SET007 Axioms: SET007+94.ax


%------------------------------------------------------------------------------
% File     : SET007+94 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : N-Tuples and Cartesian Products for n=7
% 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_4 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   60 (  17 unit)
%            Number of atoms       :  486 ( 285 equality)
%            Maximal formula depth :   42 (  19 average)
%            Number of connectives :  586 ( 160 ~  ;  58  |; 224  &)
%                                         (  10 <=>; 134 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    6 (   1 propositional; 0-2 arity)
%            Number of functors    :   24 (   1 constant; 0-8 arity)
%            Number of variables   :  642 (   0 singleton; 617 !;  25 ?)
%            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(t1_mcart_4,axiom,(
    ! [A] :
      ~ ( A != k1_xboole_0
        & ! [B] :
            ~ ( r2_hidden(B,A)
              & ! [C,D,E,F,G,H,I,J,K,L] :
                  ( ( 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,B) )
                 => r1_xboole_0(C,A) ) ) ) )).

fof(t2_mcart_4,axiom,(
    ! [A] :
      ~ ( A != k1_xboole_0
        & ! [B] :
            ~ ( r2_hidden(B,A)
              & ! [C,D,E,F,G,H,I,J,K,L,M] :
                  ( ( 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,B) )
                 => r1_xboole_0(C,A) ) ) ) )).

fof(d1_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] : k1_mcart_4(A,B,C,D,E,F,G) = k4_tarski(k1_mcart_3(A,B,C,D,E,F),G) )).

fof(t3_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] : k1_mcart_4(A,B,C,D,E,F,G) = k4_tarski(k4_tarski(k4_tarski(k4_tarski(k4_tarski(k4_tarski(A,B),C),D),E),F),G) )).

fof(t4_mcart_4,axiom,(
    $true )).

fof(t5_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] : k1_mcart_4(A,B,C,D,E,F,G) = k3_mcart_1(k1_mcart_2(A,B,C,D,E),F,G) )).

fof(t6_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] : k1_mcart_4(A,B,C,D,E,F,G) = k4_mcart_1(k4_mcart_1(A,B,C,D),E,F,G) )).

fof(t7_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] : k1_mcart_4(A,B,C,D,E,F,G) = k1_mcart_2(k3_mcart_1(A,B,C),D,E,F,G) )).

fof(t8_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] : k1_mcart_4(A,B,C,D,E,F,G) = k1_mcart_3(k4_tarski(A,B),C,D,E,F,G) )).

fof(t9_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N] :
      ( k1_mcart_4(A,B,C,D,E,F,G) = k1_mcart_4(H,I,J,K,L,M,N)
     => ( A = H
        & B = I
        & C = J
        & D = K
        & E = L
        & F = M
        & G = N ) ) )).

fof(t10_mcart_4,axiom,(
    ! [A] :
      ~ ( A != k1_xboole_0
        & ! [B] :
            ~ ( r2_hidden(B,A)
              & ! [C,D,E,F,G,H,I] :
                  ~ ( ( r2_hidden(C,A)
                      | r2_hidden(D,A) )
                    & B = k1_mcart_4(C,D,E,F,G,H,I) ) ) ) )).

fof(d2_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] : k2_mcart_4(A,B,C,D,E,F,G) = k2_zfmisc_1(k2_mcart_3(A,B,C,D,E,F),G) )).

fof(t11_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] : k2_mcart_4(A,B,C,D,E,F,G) = 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) )).

fof(t12_mcart_4,axiom,(
    $true )).

fof(t13_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] : k2_mcart_4(A,B,C,D,E,F,G) = k3_zfmisc_1(k2_mcart_2(A,B,C,D,E),F,G) )).

fof(t14_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] : k2_mcart_4(A,B,C,D,E,F,G) = k4_zfmisc_1(k4_zfmisc_1(A,B,C,D),E,F,G) )).

fof(t15_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] : k2_mcart_4(A,B,C,D,E,F,G) = k2_mcart_2(k3_zfmisc_1(A,B,C),D,E,F,G) )).

fof(t16_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] : k2_mcart_4(A,B,C,D,E,F,G) = k2_mcart_3(k2_zfmisc_1(A,B),C,D,E,F,G) )).

fof(t17_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( 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 )
    <=> k2_mcart_4(A,B,C,D,E,F,G) != k1_xboole_0 ) )).

