SET007 Axioms: SET007+468.ax


%------------------------------------------------------------------------------
% File     : SET007+468 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Inverse Limits of Many 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    : msalimit [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   37 (   2 unit)
%            Number of atoms       :  370 (  21 equality)
%            Maximal formula depth :   28 (  12 average)
%            Number of connectives :  417 (  84 ~  ;   1  |; 213  &)
%                                         (  13 <=>; 106 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   33 (   1 propositional; 0-4 arity)
%            Number of functors    :   22 (   1 constant; 0-6 arity)
%            Number of variables   :  143 (   0 singleton; 133 !;  10 ?)
%            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(fc1_msalimit,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & m2_pralg_2(C,A,B)
        & m1_subset_1(D,A)
        & m1_subset_1(E,u1_msualg_1(B)) )
     => ( v1_relat_1(k1_funct_1(k1_funct_1(k12_pralg_2(A,B,C),D),E))
        & v1_funct_1(k1_funct_1(k1_funct_1(k12_pralg_2(A,B,C),D),E)) ) ) )).

fof(fc2_msalimit,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & m2_pralg_2(C,A,B)
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( ~ v1_xboole_0(k1_funct_1(k11_pralg_2(A,B,C),D))
        & v1_fraenkel(k1_funct_1(k11_pralg_2(A,B,C),D)) ) ) )).

fof(fc3_msalimit,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & m1_msalimit(C,A,B)
        & m2_msalimit(D,A,B,C) )
     => ( v1_relat_1(k2_msalimit(A,B,C,D))
        & v1_funct_1(k2_msalimit(A,B,C,D))
        & v1_funcop_1(k2_msalimit(A,B,C,D))
        & v1_msalimit(k2_msalimit(A,B,C,D),A,B,C) ) ) )).

fof(rc1_msalimit,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & m1_msalimit(C,A,B) )
     => ? [D] :
          ( m2_msalimit(D,A,B,C)
          & v1_relat_1(D)
          & v1_funct_1(D)
          & v1_funcop_1(D)
          & v1_msalimit(D,A,B,C) ) ) )).

fof(rc2_msalimit,axiom,(
    ? [A] :
      ( ~ v1_xboole_0(A)
      & v2_msalimit(A) ) )).

fof(fc4_msalimit,axiom,
    ( v3_struct_0(k4_msalimit)
    & v1_msualg_1(k4_msalimit)
    & v2_msualg_1(k4_msalimit) )).

fof(rc3_msalimit,axiom,(
    ? [A] :
      ( l1_msualg_1(A)
      & v3_struct_0(A)
      & v1_msualg_1(A)
      & v2_msualg_1(A) ) )).

fof(fc5_msalimit,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( ~ v1_xboole_0(k5_msalimit(A))
        & v2_msalimit(k5_msalimit(A)) ) ) )).

fof(d1_msalimit,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( m2_pralg_2(C,u1_struct_0(A),B)
             => ( m1_msalimit(C,A,B)
              <=> ? [D] :
                    ( v1_funcop_1(D)
                    & m1_pboole(D,u1_orders_2(A))
                    & ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ~ ( r1_orders_2(A,F,E)
                                    & r1_orders_2(A,G,F)
                                    & ! [H] :
                                        ( m3_pboole(H,u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,E)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F)))
                                       => ! [I] :
                                            ( m3_pboole(I,u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,G)))
                                           => ~ ( H = k1_binop_1(D,F,E)
                                                & I = k1_binop_1(D,G,F)
                                                & k1_binop_1(D,G,E) = k3_msualg_3(u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,E)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,G)),H,I)
                                                & r1_msualg_3(B,k6_pralg_2(u1_struct_0(A),B,C,E),k6_pralg_2(u1_struct_0(A),B,C,F),H) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d2_msalimit,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( m1_msalimit(C,A,B)
             => ! [D] :
                  ( ( v1_funcop_1(D)
                    & m1_pboole(D,u1_orders_2(A)) )
                 => ( m2_msalimit(D,A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ~ ( r1_orders_2(A,F,E)
                                    & r1_orders_2(A,G,F)
                                    & ! [H] :
                                        ( m3_pboole(H,u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,E)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F)))
                                       => ! [I] :
                                            ( m3_pboole(I,u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,G)))
                                           => ~ ( H = k1_binop_1(D,F,E)
                                                & I = k1_binop_1(D,G,F)
                                                & k1_binop_1(D,G,E) = k3_msualg_3(u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,E)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,G)),H,I)
                                                & r1_msualg_3(B,k6_pralg_2(u1_struct_0(A),B,C,E),k6_pralg_2(u1_struct_0(A),B,C,F),H) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d3_msalimit,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( m1_msalimit(C,A,B)
             => ! [D] :
                  ( m2_msalimit(D,A,B,C)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( r1_orders_2(A,F,E)
                           => k1_msalimit(A,B,C,D,E,F) = k1_binop_1(D,F,E) ) ) ) ) ) ) ) )).

