% Mizar problem: t23_mcart_4,mcart_4,1144,40 
fof(t23_mcart_4,conjecture,(
    ! [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)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,d1_mcart_4,d2_mcart_4,d3_mcart_4,d4_mcart_4,d5_mcart_4,d6_mcart_4,d7_mcart_4,d8_mcart_4,d9_mcart_4,dt_k1_mcart_3,dt_k1_mcart_4,dt_k1_xboole_0,dt_k2_mcart_3,dt_k2_mcart_4,dt_k2_zfmisc_1,dt_k3_mcart_4,dt_k4_mcart_4,dt_k4_tarski,dt_k5_mcart_4,dt_k6_mcart_4,dt_k7_mcart_4,dt_k8_mcart_4,dt_k9_mcart_4,dt_m1_subset_1,existence_m1_subset_1,fc1_xboole_0,rc1_xboole_0,rc2_xboole_0,t1_subset,t21_mcart_4,t2_subset,t6_boole,t7_boole,t8_boole]),
    [file(mcart_4,t23_mcart_4)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

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) ),
    file(mcart_4,d1_mcart_4),
    []).

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) ),
    file(mcart_4,d2_mcart_4),
    []).

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 ) ) ) ) ) ),
    file(mcart_4,d3_mcart_4),
    []).

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 ) ) ) ) ) ),
    file(mcart_4,d4_mcart_4),
    []).

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 ) ) ) ) ) ),
    file(mcart_4,d5_mcart_4),
    []).

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 ) ) ) ) ) ),
    file(mcart_4,d6_mcart_4),
    []).

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 ) ) ) ) ) ),
    file(mcart_4,d7_mcart_4),
    []).

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 ) ) ) ) ) ),
    file(mcart_4,d8_mcart_4),
    []).

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 ) ) ) ) ) ),
    file(mcart_4,d9_mcart_4),
    []).

fof(dt_k1_mcart_3,axiom,(
    $true ),
    file(mcart_3,k1_mcart_3),
    []).

fof(dt_k1_mcart_4,axiom,(
    $true ),
    file(mcart_4,k1_mcart_4),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k2_mcart_3,axiom,(
    $true ),
    file(mcart_3,k2_mcart_3),
    []).

fof(dt_k2_mcart_4,axiom,(
    $true ),
    file(mcart_4,k2_mcart_4),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

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) ) ),
    file(mcart_4,k3_mcart_4),
    []).

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) ) ),
    file(mcart_4,k4_mcart_4),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

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) ) ),
    file(mcart_4,k5_mcart_4),
    []).

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) ) ),
    file(mcart_4,k6_mcart_4),
    []).

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) ) ),
    file(mcart_4,k7_mcart_4),
    []).

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) ) ),
    file(mcart_4,k8_mcart_4),
    []).

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) ) ),
    file(mcart_4,k9_mcart_4),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

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) ) ) ) ) ) ) ) ) ) ),
    file(mcart_4,t21_mcart_4),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).