fof(t18_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N] :
      ( k2_mcart_4(A,B,C,D,E,F,G) = k2_mcart_4(H,I,J,K,L,M,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
        | ( A = H
          & B = I
          & C = J
          & D = K
          & E = L
          & F = M
          & G = N ) ) ) )).

fof(t19_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N] :
      ( k2_mcart_4(A,B,C,D,E,F,G) = k2_mcart_4(H,I,J,K,L,M,N)
     => ( k2_mcart_4(A,B,C,D,E,F,G) = k1_xboole_0
        | ( A = H
          & B = I
          & C = J
          & D = K
          & E = L
          & F = M
          & G = N ) ) ) )).

fof(t20_mcart_4,axiom,(
    ! [A,B] :
      ( k2_mcart_4(A,A,A,A,A,A,A) = k2_mcart_4(B,B,B,B,B,B,B)
     => A = B ) )).

fof(t21_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] :
      ~ ( 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] :
            ( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
            & ! [I] :
                ( m1_subset_1(I,A)
               => ! [J] :
                    ( m1_subset_1(J,B)
                   => ! [K] :
                        ( m1_subset_1(K,C)
                       => ! [L] :
                            ( m1_subset_1(L,D)
                           => ! [M] :
                                ( m1_subset_1(M,E)
                               => ! [N] :
                                    ( m1_subset_1(N,F)
                                   => ! [O] :
                                        ( m1_subset_1(O,G)
                                       => H != k1_mcart_4(I,J,K,L,M,N,O) ) ) ) ) ) ) ) ) ) )).

fof(d3_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] :
      ~ ( 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] :
              ( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
             => ! [I] :
                  ( m1_subset_1(I,A)
                 => ( I = k3_mcart_4(A,B,C,D,E,F,G,H)
                  <=> ! [J,K,L,M,N,O,P] :
                        ( H = k1_mcart_4(J,K,L,M,N,O,P)
                       => I = J ) ) ) ) ) )).

fof(d4_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] :
      ~ ( 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] :
              ( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
             => ! [I] :
                  ( m1_subset_1(I,B)
                 => ( I = k4_mcart_4(A,B,C,D,E,F,G,H)
                  <=> ! [J,K,L,M,N,O,P] :
                        ( H = k1_mcart_4(J,K,L,M,N,O,P)
                       => I = K ) ) ) ) ) )).

fof(d5_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] :
      ~ ( 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] :
              ( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
             => ! [I] :
                  ( m1_subset_1(I,C)
                 => ( I = k5_mcart_4(A,B,C,D,E,F,G,H)
                  <=> ! [J,K,L,M,N,O,P] :
                        ( H = k1_mcart_4(J,K,L,M,N,O,P)
                       => I = L ) ) ) ) ) )).

fof(d6_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] :
      ~ ( 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] :
              ( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
             => ! [I] :
                  ( m1_subset_1(I,D)
                 => ( I = k6_mcart_4(A,B,C,D,E,F,G,H)
                  <=> ! [J,K,L,M,N,O,P] :
                        ( H = k1_mcart_4(J,K,L,M,N,O,P)
                       => I = M ) ) ) ) ) )).

fof(d7_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] :
      ~ ( 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] :
              ( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
             => ! [I] :
                  ( m1_subset_1(I,E)
                 => ( I = k7_mcart_4(A,B,C,D,E,F,G,H)
                  <=> ! [J,K,L,M,N,O,P] :
                        ( H = k1_mcart_4(J,K,L,M,N,O,P)
                       => I = N ) ) ) ) ) )).

fof(d8_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] :
      ~ ( 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] :
              ( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
             => ! [I] :
                  ( m1_subset_1(I,F)
                 => ( I = k8_mcart_4(A,B,C,D,E,F,G,H)
                  <=> ! [J,K,L,M,N,O,P] :
                        ( H = k1_mcart_4(J,K,L,M,N,O,P)
                       => I = O ) ) ) ) ) )).

fof(d9_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] :
      ~ ( 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] :
              ( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
             => ! [I] :
                  ( m1_subset_1(I,G)
                 => ( I = k9_mcart_4(A,B,C,D,E,F,G,H)
                  <=> ! [J,K,L,M,N,O,P] :
                        ( H = k1_mcart_4(J,K,L,M,N,O,P)
                       => I = P ) ) ) ) ) )).

