SET007 Axioms: SET007+96.ax


%------------------------------------------------------------------------------
% File     : SET007+96 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : N-Tuples and Cartesian Products for n=9
% 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    : mcart_6 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   68 (  21 unit)
%            Number of atoms       :  653 ( 394 equality)
%            Maximal formula depth :   52 (  23 average)
%            Number of connectives :  787 ( 202 ~  ;  91  |; 297  &)
%                                         (  12 <=>; 185 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    6 (   1 propositional; 0-2 arity)
%            Number of functors    :   30 (   1 constant; 0-10 arity)
%            Number of variables   :  928 (   0 singleton; 897 !;  31 ?)
%            Maximal term depth    :    9 (   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(t1_mcart_6,axiom,(
    ! [A] :
      ~ ( A != k1_xboole_0
        & ! [B] :
            ~ ( r2_hidden(B,A)
              & ! [C,D,E,F,G,H,I,J,K,L,M,N,O,P] :
                  ( ( r2_hidden(C,D)
                    & r2_hidden(D,E)
                    & r2_hidden(E,F)
                    & r2_hidden(F,G)
                    & r2_hidden(G,H)
                    & r2_hidden(H,I)
                    & r2_hidden(I,J)
                    & r2_hidden(J,K)
                    & r2_hidden(K,L)
                    & r2_hidden(L,M)
                    & r2_hidden(M,N)
                    & r2_hidden(N,O)
                    & r2_hidden(O,P)
                    & r2_hidden(P,B) )
                 => r1_xboole_0(C,A) ) ) ) )).

fof(t2_mcart_6,axiom,(
    ! [A] :
      ~ ( A != k1_xboole_0
        & ! [B] :
            ~ ( r2_hidden(B,A)
              & ! [C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q] :
                  ( ( r2_hidden(C,D)
                    & r2_hidden(D,E)
                    & r2_hidden(E,F)
                    & r2_hidden(F,G)
                    & r2_hidden(G,H)
                    & r2_hidden(H,I)
                    & r2_hidden(I,J)
                    & r2_hidden(J,K)
                    & r2_hidden(K,L)
                    & r2_hidden(L,M)
                    & r2_hidden(M,N)
                    & r2_hidden(N,O)
                    & r2_hidden(O,P)
                    & r2_hidden(P,Q)
                    & r2_hidden(Q,B) )
                 => r1_xboole_0(C,A) ) ) ) )).

fof(d1_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k1_mcart_6(A,B,C,D,E,F,G,H,I) = k4_tarski(k1_mcart_5(A,B,C,D,E,F,G,H),I) )).

fof(t3_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k1_mcart_6(A,B,C,D,E,F,G,H,I) = k4_tarski(k4_tarski(k4_tarski(k4_tarski(k4_tarski(k4_tarski(k4_tarski(k4_tarski(A,B),C),D),E),F),G),H),I) )).

fof(t4_mcart_6,axiom,(
    $true )).

fof(t5_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k1_mcart_6(A,B,C,D,E,F,G,H,I) = k3_mcart_1(k1_mcart_4(A,B,C,D,E,F,G),H,I) )).

fof(t6_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k1_mcart_6(A,B,C,D,E,F,G,H,I) = k4_mcart_1(k1_mcart_3(A,B,C,D,E,F),G,H,I) )).

fof(t7_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k1_mcart_6(A,B,C,D,E,F,G,H,I) = k1_mcart_2(k1_mcart_2(A,B,C,D,E),F,G,H,I) )).

fof(t8_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k1_mcart_6(A,B,C,D,E,F,G,H,I) = k1_mcart_3(k4_mcart_1(A,B,C,D),E,F,G,H,I) )).

fof(t9_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k1_mcart_6(A,B,C,D,E,F,G,H,I) = k1_mcart_4(k3_mcart_1(A,B,C),D,E,F,G,H,I) )).

fof(t10_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k1_mcart_6(A,B,C,D,E,F,G,H,I) = k1_mcart_5(k4_tarski(A,B),C,D,E,F,G,H,I) )).

fof(t11_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R] :
      ( k1_mcart_6(A,B,C,D,E,F,G,H,I) = k1_mcart_6(J,K,L,M,N,O,P,Q,R)
     => ( A = J
        & B = K
        & C = L
        & D = M
        & E = N
        & F = O
        & G = P
        & H = Q
        & I = R ) ) )).

fof(d2_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k2_mcart_6(A,B,C,D,E,F,G,H,I) = k2_zfmisc_1(k2_mcart_5(A,B,C,D,E,F,G,H),I) )).

fof(t12_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k2_mcart_6(A,B,C,D,E,F,G,H,I) = k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C),D),E),F),G),H),I) )).

fof(t13_mcart_6,axiom,(
    $true )).

fof(t14_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k2_mcart_6(A,B,C,D,E,F,G,H,I) = k3_zfmisc_1(k2_mcart_4(A,B,C,D,E,F,G),H,I) )).

fof(t15_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k2_mcart_6(A,B,C,D,E,F,G,H,I) = k4_zfmisc_1(k2_mcart_3(A,B,C,D,E,F),G,H,I) )).

