),u4_msualg_1(A,k12_msualg_2(A,B,C)),u4_msualg_1(A,k10_osalg_2(A,B,C))) ) ) ) )).

fof(t38_osalg_2,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] :
              ( m2_osalg_2(C,A,B)
             => m1_msualg_2(k12_msualg_2(A,B,C),A,k10_osalg_2(A,B,C)) ) ) ) )).

fof(t39_osalg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v4_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] :
              ( m2_osalg_2(C,A,B)
             => ( r6_pboole(u1_struct_0(A),C,u4_msualg_1(A,B))
               => k10_osalg_2(A,B,C) = B ) ) ) ) )).

fof(t40_osalg_2,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] :
              ( ( v4_msualg_1(C,A)
                & v12_osalg_1(C,A)
                & m1_msualg_2(C,A,B) )
             => ! [D] :
                  ( m2_osalg_2(D,A,B)
                 => ( r6_pboole(u1_struct_0(A),D,u4_msualg_1(A,C))
                   => k10_osalg_2(A,B,D) = C ) ) ) ) ) )).

fof(t41_osalg_2,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] :
              ( ( v12_osalg_1(C,A)
                & m1_msualg_2(C,A,B) )
             => k11_msualg_2(A,B,k10_osalg_2(A,B,k3_osalg_2(A,B)),C) = k10_osalg_2(A,B,k3_osalg_2(A,B)) ) ) ) )).

fof(d14_osalg_2,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] :
              ( ( v12_osalg_1(C,A)
                & m1_msualg_2(C,A,B) )
             => ! [D] :
                  ( ( v12_osalg_1(D,A)
                    & m1_msualg_2(D,A,B) )
                 => ! [E] :
                      ( ( v4_msualg_1(E,A)
                        & v12_osalg_1(E,A)
                        & m1_msualg_2(E,A,B) )
                     => ( E = k11_osalg_2(A,B,C,D)
                      <=> ! [F] :
                            ( m2_osalg_2(F,A,B)
                           => ( r6_pboole(u1_struct_0(A),F,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D)))
                             => E = k10_osalg_2(A,B,F) ) ) ) ) ) ) ) ) )).

fof(t42_osalg_2,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] :
              ( ( v12_osalg_1(C,A)
                & m1_msualg_2(C,A,B) )
             => ! [D] :
                  ( m2_osalg_2(D,A,B)
                 => ! [E] :
                      ( m2_osalg_2(E,A,B)
                     => ( r6_pboole(u1_struct_0(A),E,k2_pboole(u1_struct_0(A),D,u4_msualg_1(A,C)))
                       => k11_osalg_2(A,B,k10_osalg_2(A,B,D),C) = k10_osalg_2(A,B,E) ) ) ) ) ) ) )).

fof(t43_osalg_2,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] :
              ( ( v12_osalg_1(C,A)
                & m1_msualg_2(C,A,B) )
             => ! [D] :
                  ( m2_osalg_2(D,A,B)
                 => ( r6_pboole(u1_struct_0(A),D,u4_msualg_1(A,B))
                   => k11_osalg_2(A,B,k10_osalg_2(A,B,D),C) = k10_osalg_2(A,B,D) ) ) ) ) ) )).

fof(t44_osalg_2,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] :
              ( ( v12_osalg_1(C,A)
                & m1_msualg_2(C,A,B) )
             => ! [D] :
                  ( ( v12_osalg_1(D,A)
                    & m1_msualg_2(D,A,B) )
                 => k11_osalg_2(A,B,C,D) = k11_osalg_2(A,B,D,C) ) ) ) ) )).

fof(t45_osalg_2,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] :
              ( ( v4_msualg_1(C,A)
                & v12_osalg_1(C,A)
                & m1_msualg_2(C,A,B) )
             => ! [D] :
                  ( ( v4_msualg_1(D,A)
                    & v12_osalg_1(D,A)
                    & m1_msualg_2(D,A,B) )
                 => k11_msualg_2(A,B,C,k11_osalg_2(A,B,C,D)) = C ) ) ) ) )).

fof(t46_osalg_2,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] :
              ( ( v4_msualg_1(C,A)
                & v12_osalg_1(C,A)
                & m1_msualg_2(C,A,B) )
             => ! [D] :
                  ( ( v4_msualg_1(D,A)
                    & v12_osalg_1(D,A)
                    & m1_msualg_2(D,A,B) )
                 => k11_osalg_2(A,B,k11_msualg_2(A,B,C,D),D) = D ) ) ) ) )).