fof(t22_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] :
      ~ ( 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] :
            ( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
            & ? [I,J,K,L,M,N,O] :
                ( H = k1_mcart_4(I,J,K,L,M,N,O)
                & ~ ( k3_mcart_4(A,B,C,D,E,F,G,H) = I
                    & k4_mcart_4(A,B,C,D,E,F,G,H) = J
                    & k5_mcart_4(A,B,C,D,E,F,G,H) = K
                    & k6_mcart_4(A,B,C,D,E,F,G,H) = L
                    & k7_mcart_4(A,B,C,D,E,F,G,H) = M
                    & k8_mcart_4(A,B,C,D,E,F,G,H) = N
                    & k9_mcart_4(A,B,C,D,E,F,G,H) = O ) ) ) ) )).

fof(t23_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] :
      ~ ( 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] :
              ( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
             => H = k1_mcart_4(k3_mcart_4(A,B,C,D,E,F,G,H),k4_mcart_4(A,B,C,D,E,F,G,H),k5_mcart_4(A,B,C,D,E,F,G,H),k6_mcart_4(A,B,C,D,E,F,G,H),k7_mcart_4(A,B,C,D,E,F,G,H),k8_mcart_4(A,B,C,D,E,F,G,H),k9_mcart_4(A,B,C,D,E,F,G,H)) ) ) )).

fof(t24_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] :
      ~ ( 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] :
              ( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
             => ( k3_mcart_4(A,B,C,D,E,F,G,H) = k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(H))))))
                & k4_mcart_4(A,B,C,D,E,F,G,H) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(H))))))
                & k5_mcart_4(A,B,C,D,E,F,G,H) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(H)))))
                & k6_mcart_4(A,B,C,D,E,F,G,H) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(H))))
                & k7_mcart_4(A,B,C,D,E,F,G,H) = k2_mcart_1(k1_mcart_1(k1_mcart_1(H)))
                & k8_mcart_4(A,B,C,D,E,F,G,H) = k2_mcart_1(k1_mcart_1(H))
                & k9_mcart_4(A,B,C,D,E,F,G,H) = k2_mcart_1(H) ) ) ) )).

fof(t25_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ~ ( ~ r1_tarski(A,k2_mcart_4(A,B,C,D,E,F,G))
          & ~ r1_tarski(A,k2_mcart_4(B,C,D,E,F,G,A))
          & ~ r1_tarski(A,k2_mcart_4(C,D,E,F,G,A,B))
          & ~ r1_tarski(A,k2_mcart_4(D,E,F,G,A,B,C))
          & ~ r1_tarski(A,k2_mcart_4(E,F,G,A,B,C,D))
          & ~ r1_tarski(A,k2_mcart_4(F,G,A,B,C,D,E))
          & ~ r1_tarski(A,k2_mcart_4(G,A,B,C,D,E,F)) )
     => A = k1_xboole_0 ) )).

fof(t26_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N] :
      ( ~ r1_xboole_0(k2_mcart_4(A,B,C,D,E,F,G),k2_mcart_4(H,I,J,K,L,M,N))
     => ( ~ r1_xboole_0(A,H)
        & ~ r1_xboole_0(B,I)
        & ~ r1_xboole_0(C,J)
        & ~ r1_xboole_0(D,K)
        & ~ r1_xboole_0(E,L)
        & ~ r1_xboole_0(F,M)
        & ~ r1_xboole_0(G,N) ) ) )).

fof(t27_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] : k2_mcart_4(k1_tarski(A),k1_tarski(B),k1_tarski(C),k1_tarski(D),k1_tarski(E),k1_tarski(F),k1_tarski(G)) = k1_tarski(k1_mcart_4(A,B,C,D,E,F,G)) )).

fof(t28_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
     => ~ ( 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
          & ? [I,J,K,L,M,N,O] :
              ( H = k1_mcart_4(I,J,K,L,M,N,O)
              & ~ ( k3_mcart_4(A,B,C,D,E,F,G,H) = I
                  & k4_mcart_4(A,B,C,D,E,F,G,H) = J
                  & k5_mcart_4(A,B,C,D,E,F,G,H) = K
                  & k6_mcart_4(A,B,C,D,E,F,G,H) = L
                  & k7_mcart_4(A,B,C,D,E,F,G,H) = M
                  & k8_mcart_4(A,B,C,D,E,F,G,H) = N
                  & k9_mcart_4(A,B,C,D,E,F,G,H) = O ) ) ) ) )).