fof(t16_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k2_mcart_6(A,B,C,D,E,F,G,H,I) = k2_mcart_2(k2_mcart_2(A,B,C,D,E),F,G,H,I) )).

fof(t17_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k2_mcart_6(A,B,C,D,E,F,G,H,I) = k2_mcart_3(k4_zfmisc_1(A,B,C,D),E,F,G,H,I) )).

fof(t18_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k2_mcart_6(A,B,C,D,E,F,G,H,I) = k2_mcart_4(k3_zfmisc_1(A,B,C),D,E,F,G,H,I) )).

fof(t19_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k2_mcart_6(A,B,C,D,E,F,G,H,I) = k2_mcart_5(k2_zfmisc_1(A,B),C,D,E,F,G,H,I) )).

fof(t20_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ( ( A != k1_xboole_0
        & B != k1_xboole_0
        & C != k1_xboole_0
        & D != k1_xboole_0
        & E != k1_xboole_0
        & F != k1_xboole_0
        & G != k1_xboole_0
        & H != k1_xboole_0
        & I != k1_xboole_0 )
    <=> k2_mcart_6(A,B,C,D,E,F,G,H,I) != k1_xboole_0 ) )).

fof(t21_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R] :
      ( k2_mcart_6(A,B,C,D,E,F,G,H,I) = k2_mcart_6(J,K,L,M,N,O,P,Q,R)
     => ( A = k1_xboole_0
        | B = k1_xboole_0
        | C = k1_xboole_0
        | D = k1_xboole_0
        | E = k1_xboole_0
        | F = k1_xboole_0
        | G = k1_xboole_0
        | H = k1_xboole_0
        | I = k1_xboole_0
        | ( A = J
          & B = K
          & C = L
          & D = M
          & E = N
          & F = O
          & G = P
          & H = Q
          & I = R ) ) ) )).

fof(t22_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R] :
      ( k2_mcart_6(A,B,C,D,E,F,G,H,I) = k2_mcart_6(J,K,L,M,N,O,P,Q,R)
     => ( k2_mcart_6(A,B,C,D,E,F,G,H,I) = k1_xboole_0
        | ( A = J
          & B = K
          & C = L
          & D = M
          & E = N
          & F = O
          & G = P
          & H = Q
          & I = R ) ) ) )).

fof(t23_mcart_6,axiom,(
    ! [A,B] :
      ( k2_mcart_6(A,A,A,A,A,A,A,A,A) = k2_mcart_6(B,B,B,B,B,B,B,B,B)
     => A = B ) )).

fof(t24_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ~ ( A != k1_xboole_0
        & B != k1_xboole_0
        & C != k1_xboole_0
        & D != k1_xboole_0
        & E != k1_xboole_0
        & F != k1_xboole_0
        & G != k1_xboole_0
        & H != k1_xboole_0
        & I != k1_xboole_0
        & ? [J] :
            ( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
            & ! [K] :
                ( m1_subset_1(K,A)
               => ! [L] :
                    ( m1_subset_1(L,B)
                   => ! [M] :
                        ( m1_subset_1(M,C)
                       => ! [N] :
                            ( m1_subset_1(N,D)
                           => ! [O] :
                                ( m1_subset_1(O,E)
                               => ! [P] :
                                    ( m1_subset_1(P,F)
                                   => ! [Q] :
                                        ( m1_subset_1(Q,G)
                                       => ! [R] :
                                            ( m1_subset_1(R,H)
                                           => ! [S] :
                                                ( m1_subset_1(S,I)
                                               => J != k1_mcart_6(K,L,M,N,O,P,Q,R,S) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d3_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ~ ( A != k1_xboole_0
        & B != k1_xboole_0
        & C != k1_xboole_0
        & D != k1_xboole_0
        & E != k1_xboole_0
        & F != k1_xboole_0
        & G != k1_xboole_0
        & H != k1_xboole_0
        & I != k1_xboole_0
        & ~ ! [J] :
              ( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
             => ! [K] :
                  ( m1_subset_1(K,A)
                 => ( K = k3_mcart_6(A,B,C,D,E,F,G,H,I,J)
                  <=> ! [L,M,N,O,P,Q,R,S,T] :
                        ( J = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
                       => K = L ) ) ) ) ) )).

fof(d4_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ~ ( A != k1_xboole_0
        & B != k1_xboole_0
        & C != k1_xboole_0
        & D != k1_xboole_0
        & E != k1_xboole_0
        & F != k1_xboole_0
        & G != k1_xboole_0
        & H != k1_xboole_0
        & I != k1_xboole_0
        & ~ ! [J] :
              ( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
             => ! [K] :
                  ( m1_subset_1(K,B)
                 => ( K = k4_mcart_6(A,B,C,D,E,F,G,H,I,J)
                  <=> ! [L,M,N,O,P,Q,R,S,T] :
                        ( J = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
                       => K = M ) ) ) ) ) )).