fof(t1_msalimit,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & ~ v2_msualg_1(E)
                        & l1_msualg_1(E) )
                     => ! [F] :
                          ( m1_msalimit(F,A,E)
                         => ! [G] :
                              ( m2_msalimit(G,A,E,F)
                             => ( ( r1_orders_2(A,C,B)
                                  & r1_orders_2(A,D,C) )
                               => r6_pboole(u1_struct_0(E),k3_msualg_3(u1_struct_0(E),u4_msualg_1(E,k6_pralg_2(u1_struct_0(A),E,F,B)),u4_msualg_1(E,k6_pralg_2(u1_struct_0(A),E,F,C)),u4_msualg_1(E,k6_pralg_2(u1_struct_0(A),E,F,D)),k1_msalimit(A,E,F,G,B,C),k1_msalimit(A,E,F,G,C,D)),k1_msalimit(A,E,F,G,B,D)) ) ) ) ) ) ) ) ) )).

fof(d4_msalimit,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( m1_msalimit(C,A,B)
             => ! [D] :
                  ( m2_msalimit(D,A,B,C)
                 => ( v1_msalimit(D,A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k1_binop_1(D,E,E) = k2_msualg_3(u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,E))) ) ) ) ) ) ) )).

fof(t2_msalimit,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( m1_msalimit(C,A,B)
             => ! [D] :
                  ( m2_msalimit(D,A,B,C)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( r1_orders_2(A,F,E)
                           => ! [G] :
                                ( m3_pboole(G,u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,E)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F)))
                               => ( r6_pboole(u1_struct_0(B),G,k1_msalimit(A,B,C,D,E,F))
                                 => r1_msualg_3(B,k6_pralg_2(u1_struct_0(A),B,C,E),k6_pralg_2(u1_struct_0(A),B,C,F),G) ) ) ) ) ) ) ) ) ) )).

fof(d5_msalimit,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( m1_msalimit(C,A,B)
             => ! [D] :
                  ( m2_msalimit(D,A,B,C)
                 => ! [E] :
                      ( m2_msalimit(E,A,B,C)
                     => ( E = k2_msalimit(A,B,C,D)
                      <=> ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ( r1_orders_2(A,G,F)
                                 => k1_binop_1(E,G,F) = k1_cqc_lang(G,F,k2_msualg_3(u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F))),k3_msualg_3(u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,G)),k2_msualg_3(u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F))),k1_msalimit(A,B,C,D,F,G))) ) ) ) ) ) ) ) ) ) )).

fof(t3_msalimit,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( m1_msalimit(C,A,B)
             => ! [D] :
                  ( m2_msalimit(D,A,B,C)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( r1_orders_2(A,F,E)
                           => ( E = F
                              | k1_binop_1(D,F,E) = k1_binop_1(k2_msalimit(A,B,C,D),F,E) ) ) ) ) ) ) ) ) )).

fof(t4_msalimit,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( m1_msalimit(C,A,B)
             => ! [D] :
                  ( ( v1_msalimit(D,A,B,C)
                    & m2_msalimit(D,A,B,C) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( r1_orders_2(A,F,E)
                           => k1_binop_1(k2_msalimit(A,B,C,D),F,E) = k1_binop_1(D,F,E) ) ) ) ) ) ) ) )).

fof(d6_msalimit,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( m1_msalimit(C,A,B)
             => ! [D] :
                  ( m2_msalimit(D,A,B,C)
                 => ! [E] :
                      ( ( v4_msualg_1(E,B)
                        & m1_msualg_2(E,B,k15_pralg_2(u1_struct_0(A),B,C)) )
                     => ( E = k3_msalimit(A,B,C,D)
                      <=> ! [F] :
                            ( m1_subset_1(F,u1_struct_0(B))
                           => ! [G] :
                                ( m1_subset_1(G,k1_funct_1(k11_pralg_2(u1_struct_0(A),B,C),F))
                               => ( r2_hidden(G,k1_funct_1(u4_msualg_1(B,E),F))
                                <=> ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(A))
                                     => ! [I] :
                                          ( m1_subset_1(I,u1_struct_0(A))
                                         => ( r1_orders_2(A,I,H)
                                           => k1_funct_1(k1_msualg_3(u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,H)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,I)),k1_msalimit(A,B,C,D,H,I),F),k1_funct_1(G,H)) = k1_funct_1(G,I) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t5_msalimit,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_orders_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] :
              ( m1_msalimit(C,A,B)
             => ! [D] :
                  ( ( v1_msalimit(D,A,B,C)
                    & m2_msalimit(D,A,B,C) )
                 => k3_msalimit(A,B,C,D) = k15_pralg_2(u1_struct_0(A),B,C) ) ) ) ) )).

