% Mizar problem: t34_mcart_5,mcart_5,1751,18 
fof(t34_mcart_5,conjecture,(
    ! [A,B,C,D,E,F,G,H,I,J] : 
      ( m1_subset_1(J,k2_mcart_5(B,C,D,E,F,G,H,I))
     => ( ! [K] : 
            ( m1_subset_1(K,B)
           => ! [L] : 
                ( m1_subset_1(L,C)
               => ! [M] : 
                    ( m1_subset_1(M,D)
                   => ! [N] : 
                        ( m1_subset_1(N,E)
                       => ! [O] : 
                            ( m1_subset_1(O,F)
                           => ! [P] : 
                                ( m1_subset_1(P,G)
                               => ! [Q] : 
                                    ( m1_subset_1(Q,H)
                                   => ! [R] : 
                                        ( m1_subset_1(R,I)
                                       => ( J = k1_mcart_5(K,L,M,N,O,P,Q,R)
                                         => 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
          | I = k1_xboole_0
          | A = k6_mcart_5(B,C,D,E,F,G,H,I,J) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,d1_mcart_5,d2_mcart_5,dt_k10_mcart_5,dt_k1_mcart_4,dt_k1_mcart_5,dt_k1_xboole_0,dt_k2_mcart_4,dt_k2_mcart_5,dt_k2_zfmisc_1,dt_k3_mcart_5,dt_k4_mcart_5,dt_k4_tarski,dt_k5_mcart_5,dt_k6_mcart_5,dt_k7_mcart_5,dt_k8_mcart_5,dt_k9_mcart_5,dt_m1_subset_1,existence_m1_subset_1,fc1_xboole_0,rc1_xboole_0,rc2_xboole_0,t1_subset,t25_mcart_5,t2_subset,t6_boole,t7_boole,t8_boole]),
    [file(mcart_5,t34_mcart_5)]).

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

fof(d1_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H] : k1_mcart_5(A,B,C,D,E,F,G,H) = k4_tarski(k1_mcart_4(A,B,C,D,E,F,G),H) ),
    file(mcart_5,d1_mcart_5),
    []).

fof(d2_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H] : k2_mcart_5(A,B,C,D,E,F,G,H) = k2_zfmisc_1(k2_mcart_4(A,B,C,D,E,F,G),H) ),
    file(mcart_5,d2_mcart_5),
    []).

fof(dt_k10_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : 
      ( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
     => m1_subset_1(k10_mcart_5(A,B,C,D,E,F,G,H,I),H) ) ),
    file(mcart_5,k10_mcart_5),
    []).

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

fof(dt_k1_mcart_5,axiom,(
    $true ),
    file(mcart_5,k1_mcart_5),
    []).

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

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

fof(dt_k2_mcart_5,axiom,(
    $true ),
    file(mcart_5,k2_mcart_5),
    []).

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

fof(dt_k3_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : 
      ( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
     => m1_subset_1(k3_mcart_5(A,B,C,D,E,F,G,H,I),A) ) ),
    file(mcart_5,k3_mcart_5),
    []).

fof(dt_k4_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : 
      ( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
     => m1_subset_1(k4_mcart_5(A,B,C,D,E,F,G,H,I),B) ) ),
    file(mcart_5,k4_mcart_5),
    []).

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

fof(dt_k5_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : 
      ( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
     => m1_subset_1(k5_mcart_5(A,B,C,D,E,F,G,H,I),C) ) ),
    file(mcart_5,k5_mcart_5),
    []).

fof(dt_k6_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : 
      ( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
     => m1_subset_1(k6_mcart_5(A,B,C,D,E,F,G,H,I),D) ) ),
    file(mcart_5,k6_mcart_5),
    []).

fof(dt_k7_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : 
      ( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
     => m1_subset_1(k7_mcart_5(A,B,C,D,E,F,G,H,I),E) ) ),
    file(mcart_5,k7_mcart_5),
    []).

fof(dt_k8_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : 
      ( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
     => m1_subset_1(k8_mcart_5(A,B,C,D,E,F,G,H,I),F) ) ),
    file(mcart_5,k8_mcart_5),
    []).

fof(dt_k9_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : 
      ( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
     => m1_subset_1(k9_mcart_5(A,B,C,D,E,F,G,H,I),G) ) ),
    file(mcart_5,k9_mcart_5),
    []).

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(t25_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H] : ~ ( 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] : 
            ( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
           => I = k1_mcart_5(k3_mcart_5(A,B,C,D,E,F,G,H,I),k4_mcart_5(A,B,C,D,E,F,G,H,I),k5_mcart_5(A,B,C,D,E,F,G,H,I),k6_mcart_5(A,B,C,D,E,F,G,H,I),k7_mcart_5(A,B,C,D,E,F,G,H,I),k8_mcart_5(A,B,C,D,E,F,G,H,I),k9_mcart_5(A,B,C,D,E,F,G,H,I),k10_mcart_5(A,B,C,D,E,F,G,H,I)) ) ) ),
    file(mcart_5,t25_mcart_5),
    []).

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),
    []).