fof(d5_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ~ ( A != k1_xboole_0
        & B != k1_xboole_0
        & C != k1_xboole_0
        & D != k1_xboole_0
        & E != k1_xboole_0
        & F != k1_xboole_0
        & G != k1_xboole_0
        & H != k1_xboole_0
        & I != k1_xboole_0
        & ~ ! [J] :
              ( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
             => ! [K] :
                  ( m1_subset_1(K,C)
                 => ( K = k5_mcart_6(A,B,C,D,E,F,G,H,I,J)
                  <=> ! [L,M,N,O,P,Q,R,S,T] :
                        ( J = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
                       => K = N ) ) ) ) ) )).

fof(d6_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ~ ( A != k1_xboole_0
        & B != k1_xboole_0
        & C != k1_xboole_0
        & D != k1_xboole_0
        & E != k1_xboole_0
        & F != k1_xboole_0
        & G != k1_xboole_0
        & H != k1_xboole_0
        & I != k1_xboole_0
        & ~ ! [J] :
              ( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
             => ! [K] :
                  ( m1_subset_1(K,D)
                 => ( K = k6_mcart_6(A,B,C,D,E,F,G,H,I,J)
                  <=> ! [L,M,N,O,P,Q,R,S,T] :
                        ( J = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
                       => K = O ) ) ) ) ) )).

fof(d7_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ~ ( A != k1_xboole_0
        & B != k1_xboole_0
        & C != k1_xboole_0
        & D != k1_xboole_0
        & E != k1_xboole_0
        & F != k1_xboole_0
        & G != k1_xboole_0
        & H != k1_xboole_0
        & I != k1_xboole_0
        & ~ ! [J] :
              ( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
             => ! [K] :
                  ( m1_subset_1(K,E)
                 => ( K = k7_mcart_6(A,B,C,D,E,F,G,H,I,J)
                  <=> ! [L,M,N,O,P,Q,R,S,T] :
                        ( J = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
                       => K = P ) ) ) ) ) )).

fof(d8_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ~ ( A != k1_xboole_0
        & B != k1_xboole_0
        & C != k1_xboole_0
        & D != k1_xboole_0
        & E != k1_xboole_0
        & F != k1_xboole_0
        & G != k1_xboole_0
        & H != k1_xboole_0
        & I != k1_xboole_0
        & ~ ! [J] :
              ( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
             => ! [K] :
                  ( m1_subset_1(K,F)
                 => ( K = k8_mcart_6(A,B,C,D,E,F,G,H,I,J)
                  <=> ! [L,M,N,O,P,Q,R,S,T] :
                        ( J = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
                       => K = Q ) ) ) ) ) )).

fof(d9_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ~ ( A != k1_xboole_0
        & B != k1_xboole_0
        & C != k1_xboole_0
        & D != k1_xboole_0
        & E != k1_xboole_0
        & F != k1_xboole_0
        & G != k1_xboole_0
        & H != k1_xboole_0
        & I != k1_xboole_0
        & ~ ! [J] :
              ( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
             => ! [K] :
                  ( m1_subset_1(K,G)
                 => ( K = k9_mcart_6(A,B,C,D,E,F,G,H,I,J)
                  <=> ! [L,M,N,O,P,Q,R,S,T] :
                        ( J = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
                       => K = R ) ) ) ) ) )).

fof(d10_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ~ ( A != k1_xboole_0
        & B != k1_xboole_0
        & C != k1_xboole_0
        & D != k1_xboole_0
        & E != k1_xboole_0
        & F != k1_xboole_0
        & G != k1_xboole_0
        & H != k1_xboole_0
        & I != k1_xboole_0
        & ~ ! [J] :
              ( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
             => ! [K] :
                  ( m1_subset_1(K,H)
                 => ( K = k10_mcart_6(A,B,C,D,E,F,G,H,I,J)
                  <=> ! [L,M,N,O,P,Q,R,S,T] :
                        ( J = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
                       => K = S ) ) ) ) ) )).

fof(d11_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ~ ( A != k1_xboole_0
        & B != k1_xboole_0
        & C != k1_xboole_0
        & D != k1_xboole_0
        & E != k1_xboole_0
        & F != k1_xboole_0
        & G != k1_xboole_0
        & H != k1_xboole_0
        & I != k1_xboole_0
        & ~ ! [J] :
              ( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
             => ! [K] :
                  ( m1_subset_1(K,I)
                 => ( K = k11_mcart_6(A,B,C,D,E,F,G,H,I,J)
                  <=> ! [L,M,N,O,P,Q,R,S,T] :
                        ( J = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
                       => K = T ) ) ) ) ) )).

fof(t25_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ~ ( A != k1_xboole_0
        & B != k1_xboole_0
        & C != k1_xboole_0
        & D != k1_xboole_0
        & E != k1_xboole_0
        & F != k1_xboole_0
        & G != k1_xboole_0
        & H != k1_xboole_0
        & I != k1_xboole_0
        & ? [J] :
            ( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
            & ? [K,L,M,N,O,P,Q,R,S] :
                ( J = k1_mcart_6(K,L,M,N,O,P,Q,R,S)
                & ~ ( k3_mcart_6(A,B,C,D,E,F,G,H,I,J) = K
                    & k4_mcart_6(A,B,C,D,E,F,G,H,I,J) = L
                    & k5_mcart_6(A,B,C,D,E,F,G,H,I,J) = M
                    & k6_mcart_6(A,B,C,D,E,F,G,H,I,J) = N
                    & k7_mcart_6(A,B,C,D,E,F,G,H,I,J) = O
                    & k8_mcart_6(A,B,C,D,E,F,G,H,I,J) = P
                    & k9_mcart_6(A,B,C,D,E,F,G,H,I,J) = Q
                    & k10_mcart_6(A,B,C,D,E,F,G,H,I,J) = R
                    & k11_mcart_6(A,B,C,D,E,F,G,H,I,J) = S ) ) ) ) )).