fof(t29_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ( m1_subset_1(I,k2_mcart_4(B,C,D,E,F,G,H))
     => ( ! [J] :
            ( m1_subset_1(J,B)
           => ! [K] :
                ( m1_subset_1(K,C)
               => ! [L] :
                    ( m1_subset_1(L,D)
                   => ! [M] :
                        ( m1_subset_1(M,E)
                       => ! [N] :
                            ( m1_subset_1(N,F)
                           => ! [O] :
                                ( m1_subset_1(O,G)
                               => ! [P] :
                                    ( m1_subset_1(P,H)
                                   => ( I = k1_mcart_4(J,K,L,M,N,O,P)
                                     => A = J ) ) ) ) ) ) ) )
       => ( 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
          | A = k3_mcart_4(B,C,D,E,F,G,H,I) ) ) ) )).

fof(t30_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ( m1_subset_1(I,k2_mcart_4(B,C,D,E,F,G,H))
     => ( ! [J] :
            ( m1_subset_1(J,B)
           => ! [K] :
                ( m1_subset_1(K,C)
               => ! [L] :
                    ( m1_subset_1(L,D)
                   => ! [M] :
                        ( m1_subset_1(M,E)
                       => ! [N] :
                            ( m1_subset_1(N,F)
                           => ! [O] :
                                ( m1_subset_1(O,G)
                               => ! [P] :
                                    ( m1_subset_1(P,H)
                                   => ( I = k1_mcart_4(J,K,L,M,N,O,P)
                                     => A = K ) ) ) ) ) ) ) )
       => ( 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
          | A = k4_mcart_4(B,C,D,E,F,G,H,I) ) ) ) )).

fof(t31_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ( m1_subset_1(I,k2_mcart_4(B,C,D,E,F,G,H))
     => ( ! [J] :
            ( m1_subset_1(J,B)
           => ! [K] :
                ( m1_subset_1(K,C)
               => ! [L] :
                    ( m1_subset_1(L,D)
                   => ! [M] :
                        ( m1_subset_1(M,E)
                       => ! [N] :
                            ( m1_subset_1(N,F)
                           => ! [O] :
                                ( m1_subset_1(O,G)
                               => ! [P] :
                                    ( m1_subset_1(P,H)
                                   => ( I = k1_mcart_4(J,K,L,M,N,O,P)
                                     => A = L ) ) ) ) ) ) ) )
       => ( 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
          | A = k5_mcart_4(B,C,D,E,F,G,H,I) ) ) ) )).

fof(t32_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ( m1_subset_1(I,k2_mcart_4(B,C,D,E,F,G,H))
     => ( ! [J] :
            ( m1_subset_1(J,B)
           => ! [K] :
                ( m1_subset_1(K,C)
               => ! [L] :
                    ( m1_subset_1(L,D)
                   => ! [M] :
                        ( m1_subset_1(M,E)
                       => ! [N] :
                            ( m1_subset_1(N,F)
                           => ! [O] :
                                ( m1_subset_1(O,G)
                               => ! [P] :
                                    ( m1_subset_1(P,H)
                                   => ( I = k1_mcart_4(J,K,L,M,N,O,P)
                                     => A = M ) ) ) ) ) ) ) )
       => ( 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
          | A = k6_mcart_4(B,C,D,E,F,G,H,I) ) ) ) )).

fof(t33_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ( m1_subset_1(I,k2_mcart_4(B,C,D,E,F,G,H))
     => ( ! [J] :
            ( m1_subset_1(J,B)
           => ! [K] :
                ( m1_subset_1(K,C)
               => ! [L] :
                    ( m1_subset_1(L,D)
                   => ! [M] :
                        ( m1_subset_1(M,E)
                       => ! [N] :
                            ( m1_subset_1(N,F)
                           => ! [O] :
                                ( m1_subset_1(O,G)
                               => ! [P] :
                                    ( m1_subset_1(P,H)
                                   => ( I = k1_mcart_4(J,K,L,M,N,O,P)
                                     => A = N ) ) ) ) ) ) ) )
       => ( 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
          | A = k7_mcart_4(B,C,D,E,F,G,H,I) ) ) ) )).

