SET007 Axioms: SET007+691.ax


%------------------------------------------------------------------------------
% File     : SET007+691 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Properties of Fuzzy Relation
% 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    : fuzzy_4 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   33 (   0 unit)
%            Number of atoms       :  205 (  27 equality)
%            Maximal formula depth :   23 (  11 average)
%            Number of connectives :  249 (  77 ~  ;   0  |;  26  &)
%                                         (   4 <=>; 142 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    8 (   0 propositional; 1-2 arity)
%            Number of functors    :   23 (   3 constant; 0-7 arity)
%            Number of variables   :  159 (   0 singleton; 159 !;   0 ?)
%            Maximal term depth    :    4 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_fuzzy_4,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_fuzzy_1(B,A) )
     => ~ v1_xboole_0(k2_relat_1(B)) ) )).

fof(t1_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_fuzzy_1(B,A)
         => ( v3_seq_4(k5_relset_1(A,k1_numbers,B))
            & ! [C] :
                ( r2_hidden(C,k4_relset_1(A,k1_numbers,B))
               => r1_xreal_0(k2_seq_1(A,k1_numbers,B,C),k3_pscomp_1(k5_relset_1(A,k1_numbers,B))) )
            & ! [C] :
                ( r2_hidden(C,k4_relset_1(A,k1_numbers,B))
               => r1_xreal_0(k4_pscomp_1(k5_relset_1(A,k1_numbers,B)),k2_seq_1(A,k1_numbers,B,C)) ) ) ) ) )).

fof(t2_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_fuzzy_1(B,A)
         => ! [C] :
              ( m1_fuzzy_1(C,A)
             => ( ! [D] :
                    ( r2_hidden(D,A)
                   => r1_xreal_0(k2_seq_1(A,k1_numbers,B,D),k2_seq_1(A,k1_numbers,C,D)) )
               => r1_xreal_0(k3_pscomp_1(k5_relset_1(A,k1_numbers,B)),k3_pscomp_1(k5_relset_1(A,k1_numbers,C))) ) ) ) ) )).

fof(t3_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_fuzzy_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => ( r1_xreal_0(np__0,k2_seq_1(k2_zfmisc_1(A,B),k1_numbers,C,D))
                    & r1_xreal_0(k2_seq_1(k2_zfmisc_1(A,B),k1_numbers,C,D),np__1) ) ) ) ) ) )).

fof(t4_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_fuzzy_1(C,k2_zfmisc_1(A,B))
             => ! [D,E] :
                  ( r2_hidden(k4_tarski(D,E),k2_zfmisc_1(A,B))
                 => ( r1_xreal_0(np__0,k2_seq_1(k2_zfmisc_1(A,B),k1_numbers,C,k4_tarski(D,E)))
                    & r1_xreal_0(k2_seq_1(k2_zfmisc_1(A,B),k1_numbers,C,k4_tarski(D,E)),np__1) ) ) ) ) ) )).

fof(d1_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_fuzzy_1(C,k2_zfmisc_1(B,A))
             => ! [D] :
                  ( m1_fuzzy_1(D,k2_zfmisc_1(A,B))
                 => ( D = k1_fuzzy_4(A,B,C)
                  <=> ! [E,F] :
                        ( r2_hidden(k4_tarski(E,F),k2_zfmisc_1(A,B))
                       => k2_seq_1(k2_zfmisc_1(A,B),k1_numbers,D,k4_tarski(E,F)) = k2_seq_1(k2_zfmisc_1(B,A),k1_numbers,C,k4_tarski(F,E)) ) ) ) ) ) ) )).

fof(t5_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_fuzzy_1(C,k2_zfmisc_1(A,B))
             => k1_fuzzy_4(A,B,k1_fuzzy_4(B,A,C)) = C ) ) ) )).

fof(t6_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_fuzzy_1(C,k2_zfmisc_1(A,B))
             => k3_fuzzy_1(k2_zfmisc_1(B,A),k1_fuzzy_4(B,A,C)) = k1_fuzzy_4(B,A,k3_fuzzy_1(k2_zfmisc_1(A,B),C)) ) ) ) )).