fof(t26_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ~ ( A != k1_xboole_0
        & B != k1_xboole_0
        & C != k1_xboole_0
        & D != k1_xboole_0
        & E != k1_xboole_0
        & F != k1_xboole_0
        & G != k1_xboole_0
        & H != k1_xboole_0
        & I != k1_xboole_0
        & ~ ! [J] :
              ( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
             => J = k1_mcart_6(k3_mcart_6(A,B,C,D,E,F,G,H,I,J),k4_mcart_6(A,B,C,D,E,F,G,H,I,J),k5_mcart_6(A,B,C,D,E,F,G,H,I,J),k6_mcart_6(A,B,C,D,E,F,G,H,I,J),k7_mcart_6(A,B,C,D,E,F,G,H,I,J),k8_mcart_6(A,B,C,D,E,F,G,H,I,J),k9_mcart_6(A,B,C,D,E,F,G,H,I,J),k10_mcart_6(A,B,C,D,E,F,G,H,I,J),k11_mcart_6(A,B,C,D,E,F,G,H,I,J)) ) ) )).

fof(t27_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ~ ( A != k1_xboole_0
        & B != k1_xboole_0
        & C != k1_xboole_0
        & D != k1_xboole_0
        & E != k1_xboole_0
        & F != k1_xboole_0
        & G != k1_xboole_0
        & H != k1_xboole_0
        & I != k1_xboole_0
        & ~ ! [J] :
              ( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
             => ( k3_mcart_6(A,B,C,D,E,F,G,H,I,J) = k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(J))))))))
                & k4_mcart_6(A,B,C,D,E,F,G,H,I,J) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(J))))))))
                & k5_mcart_6(A,B,C,D,E,F,G,H,I,J) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(J)))))))
                & k6_mcart_6(A,B,C,D,E,F,G,H,I,J) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(J))))))
                & k7_mcart_6(A,B,C,D,E,F,G,H,I,J) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(J)))))
                & k8_mcart_6(A,B,C,D,E,F,G,H,I,J) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(J))))
                & k9_mcart_6(A,B,C,D,E,F,G,H,I,J) = k2_mcart_1(k1_mcart_1(k1_mcart_1(J)))
                & k10_mcart_6(A,B,C,D,E,F,G,H,I,J) = k2_mcart_1(k1_mcart_1(J))
                & k11_mcart_6(A,B,C,D,E,F,G,H,I,J) = k2_mcart_1(J) ) ) ) )).

fof(t28_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R] :
      ( ~ r1_xboole_0(k2_mcart_6(A,B,C,D,E,F,G,H,I),k2_mcart_6(J,K,L,M,N,O,P,Q,R))
     => ( ~ r1_xboole_0(A,J)
        & ~ r1_xboole_0(B,K)
        & ~ r1_xboole_0(C,L)
        & ~ r1_xboole_0(D,M)
        & ~ r1_xboole_0(E,N)
        & ~ r1_xboole_0(F,O)
        & ~ r1_xboole_0(G,P)
        & ~ r1_xboole_0(H,Q)
        & ~ r1_xboole_0(I,R) ) ) )).

fof(t29_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k2_mcart_6(k1_tarski(A),k1_tarski(B),k1_tarski(C),k1_tarski(D),k1_tarski(E),k1_tarski(F),k1_tarski(G),k1_tarski(H),k1_tarski(I)) = k1_tarski(k1_mcart_6(A,B,C,D,E,F,G,H,I)) )).

fof(t30_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] :
      ( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
     => ~ ( A != k1_xboole_0
          & B != k1_xboole_0
          & C != k1_xboole_0
          & D != k1_xboole_0
          & E != k1_xboole_0
          & F != k1_xboole_0
          & G != k1_xboole_0
          & H != k1_xboole_0
          & I != k1_xboole_0
          & ? [K,L,M,N,O,P,Q,R,S] :
              ( J = k1_mcart_6(K,L,M,N,O,P,Q,R,S)
              & ~ ( k3_mcart_6(A,B,C,D,E,F,G,H,I,J) = K
                  & k4_mcart_6(A,B,C,D,E,F,G,H,I,J) = L
                  & k5_mcart_6(A,B,C,D,E,F,G,H,I,J) = M
                  & k6_mcart_6(A,B,C,D,E,F,G,H,I,J) = N
                  & k7_mcart_6(A,B,C,D,E,F,G,H,I,J) = O
                  & k8_mcart_6(A,B,C,D,E,F,G,H,I,J) = P
                  & k9_mcart_6(A,B,C,D,E,F,G,H,I,J) = Q
                  & k10_mcart_6(A,B,C,D,E,F,G,H,I,J) = R
                  & k11_mcart_6(A,B,C,D,E,F,G,H,I,J) = S ) ) ) ) )).