fof(t34_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ( m1_subset_1(I,k2_mcart_4(B,C,D,E,F,G,H))
     => ( ! [J] :
            ( m1_subset_1(J,B)
           => ! [K] :
                ( m1_subset_1(K,C)
               => ! [L] :
                    ( m1_subset_1(L,D)
                   => ! [M] :
                        ( m1_subset_1(M,E)
                       => ! [N] :
                            ( m1_subset_1(N,F)
                           => ! [O] :
                                ( m1_subset_1(O,G)
                               => ! [P] :
                                    ( m1_subset_1(P,H)
                                   => ( I = k1_mcart_4(J,K,L,M,N,O,P)
                                     => A = O ) ) ) ) ) ) ) )
       => ( 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
          | A = k8_mcart_4(B,C,D,E,F,G,H,I) ) ) ) )).

fof(t35_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ( m1_subset_1(I,k2_mcart_4(B,C,D,E,F,G,H))
     => ( ! [J] :
            ( m1_subset_1(J,B)
           => ! [K] :
                ( m1_subset_1(K,C)
               => ! [L] :
                    ( m1_subset_1(L,D)
                   => ! [M] :
                        ( m1_subset_1(M,E)
                       => ! [N] :
                            ( m1_subset_1(N,F)
                           => ! [O] :
                                ( m1_subset_1(O,G)
                               => ! [P] :
                                    ( m1_subset_1(P,H)
                                   => ( I = k1_mcart_4(J,K,L,M,N,O,P)
                                     => A = P ) ) ) ) ) ) ) )
       => ( 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
          | A = k9_mcart_4(B,C,D,E,F,G,H,I) ) ) ) )).

fof(t36_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ~ ( r2_hidden(A,k2_mcart_4(B,C,D,E,F,G,H))
        & ! [I,J,K,L,M,N,O] :
            ~ ( r2_hidden(I,B)
              & r2_hidden(J,C)
              & r2_hidden(K,D)
              & r2_hidden(L,E)
              & r2_hidden(M,F)
              & r2_hidden(N,G)
              & r2_hidden(O,H)
              & A = k1_mcart_4(I,J,K,L,M,N,O) ) ) )).

fof(t37_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N] :
      ( r2_hidden(k1_mcart_4(A,B,C,D,E,F,G),k2_mcart_4(H,I,J,K,L,M,N))
    <=> ( r2_hidden(A,H)
        & r2_hidden(B,I)
        & r2_hidden(C,J)
        & r2_hidden(D,K)
        & r2_hidden(E,L)
        & r2_hidden(F,M)
        & r2_hidden(G,N) ) ) )).

fof(t38_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( ! [I] :
          ( r2_hidden(I,H)
        <=> ? [J,K,L,M,N,O,P] :
              ( r2_hidden(J,A)
              & r2_hidden(K,B)
              & r2_hidden(L,C)
              & r2_hidden(M,D)
              & r2_hidden(N,E)
              & r2_hidden(O,F)
              & r2_hidden(P,G)
              & I = k1_mcart_4(J,K,L,M,N,O,P) ) )
     => H = k2_mcart_4(A,B,C,D,E,F,G) ) )).

fof(t39_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,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 != k1_xboole_0
        & K != k1_xboole_0
        & L != k1_xboole_0
        & M != k1_xboole_0
        & N != k1_xboole_0
        & ? [O] :
            ( m1_subset_1(O,k2_mcart_4(A,B,C,D,E,F,G))
            & ? [P] :
                ( m1_subset_1(P,k2_mcart_4(H,I,J,K,L,M,N))
                & O = P
                & ~ ( k3_mcart_4(A,B,C,D,E,F,G,O) = k3_mcart_4(H,I,J,K,L,M,N,P)
                    & k4_mcart_4(A,B,C,D,E,F,G,O) = k4_mcart_4(H,I,J,K,L,M,N,P)
                    & k5_mcart_4(A,B,C,D,E,F,G,O) = k5_mcart_4(H,I,J,K,L,M,N,P)
                    & k6_mcart_4(A,B,C,D,E,F,G,O) = k6_mcart_4(H,I,J,K,L,M,N,P)
                    & k7_mcart_4(A,B,C,D,E,F,G,O) = k7_mcart_4(H,I,J,K,L,M,N,P)
                    & k8_mcart_4(A,B,C,D,E,F,G,O) = k8_mcart_4(H,I,J,K,L,M,N,P)
                    & k9_mcart_4(A,B,C,D,E,F,G,O) = k9_mcart_4(H,I,J,K,L,M,N,P) ) ) ) ) )).