fof(t7_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_fuzzy_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_fuzzy_1(D,k2_zfmisc_1(A,B))
                 => k1_fuzzy_4(B,A,k2_fuzzy_1(k2_zfmisc_1(A,B),C,D)) = k2_fuzzy_1(k2_zfmisc_1(B,A),k1_fuzzy_4(B,A,C),k1_fuzzy_4(B,A,D)) ) ) ) ) )).

fof(t8_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_fuzzy_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_fuzzy_1(D,k2_zfmisc_1(A,B))
                 => k1_fuzzy_4(B,A,k1_fuzzy_1(k2_zfmisc_1(A,B),C,D)) = k1_fuzzy_1(k2_zfmisc_1(B,A),k1_fuzzy_4(B,A,C),k1_fuzzy_4(B,A,D)) ) ) ) ) )).

fof(t9_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_fuzzy_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_fuzzy_1(D,k2_zfmisc_1(A,B))
                 => ! [E,F] :
                      ( ( r2_hidden(E,A)
                        & r2_hidden(F,B)
                        & r1_xreal_0(k2_seq_1(k2_zfmisc_1(A,B),k1_numbers,C,k4_tarski(E,F)),k2_seq_1(k2_zfmisc_1(A,B),k1_numbers,D,k4_tarski(E,F))) )
                     => r1_xreal_0(k2_seq_1(k2_zfmisc_1(B,A),k1_numbers,k1_fuzzy_4(B,A,C),k4_tarski(F,E)),k2_seq_1(k2_zfmisc_1(B,A),k1_numbers,k1_fuzzy_4(B,A,D),k4_tarski(F,E))) ) ) ) ) ) )).

fof(t10_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_fuzzy_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_fuzzy_1(D,k2_zfmisc_1(A,B))
                 => ( r1_fuzzy_1(C,D)
                   => r1_fuzzy_1(k1_fuzzy_4(B,A,C),k1_fuzzy_4(B,A,D)) ) ) ) ) ) )).

fof(t11_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_fuzzy_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_fuzzy_1(D,k2_zfmisc_1(A,B))
                 => k1_fuzzy_4(B,A,k1_fuzzy_2(k2_zfmisc_1(A,B),C,D)) = k1_fuzzy_2(k2_zfmisc_1(B,A),k1_fuzzy_4(B,A,C),k1_fuzzy_4(B,A,D)) ) ) ) ) )).

fof(t12_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_fuzzy_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_fuzzy_1(D,k2_zfmisc_1(A,B))
                 => k1_fuzzy_4(B,A,k6_fuzzy_1(k2_zfmisc_1(A,B),C,D)) = k6_fuzzy_1(k2_zfmisc_1(B,A),k1_fuzzy_4(B,A,C),k1_fuzzy_4(B,A,D)) ) ) ) ) )).

fof(d2_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_fuzzy_1(D,k2_zfmisc_1(A,B))
                 => ! [E] :
                      ( m1_fuzzy_1(E,k2_zfmisc_1(B,C))
                     => ! [F,G] :
                          ( ( r2_hidden(F,A)
                            & r2_hidden(G,C) )
                         => ! [H] :
                              ( m1_fuzzy_1(H,B)
                             => ( H = k2_fuzzy_4(A,B,C,D,E,F,G)
                              <=> ! [I] :
                                    ( m1_subset_1(I,B)
                                   => k2_seq_1(B,k1_numbers,H,I) = k3_square_1(k2_seq_1(k2_zfmisc_1(A,B),k1_numbers,D,k4_tarski(F,I)),k2_seq_1(k2_zfmisc_1(B,C),k1_numbers,E,k4_tarski(I,G))) ) ) ) ) ) ) ) ) ) )).

fof(d3_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_fuzzy_1(D,k2_zfmisc_1(A,B))
                 => ! [E] :
                      ( m1_fuzzy_1(E,k2_zfmisc_1(B,C))
                     => ! [F] :
                          ( m1_fuzzy_1(F,k2_zfmisc_1(A,C))
                         => ( F = k3_fuzzy_4(A,B,C,D,E)
                          <=> ! [G,H] :
                                ( r2_hidden(k4_tarski(G,H),k2_zfmisc_1(A,C))
                               => k2_seq_1(k2_zfmisc_1(A,C),k1_numbers,F,k4_tarski(G,H)) = k3_pscomp_1(k5_relset_1(B,k1_numbers,k2_fuzzy_4(A,B,C,D,E,G,H))) ) ) ) ) ) ) ) ) )).