fof(t31_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K] :
      ( m1_subset_1(K,k2_mcart_6(A,B,C,D,E,F,G,H,I))
     => ( ! [L] :
            ( m1_subset_1(L,A)
           => ! [M] :
                ( m1_subset_1(M,B)
               => ! [N] :
                    ( m1_subset_1(N,C)
                   => ! [O] :
                        ( m1_subset_1(O,D)
                       => ! [P] :
                            ( m1_subset_1(P,E)
                           => ! [Q] :
                                ( m1_subset_1(Q,F)
                               => ! [R] :
                                    ( m1_subset_1(R,G)
                                   => ! [S] :
                                        ( m1_subset_1(S,H)
                                       => ! [T] :
                                            ( m1_subset_1(T,I)
                                           => ( K = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
                                             => J = L ) ) ) ) ) ) ) ) ) )
       => ( A = k1_xboole_0
          | B = k1_xboole_0
          | C = k1_xboole_0
          | D = k1_xboole_0
          | E = k1_xboole_0
          | F = k1_xboole_0
          | G = k1_xboole_0
          | H = k1_xboole_0
          | I = k1_xboole_0
          | J = k3_mcart_6(A,B,C,D,E,F,G,H,I,K) ) ) ) )).

fof(t32_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K] :
      ( m1_subset_1(K,k2_mcart_6(A,B,C,D,E,F,G,H,I))
     => ( ! [L] :
            ( m1_subset_1(L,A)
           => ! [M] :
                ( m1_subset_1(M,B)
               => ! [N] :
                    ( m1_subset_1(N,C)
                   => ! [O] :
                        ( m1_subset_1(O,D)
                       => ! [P] :
                            ( m1_subset_1(P,E)
                           => ! [Q] :
                                ( m1_subset_1(Q,F)
                               => ! [R] :
                                    ( m1_subset_1(R,G)
                                   => ! [S] :
                                        ( m1_subset_1(S,H)
                                       => ! [T] :
                                            ( m1_subset_1(T,I)
                                           => ( K = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
                                             => J = M ) ) ) ) ) ) ) ) ) )
       => ( A = k1_xboole_0
          | B = k1_xboole_0
          | C = k1_xboole_0
          | D = k1_xboole_0
          | E = k1_xboole_0
          | F = k1_xboole_0
          | G = k1_xboole_0
          | H = k1_xboole_0
          | I = k1_xboole_0
          | J = k4_mcart_6(A,B,C,D,E,F,G,H,I,K) ) ) ) )).

fof(t33_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K] :
      ( m1_subset_1(K,k2_mcart_6(A,B,C,D,E,F,G,H,I))
     => ( ! [L] :
            ( m1_subset_1(L,A)
           => ! [M] :
                ( m1_subset_1(M,B)
               => ! [N] :
                    ( m1_subset_1(N,C)
                   => ! [O] :
                        ( m1_subset_1(O,D)
                       => ! [P] :
                            ( m1_subset_1(P,E)
                           => ! [Q] :
                                ( m1_subset_1(Q,F)
                               => ! [R] :
                                    ( m1_subset_1(R,G)
                                   => ! [S] :
                                        ( m1_subset_1(S,H)
                                       => ! [T] :
                                            ( m1_subset_1(T,I)
                                           => ( K = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
                                             => J = N ) ) ) ) ) ) ) ) ) )
       => ( A = k1_xboole_0
          | B = k1_xboole_0
          | C = k1_xboole_0
          | D = k1_xboole_0
          | E = k1_xboole_0
          | F = k1_xboole_0
          | G = k1_xboole_0
          | H = k1_xboole_0
          | I = k1_xboole_0
          | J = k5_mcart_6(A,B,C,D,E,F,G,H,I,K) ) ) ) )).

fof(t34_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K] :
      ( m1_subset_1(K,k2_mcart_6(A,B,C,D,E,F,G,H,I))
     => ( ! [L] :
            ( m1_subset_1(L,A)
           => ! [M] :
                ( m1_subset_1(M,B)
               => ! [N] :
                    ( m1_subset_1(N,C)
                   => ! [O] :
                        ( m1_subset_1(O,D)
                       => ! [P] :
                            ( m1_subset_1(P,E)
                           => ! [Q] :
                                ( m1_subset_1(Q,F)
                               => ! [R] :
                                    ( m1_subset_1(R,G)
                                   => ! [S] :
                                        ( m1_subset_1(S,H)
                                       => ! [T] :
                                            ( m1_subset_1(T,I)
                                           => ( K = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
                                             => J = O ) ) ) ) ) ) ) ) ) )
       => ( A = k1_xboole_0
          | B = k1_xboole_0
          | C = k1_xboole_0
          | D = k1_xboole_0
          | E = k1_xboole_0
          | F = k1_xboole_0
          | G = k1_xboole_0
          | H = k1_xboole_0
          | I = k1_xboole_0
          | J = k6_mcart_6(A,B,C,D,E,F,G,H,I,K) ) ) ) )).