fof(t40_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( m1_subset_1(H,k1_zfmisc_1(A))
     => ! [I] :
          ( m1_subset_1(I,k1_zfmisc_1(B))
         => ! [J] :
              ( m1_subset_1(J,k1_zfmisc_1(C))
             => ! [K] :
                  ( m1_subset_1(K,k1_zfmisc_1(D))
                 => ! [L] :
                      ( m1_subset_1(L,k1_zfmisc_1(E))
                     => ! [M] :
                          ( m1_subset_1(M,k1_zfmisc_1(F))
                         => ! [N] :
                              ( m1_subset_1(N,k1_zfmisc_1(G))
                             => ! [O] :
                                  ( m1_subset_1(O,k2_mcart_4(A,B,C,D,E,F,G))
                                 => ( r2_hidden(O,k2_mcart_4(H,I,J,K,L,M,N))
                                   => ( r2_hidden(k3_mcart_4(A,B,C,D,E,F,G,O),H)
                                      & r2_hidden(k4_mcart_4(A,B,C,D,E,F,G,O),I)
                                      & r2_hidden(k5_mcart_4(A,B,C,D,E,F,G,O),J)
                                      & r2_hidden(k6_mcart_4(A,B,C,D,E,F,G,O),K)
                                      & r2_hidden(k7_mcart_4(A,B,C,D,E,F,G,O),L)
                                      & r2_hidden(k8_mcart_4(A,B,C,D,E,F,G,O),M)
                                      & r2_hidden(k9_mcart_4(A,B,C,D,E,F,G,O),N) ) ) ) ) ) ) ) ) ) ) )).

fof(t41_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N] :
      ( ( r1_tarski(A,H)
        & r1_tarski(B,I)
        & r1_tarski(C,J)
        & r1_tarski(D,K)
        & r1_tarski(E,L)
        & r1_tarski(F,M)
        & r1_tarski(G,N) )
     => r1_tarski(k2_mcart_4(A,B,C,D,E,F,G),k2_mcart_4(H,I,J,K,L,M,N)) ) )).

fof(t42_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( m1_subset_1(H,k1_zfmisc_1(A))
     => ! [I] :
          ( m1_subset_1(I,k1_zfmisc_1(B))
         => ! [J] :
              ( m1_subset_1(J,k1_zfmisc_1(C))
             => ! [K] :
                  ( m1_subset_1(K,k1_zfmisc_1(D))
                 => ! [L] :
                      ( m1_subset_1(L,k1_zfmisc_1(E))
                     => ! [M] :
                          ( m1_subset_1(M,k1_zfmisc_1(F))
                         => ! [N] :
                              ( m1_subset_1(N,k1_zfmisc_1(G))
                             => m1_subset_1(k2_mcart_4(H,I,J,K,L,M,N),k1_zfmisc_1(k2_mcart_4(A,B,C,D,E,F,G))) ) ) ) ) ) ) ) )).

fof(dt_k1_mcart_4,axiom,(
    $true )).

fof(dt_k2_mcart_4,axiom,(
    $true )).

fof(dt_k3_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
     => m1_subset_1(k3_mcart_4(A,B,C,D,E,F,G,H),A) ) )).

fof(dt_k4_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
     => m1_subset_1(k4_mcart_4(A,B,C,D,E,F,G,H),B) ) )).

fof(dt_k5_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
     => m1_subset_1(k5_mcart_4(A,B,C,D,E,F,G,H),C) ) )).

fof(dt_k6_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
     => m1_subset_1(k6_mcart_4(A,B,C,D,E,F,G,H),D) ) )).

fof(dt_k7_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
     => m1_subset_1(k7_mcart_4(A,B,C,D,E,F,G,H),E) ) )).

fof(dt_k8_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
     => m1_subset_1(k8_mcart_4(A,B,C,D,E,F,G,H),F) ) )).

fof(dt_k9_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
     => m1_subset_1(k9_mcart_4(A,B,C,D,E,F,G,H),G) ) )).
%------------------------------------------------------------------------------