fof(d15_osalg_2,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] :
              ( C = k12_osalg_2(A,B)
            <=> ! [D] :
                  ( r2_hidden(D,C)
                <=> ( v4_msualg_1(D,A)
                    & v12_osalg_1(D,A)
                    & m1_msualg_2(D,A,B) ) ) ) ) ) )).

fof(t47_osalg_2,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) )
         => r1_tarski(k12_osalg_2(A,B),k14_msualg_2(A,B)) ) ) )).

fof(d16_osalg_2,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(k13_osalg_2(A,B),k13_osalg_2(A,B)),k13_osalg_2(A,B))
                & m2_relset_1(C,k2_zfmisc_1(k13_osalg_2(A,B),k13_osalg_2(A,B)),k13_osalg_2(A,B)) )
             => ( C = k14_osalg_2(A,B)
              <=> ! [D] :
                    ( m2_subset_1(D,k14_msualg_2(A,B),k13_osalg_2(A,B))
                   => ! [E] :
                        ( m2_subset_1(E,k14_msualg_2(A,B),k13_osalg_2(A,B))
                       => ! [F] :
                            ( ( v4_msualg_1(F,A)
                              & v12_osalg_1(F,A)
                              & m1_msualg_2(F,A,B) )
                           => ! [G] :
                                ( ( v4_msualg_1(G,A)
                                  & v12_osalg_1(G,A)
                                  & m1_msualg_2(G,A,B) )
                               => ( ( D = F
                                    & E = G )
                                 => k2_binop_1(k13_osalg_2(A,B),k13_osalg_2(A,B),k13_osalg_2(A,B),C,D,E) = k11_osalg_2(A,B,F,G) ) ) ) ) ) ) ) ) ) )).

fof(d17_osalg_2,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(k13_osalg_2(A,B),k13_osalg_2(A,B)),k13_osalg_2(A,B))
                & m2_relset_1(C,k2_zfmisc_1(k13_osalg_2(A,B),k13_osalg_2(A,B)),k13_osalg_2(A,B)) )
             => ( C = k15_osalg_2(A,B)
              <=> ! [D] :
                    ( m2_subset_1(D,k14_msualg_2(A,B),k13_osalg_2(A,B))
                   => ! [E] :
                        ( m2_subset_1(E,k14_msualg_2(A,B),k13_osalg_2(A,B))
                       => ! [F] :
                            ( ( v4_msualg_1(F,A)
                              & v12_osalg_1(F,A)
                              & m1_msualg_2(F,A,B) )
                           => ! [G] :
                                ( ( v4_msualg_1(G,A)
                                  & v12_osalg_1(G,A)
                                  & m1_msualg_2(G,A,B) )
                               => ( ( D = F
                                    & E = G )
                                 => k2_binop_1(k13_osalg_2(A,B),k13_osalg_2(A,B),k13_osalg_2(A,B),C,D,E) = k11_msualg_2(A,B,F,G) ) ) ) ) ) ) ) ) ) )).

fof(t48_osalg_2,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] :
              ( m2_subset_1(C,k14_msualg_2(A,B),k13_osalg_2(A,B))
             => ! [D] :
                  ( m2_subset_1(D,k14_msualg_2(A,B),k13_osalg_2(A,B))
                 => k2_binop_1(k13_osalg_2(A,B),k13_osalg_2(A,B),k13_osalg_2(A,B),k15_osalg_2(A,B),C,D) = k2_binop_1(k14_msualg_2(A,B),k14_msualg_2(A,B),k14_msualg_2(A,B),k16_msualg_2(A,B),C,D) ) ) ) ) )).

fof(t49_osalg_2,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) )
         => v1_binop_1(k14_osalg_2(A,B),k13_osalg_2(A,B)) ) ) )).

fof(t50_osalg_2,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) )
         => v2_binop_1(k14_osalg_2(A,B),k13_osalg_2(A,B)) ) ) )).

fof(t51_osalg_2,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) )
         => v1_binop_1(k15_osalg_2(A,B),k13_osalg_2(A,B)) ) ) )).

fof(t52_osalg_2,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) )
         => v2_binop_1(k15_osalg_2(A,B),k13_osalg_2(A,B)) ) ) )).