fof(t35_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K] :
      ( m1_subset_1(K,k2_mcart_6(A,B,C,D,E,F,G,H,I))
     => ( ! [L] :
            ( m1_subset_1(L,A)
           => ! [M] :
                ( m1_subset_1(M,B)
               => ! [N] :
                    ( m1_subset_1(N,C)
                   => ! [O] :
                        ( m1_subset_1(O,D)
                       => ! [P] :
                            ( m1_subset_1(P,E)
                           => ! [Q] :
                                ( m1_subset_1(Q,F)
                               => ! [R] :
                                    ( m1_subset_1(R,G)
                                   => ! [S] :
                                        ( m1_subset_1(S,H)
                                       => ! [T] :
                                            ( m1_subset_1(T,I)
                                           => ( K = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
                                             => J = P ) ) ) ) ) ) ) ) ) )
       => ( A = k1_xboole_0
          | B = k1_xboole_0
          | C = k1_xboole_0
          | D = k1_xboole_0
          | E = k1_xboole_0
          | F = k1_xboole_0
          | G = k1_xboole_0
          | H = k1_xboole_0
          | I = k1_xboole_0
          | J = k7_mcart_6(A,B,C,D,E,F,G,H,I,K) ) ) ) )).

fof(t36_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K] :
      ( m1_subset_1(K,k2_mcart_6(A,B,C,D,E,F,G,H,I))
     => ( ! [L] :
            ( m1_subset_1(L,A)
           => ! [M] :
                ( m1_subset_1(M,B)
               => ! [N] :
                    ( m1_subset_1(N,C)
                   => ! [O] :
                        ( m1_subset_1(O,D)
                       => ! [P] :
                            ( m1_subset_1(P,E)
                           => ! [Q] :
                                ( m1_subset_1(Q,F)
                               => ! [R] :
                                    ( m1_subset_1(R,G)
                                   => ! [S] :
                                        ( m1_subset_1(S,H)
                                       => ! [T] :
                                            ( m1_subset_1(T,I)
                                           => ( K = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
                                             => J = Q ) ) ) ) ) ) ) ) ) )
       => ( A = k1_xboole_0
          | B = k1_xboole_0
          | C = k1_xboole_0
          | D = k1_xboole_0
          | E = k1_xboole_0
          | F = k1_xboole_0
          | G = k1_xboole_0
          | H = k1_xboole_0
          | I = k1_xboole_0
          | J = k8_mcart_6(A,B,C,D,E,F,G,H,I,K) ) ) ) )).

fof(t37_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K] :
      ( m1_subset_1(K,k2_mcart_6(A,B,C,D,E,F,G,H,I))
     => ( ! [L] :
            ( m1_subset_1(L,A)
           => ! [M] :
                ( m1_subset_1(M,B)
               => ! [N] :
                    ( m1_subset_1(N,C)
                   => ! [O] :
                        ( m1_subset_1(O,D)
                       => ! [P] :
                            ( m1_subset_1(P,E)
                           => ! [Q] :
                                ( m1_subset_1(Q,F)
                               => ! [R] :
                                    ( m1_subset_1(R,G)
                                   => ! [S] :
                                        ( m1_subset_1(S,H)
                                       => ! [T] :
                                            ( m1_subset_1(T,I)
                                           => ( K = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
                                             => J = R ) ) ) ) ) ) ) ) ) )
       => ( A = k1_xboole_0
          | B = k1_xboole_0
          | C = k1_xboole_0
          | D = k1_xboole_0
          | E = k1_xboole_0
          | F = k1_xboole_0
          | G = k1_xboole_0
          | H = k1_xboole_0
          | I = k1_xboole_0
          | J = k9_mcart_6(A,B,C,D,E,F,G,H,I,K) ) ) ) )).

fof(t38_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K] :
      ( m1_subset_1(K,k2_mcart_6(A,B,C,D,E,F,G,H,I))
     => ( ! [L] :
            ( m1_subset_1(L,A)
           => ! [M] :
                ( m1_subset_1(M,B)
               => ! [N] :
                    ( m1_subset_1(N,C)
                   => ! [O] :
                        ( m1_subset_1(O,D)
                       => ! [P] :
                            ( m1_subset_1(P,E)
                           => ! [Q] :
                                ( m1_subset_1(Q,F)
                               => ! [R] :
                                    ( m1_subset_1(R,G)
                                   => ! [S] :
                                        ( m1_subset_1(S,H)
                                       => ! [T] :
                                            ( m1_subset_1(T,I)
                                           => ( K = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
                                             => J = S ) ) ) ) ) ) ) ) ) )
       => ( A = k1_xboole_0
          | B = k1_xboole_0
          | C = k1_xboole_0
          | D = k1_xboole_0
          | E = k1_xboole_0
          | F = k1_xboole_0
          | G = k1_xboole_0
          | H = k1_xboole_0
          | I = k1_xboole_0
          | J = k10_mcart_6(A,B,C,D,E,F,G,H,I,K) ) ) ) )).