fof(t13_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_fuzzy_1(D,k2_zfmisc_1(A,B))
                 => ! [E] :
                      ( m1_fuzzy_1(E,k2_zfmisc_1(B,C))
                     => ! [F] :
                          ( m1_fuzzy_1(F,k2_zfmisc_1(B,C))
                         => k3_fuzzy_4(A,B,C,D,k2_fuzzy_1(k2_zfmisc_1(B,C),E,F)) = k2_fuzzy_1(k2_zfmisc_1(A,C),k3_fuzzy_4(A,B,C,D,E),k3_fuzzy_4(A,B,C,D,F)) ) ) ) ) ) ) )).

fof(t14_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_fuzzy_1(D,k2_zfmisc_1(A,B))
                 => ! [E] :
                      ( m1_fuzzy_1(E,k2_zfmisc_1(A,B))
                     => ! [F] :
                          ( m1_fuzzy_1(F,k2_zfmisc_1(B,C))
                         => k3_fuzzy_4(A,B,C,k2_fuzzy_1(k2_zfmisc_1(A,B),D,E),F) = k2_fuzzy_1(k2_zfmisc_1(A,C),k3_fuzzy_4(A,B,C,D,F),k3_fuzzy_4(A,B,C,E,F)) ) ) ) ) ) ) )).

fof(t15_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_fuzzy_1(D,k2_zfmisc_1(A,B))
                 => ! [E] :
                      ( m1_fuzzy_1(E,k2_zfmisc_1(B,C))
                     => ! [F] :
                          ( m1_fuzzy_1(F,k2_zfmisc_1(B,C))
                         => r1_fuzzy_1(k3_fuzzy_4(A,B,C,D,k1_fuzzy_1(k2_zfmisc_1(B,C),E,F)),k1_fuzzy_1(k2_zfmisc_1(A,C),k3_fuzzy_4(A,B,C,D,E),k3_fuzzy_4(A,B,C,D,F))) ) ) ) ) ) ) )).

fof(t16_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_fuzzy_1(D,k2_zfmisc_1(A,B))
                 => ! [E] :
                      ( m1_fuzzy_1(E,k2_zfmisc_1(A,B))
                     => ! [F] :
                          ( m1_fuzzy_1(F,k2_zfmisc_1(B,C))
                         => r1_fuzzy_1(k3_fuzzy_4(A,B,C,k1_fuzzy_1(k2_zfmisc_1(A,B),D,E),F),k1_fuzzy_1(k2_zfmisc_1(A,C),k3_fuzzy_4(A,B,C,D,F),k3_fuzzy_4(A,B,C,E,F))) ) ) ) ) ) ) )).

fof(t17_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_fuzzy_1(D,k2_zfmisc_1(A,B))
                 => ! [E] :
                      ( m1_fuzzy_1(E,k2_zfmisc_1(B,C))
                     => k1_fuzzy_4(C,A,k3_fuzzy_4(A,B,C,D,E)) = k3_fuzzy_4(C,B,A,k1_fuzzy_4(C,B,E),k1_fuzzy_4(B,A,D)) ) ) ) ) ) )).

fof(t18_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_fuzzy_1(D,k2_zfmisc_1(A,B))
                 => ! [E] :
                      ( m1_fuzzy_1(E,k2_zfmisc_1(A,B))
                     => ! [F] :
                          ( m1_fuzzy_1(F,k2_zfmisc_1(B,C))
                         => ! [G] :
                              ( m1_fuzzy_1(G,k2_zfmisc_1(B,C))
                             => ! [H,I] :
                                  ( ( r2_hidden(H,A)
                                    & r2_hidden(I,C)
                                    & ! [J] :
                                        ( r2_hidden(J,B)
                                       => ( r1_xreal_0(k2_seq_1(k2_zfmisc_1(A,B),k1_numbers,D,k4_tarski(H,J)),k2_seq_1(k2_zfmisc_1(A,B),k1_numbers,E,k4_tarski(H,J)))
                                          & r1_xreal_0(k2_seq_1(k2_zfmisc_1(B,C),k1_numbers,F,k4_tarski(J,I)),k2_seq_1(k2_zfmisc_1(B,C),k1_numbers,G,k4_tarski(J,I))) ) ) )
                                 => r1_xreal_0(k2_seq_1(k2_zfmisc_1(A,C),k1_numbers,k3_fuzzy_4(A,B,C,D,F),k4_tarski(H,I)),k2_seq_1(k2_zfmisc_1(A,C),k1_numbers,k3_fuzzy_4(A,B,C,E,G),k4_tarski(H,I))) ) ) ) ) ) ) ) ) )).