fof(d7_msalimit,axiom,(
    ! [A] :
      ( v2_msalimit(A)
    <=> ! [B] :
          ( r2_hidden(B,A)
         => ( ~ v3_struct_0(B)
            & v1_msualg_1(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) ) ) ) )).

fof(d8_msalimit,axiom,(
    ! [A] :
      ( ( v1_msualg_1(A)
        & l1_msualg_1(A) )
     => ( A = k4_msalimit
      <=> ( v3_struct_0(A)
          & v2_msualg_1(A) ) ) ) )).

fof(t6_msalimit,axiom,(
    ! [A] :
      ( ( v2_msualg_1(A)
        & l1_msualg_1(A) )
     => r3_pua2mss1(A,A,k6_partfun1(u1_struct_0(A)),k6_partfun1(u1_msualg_1(A))) ) )).

fof(d9_msalimit,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( B = k5_msalimit(A)
        <=> ! [C] :
              ( r2_hidden(C,B)
            <=> ? [D] :
                  ( ~ v3_struct_0(D)
                  & v1_msualg_1(D)
                  & ~ v2_msualg_1(D)
                  & l1_msualg_1(D)
                  & C = D
                  & r1_tarski(u1_struct_0(D),A)
                  & r1_tarski(u1_msualg_1(D),A) ) ) ) ) )).

fof(d10_msalimit,axiom,(
    ! [A] :
      ( l1_msualg_1(A)
     => ! [B] :
          ( l1_msualg_1(B)
         => ! [C] :
              ( C = k6_msalimit(A,B)
            <=> ! [D] :
                  ( r2_hidden(D,C)
                <=> ? [E] :
                      ( v1_relat_1(E)
                      & v1_funct_1(E)
                      & ? [F] :
                          ( v1_relat_1(F)
                          & v1_funct_1(F)
                          & D = k4_tarski(E,F)
                          & r3_pua2mss1(A,B,E,F) ) ) ) ) ) ) )).

fof(dt_m1_msalimit,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B) )
     => ! [C] :
          ( m1_msalimit(C,A,B)
         => m2_pralg_2(C,u1_struct_0(A),B) ) ) )).

fof(existence_m1_msalimit,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B) )
     => ? [C] : m1_msalimit(C,A,B) ) )).

fof(dt_m2_msalimit,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & m1_msalimit(C,A,B) )
     => ! [D] :
          ( m2_msalimit(D,A,B,C)
         => ( v1_funcop_1(D)
            & m1_pboole(D,u1_orders_2(A)) ) ) ) )).

fof(existence_m2_msalimit,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & m1_msalimit(C,A,B) )
     => ? [D] : m2_msalimit(D,A,B,C) ) )).

fof(dt_m3_msalimit,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v2_msalimit(A) )
     => ! [B] :
          ( m3_msalimit(B,A)
         => ( ~ v3_struct_0(B)
            & v1_msualg_1(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) ) ) ) )).

fof(existence_m3_msalimit,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v2_msalimit(A) )
     => ? [B] : m3_msalimit(B,A) ) )).

fof(redefinition_m3_msalimit,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v2_msalimit(A) )
     => ! [B] :
          ( m3_msalimit(B,A)
        <=> m1_subset_1(B,A) ) ) )).

fof(dt_k1_msalimit,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & m1_msalimit(C,A,B)
        & m2_msalimit(D,A,B,C)
        & m1_subset_1(E,u1_struct_0(A))
        & m1_subset_1(F,u1_struct_0(A)) )
     => m3_pboole(k1_msalimit(A,B,C,D,E,F),u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,E)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F))) ) )).

fof(dt_k2_msalimit,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & m1_msalimit(C,A,B)
        & m2_msalimit(D,A,B,C) )
     => m2_msalimit(k2_msalimit(A,B,C,D),A,B,C) ) )).

fof(dt_k3_msalimit,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & m1_msalimit(C,A,B)
        & m2_msalimit(D,A,B,C) )
     => ( v4_msualg_1(k3_msalimit(A,B,C,D),B)
        & m1_msualg_2(k3_msalimit(A,B,C,D),B,k15_pralg_2(u1_struct_0(A),B,C)) ) ) )).

fof(dt_k4_msalimit,axiom,
    ( v1_msualg_1(k4_msalimit)
    & l1_msualg_1(k4_msalimit) )).

fof(dt_k5_msalimit,axiom,(
    $true )).

fof(dt_k6_msalimit,axiom,(
    $true )).
%------------------------------------------------------------------------------