fof(t39_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K] :
      ( m1_subset_1(K,k2_mcart_6(A,B,C,D,E,F,G,H,I))
     => ( ! [L] :
            ( m1_subset_1(L,A)
           => ! [M] :
                ( m1_subset_1(M,B)
               => ! [N] :
                    ( m1_subset_1(N,C)
                   => ! [O] :
                        ( m1_subset_1(O,D)
                       => ! [P] :
                            ( m1_subset_1(P,E)
                           => ! [Q] :
                                ( m1_subset_1(Q,F)
                               => ! [R] :
                                    ( m1_subset_1(R,G)
                                   => ! [S] :
                                        ( m1_subset_1(S,H)
                                       => ! [T] :
                                            ( m1_subset_1(T,I)
                                           => ( K = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
                                             => J = T ) ) ) ) ) ) ) ) ) )
       => ( A = k1_xboole_0
          | B = k1_xboole_0
          | C = k1_xboole_0
          | D = k1_xboole_0
          | E = k1_xboole_0
          | F = k1_xboole_0
          | G = k1_xboole_0
          | H = k1_xboole_0
          | I = k1_xboole_0
          | J = k11_mcart_6(A,B,C,D,E,F,G,H,I,K) ) ) ) )).

fof(t40_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] :
      ~ ( r2_hidden(A,k2_mcart_6(B,C,D,E,F,G,H,I,J))
        & ! [K,L,M,N,O,P,Q,R,S] :
            ~ ( r2_hidden(K,B)
              & r2_hidden(L,C)
              & r2_hidden(M,D)
              & r2_hidden(N,E)
              & r2_hidden(O,F)
              & r2_hidden(P,G)
              & r2_hidden(Q,H)
              & r2_hidden(R,I)
              & r2_hidden(S,J)
              & A = k1_mcart_6(K,L,M,N,O,P,Q,R,S) ) ) )).

fof(t41_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R] :
      ( r2_hidden(k1_mcart_6(A,B,C,D,E,F,G,H,I),k2_mcart_6(J,K,L,M,N,O,P,Q,R))
    <=> ( r2_hidden(A,J)
        & r2_hidden(B,K)
        & r2_hidden(C,L)
        & r2_hidden(D,M)
        & r2_hidden(E,N)
        & r2_hidden(F,O)
        & r2_hidden(G,P)
        & r2_hidden(H,Q)
        & r2_hidden(I,R) ) ) )).

fof(t42_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] :
      ( ! [K] :
          ( r2_hidden(K,A)
        <=> ? [L,M,N,O,P,Q,R,S,T] :
              ( r2_hidden(L,B)
              & r2_hidden(M,C)
              & r2_hidden(N,D)
              & r2_hidden(O,E)
              & r2_hidden(P,F)
              & r2_hidden(Q,G)
              & r2_hidden(R,H)
              & r2_hidden(S,I)
              & r2_hidden(T,J)
              & K = k1_mcart_6(L,M,N,O,P,Q,R,S,T) ) )
     => A = k2_mcart_6(B,C,D,E,F,G,H,I,J) ) )).

fof(t43_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R] :
      ~ ( A != k1_xboole_0
        & B != k1_xboole_0
        & C != k1_xboole_0
        & D != k1_xboole_0
        & E != k1_xboole_0
        & F != k1_xboole_0
        & G != k1_xboole_0
        & H != k1_xboole_0
        & I != k1_xboole_0
        & J != k1_xboole_0
        & K != k1_xboole_0
        & L != k1_xboole_0
        & M != k1_xboole_0
        & N != k1_xboole_0
        & O != k1_xboole_0
        & P != k1_xboole_0
        & Q != k1_xboole_0
        & R != k1_xboole_0
        & ? [S] :
            ( m1_subset_1(S,k2_mcart_6(A,B,C,D,E,F,G,H,I))
            & ? [T] :
                ( m1_subset_1(T,k2_mcart_6(J,K,L,M,N,O,P,Q,R))
                & S = T
                & ~ ( k3_mcart_6(A,B,C,D,E,F,G,H,I,S) = k3_mcart_6(J,K,L,M,N,O,P,Q,R,T)
                    & k4_mcart_6(A,B,C,D,E,F,G,H,I,S) = k4_mcart_6(J,K,L,M,N,O,P,Q,R,T)
                    & k5_mcart_6(A,B,C,D,E,F,G,H,I,S) = k5_mcart_6(J,K,L,M,N,O,P,Q,R,T)
                    & k6_mcart_6(A,B,C,D,E,F,G,H,I,S) = k6_mcart_6(J,K,L,M,N,O,P,Q,R,T)
                    & k7_mcart_6(A,B,C,D,E,F,G,H,I,S) = k7_mcart_6(J,K,L,M,N,O,P,Q,R,T)
                    & k8_mcart_6(A,B,C,D,E,F,G,H,I,S) = k8_mcart_6(J,K,L,M,N,O,P,Q,R,T)
                    & k9_mcart_6(A,B,C,D,E,F,G,H,I,S) = k9_mcart_6(J,K,L,M,N,O,P,Q,R,T)
                    & k10_mcart_6(A,B,C,D,E,F,G,H,I,S) = k10_mcart_6(J,K,L,M,N,O,P,Q,R,T)
                    & k11_mcart_6(A,B,C,D,E,F,G,H,I,S) = k11_mcart_6(J,K,L,M,N,O,P,Q,R,T) ) ) ) ) )).