fof(t19_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_fuzzy_1(D,k2_zfmisc_1(A,B))
                 => ! [E] :
                      ( m1_fuzzy_1(E,k2_zfmisc_1(A,B))
                     => ! [F] :
                          ( m1_fuzzy_1(F,k2_zfmisc_1(B,C))
                         => ! [G] :
                              ( m1_fuzzy_1(G,k2_zfmisc_1(B,C))
                             => ( ( r1_fuzzy_1(D,E)
                                  & r1_fuzzy_1(F,G) )
                               => r1_fuzzy_1(k3_fuzzy_4(A,B,C,D,F),k3_fuzzy_4(A,B,C,E,G)) ) ) ) ) ) ) ) ) )).

fof(d4_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_fuzzy_1(C,k2_zfmisc_1(A,B))
             => ( C = k4_fuzzy_4(A,B)
              <=> ! [D,E] :
                    ( r2_hidden(k4_tarski(D,E),k2_zfmisc_1(A,B))
                   => ( ( D = E
                       => k2_seq_1(k2_zfmisc_1(A,B),k1_numbers,C,k4_tarski(D,E)) = np__1 )
                      & ( D != E
                       => k2_seq_1(k2_zfmisc_1(A,B),k1_numbers,C,k4_tarski(D,E)) = np__0 ) ) ) ) ) ) ) )).

fof(t20_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ( k2_seq_1(k2_zfmisc_1(A,B),k1_numbers,k1_fuzzy_3(A,B),C) = np__0
                & k2_seq_1(k2_zfmisc_1(A,B),k1_numbers,k2_fuzzy_3(A,B),C) = np__1 ) ) ) ) )).

fof(t21_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C,D] :
              ( r2_hidden(k4_tarski(C,D),k2_zfmisc_1(A,B))
             => ( k2_seq_1(k2_zfmisc_1(A,B),k1_numbers,k1_fuzzy_3(A,B),k4_tarski(C,D)) = np__0
                & k2_seq_1(k2_zfmisc_1(A,B),k1_numbers,k2_fuzzy_3(A,B),k4_tarski(C,D)) = np__1 ) ) ) ) )).

fof(t22_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_fuzzy_1(D,k2_zfmisc_1(A,B))
                 => k3_fuzzy_4(C,A,B,k1_fuzzy_3(C,A),D) = k1_fuzzy_3(C,B) ) ) ) ) )).

fof(t23_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_fuzzy_1(D,k2_zfmisc_1(A,B))
                 => k3_fuzzy_4(A,B,C,D,k1_fuzzy_3(B,C)) = k1_fuzzy_3(A,C) ) ) ) ) )).

fof(t24_fuzzy_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_fuzzy_1(B,k2_zfmisc_1(A,A))
         => k3_fuzzy_4(A,A,A,B,k1_fuzzy_3(A,A)) = k3_fuzzy_4(A,A,A,k1_fuzzy_3(A,A),B) ) ) )).

fof(dt_k1_fuzzy_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_fuzzy_1(C,k2_zfmisc_1(B,A)) )
     => m1_fuzzy_1(k1_fuzzy_4(A,B,C),k2_zfmisc_1(A,B)) ) )).

fof(dt_k2_fuzzy_4,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_fuzzy_1(D,k2_zfmisc_1(A,B))
        & m1_fuzzy_1(E,k2_zfmisc_1(B,C)) )
     => m1_fuzzy_1(k2_fuzzy_4(A,B,C,D,E,F,G),B) ) )).

fof(dt_k3_fuzzy_4,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_fuzzy_1(D,k2_zfmisc_1(A,B))
        & m1_fuzzy_1(E,k2_zfmisc_1(B,C)) )
     => m1_fuzzy_1(k3_fuzzy_4(A,B,C,D,E),k2_zfmisc_1(A,C)) ) )).

fof(dt_k4_fuzzy_4,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => m1_fuzzy_1(k4_fuzzy_4(A,B),k2_zfmisc_1(A,B)) ) )).
%------------------------------------------------------------------------------