fof(d18_osalg_2,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) )
         => k16_osalg_2(A,B) = g3_lattices(k13_osalg_2(A,B),k14_osalg_2(A,B),k15_osalg_2(A,B)) ) ) )).

fof(t53_osalg_2,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) )
         => v15_lattices(k16_osalg_2(A,B)) ) ) )).

fof(t54_osalg_2,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) )
         => k5_lattices(k16_osalg_2(A,B)) = k10_osalg_2(A,B,k3_osalg_2(A,B)) ) ) )).

fof(t55_osalg_2,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] :
              ( m2_osalg_2(C,A,B)
             => ( r6_pboole(u1_struct_0(A),C,u4_msualg_1(A,B))
               => k6_lattices(k16_osalg_2(A,B)) = k10_osalg_2(A,B,C) ) ) ) ) )).

fof(t56_osalg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( ( v4_msualg_1(B,A)
            & v5_msualg_1(B,A)
            & v12_osalg_1(B,A)
            & l3_msualg_1(B,A) )
         => k6_lattices(k16_osalg_2(A,B)) = B ) ) )).

fof(dt_m1_osalg_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & v11_osalg_1(B,A)
        & m1_pboole(B,u1_struct_0(A)) )
     => ! [C] :
          ( m1_osalg_2(C,A,B)
         => m4_pboole(C,u1_struct_0(A),B) ) ) )).

fof(existence_m1_osalg_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & v11_osalg_1(B,A)
        & m1_pboole(B,u1_struct_0(A)) )
     => ? [C] : m1_osalg_2(C,A,B) ) )).

fof(dt_m2_osalg_2,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] :
          ( m2_osalg_2(C,A,B)
         => m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) ) ) )).

fof(existence_m2_osalg_2,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] : m2_osalg_2(C,A,B) ) )).

fof(dt_k1_osalg_2,axiom,(
    ! [A,B,C] :
      ( ( ~ 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)
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k1_osalg_2(A,B,C),k1_zfmisc_1(k1_funct_1(u4_msualg_1(A,B),C))) ) )).

fof(dt_k2_osalg_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( v11_osalg_1(k2_osalg_2(A,B),A)
        & m1_pboole(k2_osalg_2(A,B),u1_struct_0(A)) ) ) )).

fof(dt_k3_osalg_2,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) )
     => m2_osalg_2(k3_osalg_2(A,B),A,B) ) )).

fof(dt_k4_osalg_2,axiom,(
    $true )).

fof(dt_k5_osalg_2,axiom,(
    $true )).

fof(dt_k6_osalg_2,axiom,(
    $true )).

fof(dt_k7_osalg_2,axiom,(
    ! [A,B,C] :
      ( ( ~ 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)
        & m1_subset_1(C,k6_osalg_2(A,B)) )
     => m2_osalg_2(k7_osalg_2(A,B,C),A,B) ) )).

fof(dt_k8_osalg_2,axiom,(
    $true )).

fof(dt_k9_osalg_2,axiom,(
    ! [A,B,C] :
      ( ( ~ 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)
        & m2_osalg_2(C,A,B) )
     => m2_osalg_2(k9_osalg_2(A,B,C),A,B) ) )).

fof(dt_k10_osalg_2,axiom,(
    ! [A,B,C] :
      ( ( ~ 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)
        & m2_osalg_2(C,A,B) )
     => ( v4_msualg_1(k10_osalg_2(A,B,C),A)
        & v12_osalg_1(k10_osalg_2(A,B,C),A)
        & m1_msualg_2(k10_osalg_2(A,B,C),A,B) ) ) )).

fof(dt_k11_osalg_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v5_msualg_1(B,A)
        & v12_osalg_1(B,A)
        & l3_msualg_1(B,A)
        & v12_osalg_1(C,A)
        & m1_msualg_2(C,A,B)
        & v12_osalg_1(D,A)
        & m1_msualg_2(D,A,B) )
     => ( v4_msualg_1(k11_osalg_2(A,B,C,D),A)
        & v12_osalg_1(k11_osalg_2(A,B,C,D),A)
        & m1_msualg_2(k11_osalg_2(A,B,C,D),A,B) ) ) )).

fof(dt_k12_osalg_2,axiom,(
    $true )).