fof(t44_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] :
      ( m1_subset_1(J,k1_zfmisc_1(A))
     => ! [K] :
          ( m1_subset_1(K,k1_zfmisc_1(B))
         => ! [L] :
              ( m1_subset_1(L,k1_zfmisc_1(C))
             => ! [M] :
                  ( m1_subset_1(M,k1_zfmisc_1(D))
                 => ! [N] :
                      ( m1_subset_1(N,k1_zfmisc_1(E))
                     => ! [O] :
                          ( m1_subset_1(O,k1_zfmisc_1(F))
                         => ! [P] :
                              ( m1_subset_1(P,k1_zfmisc_1(G))
                             => ! [Q] :
                                  ( m1_subset_1(Q,k1_zfmisc_1(H))
                                 => ! [R] :
                                      ( m1_subset_1(R,k1_zfmisc_1(I))
                                     => ! [S] :
                                          ( m1_subset_1(S,k2_mcart_6(A,B,C,D,E,F,G,H,I))
                                         => ( r2_hidden(S,k2_mcart_6(J,K,L,M,N,O,P,Q,R))
                                           => ( r2_hidden(k3_mcart_6(A,B,C,D,E,F,G,H,I,S),J)
                                              & r2_hidden(k4_mcart_6(A,B,C,D,E,F,G,H,I,S),K)
                                              & r2_hidden(k5_mcart_6(A,B,C,D,E,F,G,H,I,S),L)
                                              & r2_hidden(k6_mcart_6(A,B,C,D,E,F,G,H,I,S),M)
                                              & r2_hidden(k7_mcart_6(A,B,C,D,E,F,G,H,I,S),N)
                                              & r2_hidden(k8_mcart_6(A,B,C,D,E,F,G,H,I,S),O)
                                              & r2_hidden(k9_mcart_6(A,B,C,D,E,F,G,H,I,S),P)
                                              & r2_hidden(k10_mcart_6(A,B,C,D,E,F,G,H,I,S),Q)
                                              & r2_hidden(k11_mcart_6(A,B,C,D,E,F,G,H,I,S),R) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t45_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R] :
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D)
        & r1_tarski(E,F)
        & r1_tarski(G,H)
        & r1_tarski(I,J)
        & r1_tarski(K,L)
        & r1_tarski(M,N)
        & r1_tarski(O,P)
        & r1_tarski(Q,R) )
     => r1_tarski(k2_mcart_6(A,C,E,G,I,K,M,O,Q),k2_mcart_6(B,D,F,H,J,L,N,P,R)) ) )).

fof(t46_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] :
      ( m1_subset_1(J,k1_zfmisc_1(A))
     => ! [K] :
          ( m1_subset_1(K,k1_zfmisc_1(B))
         => ! [L] :
              ( m1_subset_1(L,k1_zfmisc_1(C))
             => ! [M] :
                  ( m1_subset_1(M,k1_zfmisc_1(D))
                 => ! [N] :
                      ( m1_subset_1(N,k1_zfmisc_1(E))
                     => ! [O] :
                          ( m1_subset_1(O,k1_zfmisc_1(F))
                         => ! [P] :
                              ( m1_subset_1(P,k1_zfmisc_1(G))
                             => ! [Q] :
                                  ( m1_subset_1(Q,k1_zfmisc_1(H))
                                 => ! [R] :
                                      ( m1_subset_1(R,k1_zfmisc_1(I))
                                     => m1_subset_1(k2_mcart_6(J,K,L,M,N,O,P,Q,R),k1_zfmisc_1(k2_mcart_6(A,B,C,D,E,F,G,H,I))) ) ) ) ) ) ) ) ) ) )).

fof(dt_k1_mcart_6,axiom,(
    $true )).

fof(dt_k2_mcart_6,axiom,(
    $true )).

fof(dt_k3_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] :
      ( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
     => m1_subset_1(k3_mcart_6(A,B,C,D,E,F,G,H,I,J),A) ) )).

fof(dt_k4_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] :
      ( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
     => m1_subset_1(k4_mcart_6(A,B,C,D,E,F,G,H,I,J),B) ) )).

fof(dt_k5_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] :
      ( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
     => m1_subset_1(k5_mcart_6(A,B,C,D,E,F,G,H,I,J),C) ) )).

fof(dt_k6_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] :
      ( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
     => m1_subset_1(k6_mcart_6(A,B,C,D,E,F,G,H,I,J),D) ) )).

fof(dt_k7_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] :
      ( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
     => m1_subset_1(k7_mcart_6(A,B,C,D,E,F,G,H,I,J),E) ) )).

fof(dt_k8_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] :
      ( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
     => m1_subset_1(k8_mcart_6(A,B,C,D,E,F,G,H,I,J),F) ) )).

fof(dt_k9_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] :
      ( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
     => m1_subset_1(k9_mcart_6(A,B,C,D,E,F,G,H,I,J),G) ) )).

fof(dt_k10_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] :
      ( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
     => m1_subset_1(k10_mcart_6(A,B,C,D,E,F,G,H,I,J),H) ) )).

fof(dt_k11_mcart_6,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] :
      ( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
     => m1_subset_1(k11_mcart_6(A,B,C,D,E,F,G,H,I,J),I) ) )).
%------------------------------------------------------------------------------