fof(dt_k13_osalg_2,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) )
     => m1_subset_1(k13_osalg_2(A,B),k1_zfmisc_1(k14_msualg_2(A,B))) ) )).

fof(redefinition_k13_osalg_2,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) )
     => k13_osalg_2(A,B) = k12_osalg_2(A,B) ) )).

fof(dt_k14_osalg_2,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) )
     => ( v1_funct_1(k14_osalg_2(A,B))
        & v1_funct_2(k14_osalg_2(A,B),k2_zfmisc_1(k13_osalg_2(A,B),k13_osalg_2(A,B)),k13_osalg_2(A,B))
        & m2_relset_1(k14_osalg_2(A,B),k2_zfmisc_1(k13_osalg_2(A,B),k13_osalg_2(A,B)),k13_osalg_2(A,B)) ) ) )).

fof(dt_k15_osalg_2,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) )
     => ( v1_funct_1(k15_osalg_2(A,B))
        & v1_funct_2(k15_osalg_2(A,B),k2_zfmisc_1(k13_osalg_2(A,B),k13_osalg_2(A,B)),k13_osalg_2(A,B))
        & m2_relset_1(k15_osalg_2(A,B),k2_zfmisc_1(k13_osalg_2(A,B),k13_osalg_2(A,B)),k13_osalg_2(A,B)) ) ) )).

fof(dt_k16_osalg_2,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) )
     => ( ~ v3_struct_0(k16_osalg_2(A,B))
        & v3_lattices(k16_osalg_2(A,B))
        & v10_lattices(k16_osalg_2(A,B))
        & l3_lattices(k16_osalg_2(A,B)) ) ) )).

fof(d3_osalg_2,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_subset_1(C,u1_struct_0(A))
             => k1_osalg_2(A,B,C) = k3_tarski(a_3_0_osalg_2(A,B,C)) ) ) ) )).

fof(d4_osalg_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] :
          ( m1_pboole(B,u1_struct_0(A))
         => ! [C] :
              ( ( v11_osalg_1(C,A)
                & m1_pboole(C,u1_struct_0(A)) )
             => ( C = k2_osalg_2(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k1_funct_1(C,D) = k3_tarski(a_3_1_osalg_2(A,B,D)) ) ) ) ) ) )).

fof(d7_osalg_2,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] :
              ( m2_osalg_2(C,A,B)
             => k5_osalg_2(A,B,C) = a_3_2_osalg_2(A,B,C) ) ) ) )).

fof(d8_osalg_2,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) )
         => k6_osalg_2(A,B) = a_2_0_osalg_2(A,B) ) ) )).

fof(fraenkel_a_3_0_osalg_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & v4_osalg_1(B)
        & v5_osalg_1(B)
        & l3_osalg_1(B)
        & v12_osalg_1(C,B)
        & l3_msualg_1(C,B)
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_0_osalg_2(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = k1_msualg_2(B,C,E)
            & r3_orders_2(B,E,D) ) ) ) )).

fof(fraenkel_a_3_1_osalg_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & v4_osalg_1(B)
        & v5_osalg_1(B)
        & l3_osalg_1(B)
        & m1_pboole(C,u1_struct_0(B))
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_1_osalg_2(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = k1_funct_1(C,E)
            & r3_orders_2(B,E,D) ) ) ) )).

fof(fraenkel_a_3_2_osalg_2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & v4_osalg_1(B)
        & v5_osalg_1(B)
        & l3_osalg_1(B)
        & v12_osalg_1(C,B)
        & l3_msualg_1(C,B)
        & m2_osalg_2(D,B,C) )
     => ( r2_hidden(A,a_3_2_osalg_2(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,k5_msualg_2(B,C,D))
            & A = E
            & v11_osalg_1(E,B)
            & m1_pboole(E,u1_struct_0(B)) ) ) ) )).

fof(fraenkel_a_2_0_osalg_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & v4_osalg_1(B)
        & v5_osalg_1(B)
        & l3_osalg_1(B)
        & v12_osalg_1(C,B)
        & l3_msualg_1(C,B) )
     => ( r2_hidden(A,a_2_0_osalg_2(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k6_msualg_2(B,C))
            & A = D
            & v11_osalg_1(D,B)
            & m1_pboole(D,u1_struct_0(B)) ) ) ) )).
%------------------------------------------------------------------------------