% Mizar problem: t27_mcart_6,mcart_6,1695,15 
fof(t27_mcart_6,conjecture,(
    ! [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) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,d1_mcart_2,d1_mcart_3,d1_mcart_4,d1_mcart_5,d1_mcart_6,d2_mcart_6,d3_mcart_1,d4_mcart_1,dt_k10_mcart_6,dt_k11_mcart_6,dt_k1_mcart_1,dt_k1_mcart_2,dt_k1_mcart_3,dt_k1_mcart_4,dt_k1_mcart_5,dt_k1_mcart_6,dt_k1_xboole_0,dt_k2_mcart_1,dt_k2_mcart_5,dt_k2_mcart_6,dt_k2_zfmisc_1,dt_k3_mcart_1,dt_k3_mcart_6,dt_k4_mcart_1,dt_k4_mcart_6,dt_k4_tarski,dt_k5_mcart_6,dt_k6_mcart_6,dt_k7_mcart_6,dt_k8_mcart_6,dt_k9_mcart_6,dt_m1_subset_1,existence_m1_subset_1,fc1_xboole_0,rc1_xboole_0,rc2_xboole_0,t1_subset,t26_mcart_6,t2_subset,t6_boole,t7_boole,t7_mcart_1,t8_boole]),
    [file(mcart_6,t27_mcart_6)]).

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

fof(d1_mcart_2,axiom,(
    ! [A,B,C,D,E] : k1_mcart_2(A,B,C,D,E) = k4_tarski(k4_mcart_1(A,B,C,D),E) ),
    file(mcart_2,d1_mcart_2),
    []).

fof(d1_mcart_3,axiom,(
    ! [A,B,C,D,E,F] : k1_mcart_3(A,B,C,D,E,F) = k4_tarski(k1_mcart_2(A,B,C,D,E),F) ),
    file(mcart_3,d1_mcart_3),
    []).

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(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(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) ),
    file(mcart_6,d1_mcart_6),
    []).

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) ),
    file(mcart_6,d2_mcart_6),
    []).

fof(d3_mcart_1,axiom,(
    ! [A,B,C] : k3_mcart_1(A,B,C) = k4_tarski(k4_tarski(A,B),C) ),
    file(mcart_1,d3_mcart_1),
    []).

fof(d4_mcart_1,axiom,(
    ! [A,B,C,D] : k4_mcart_1(A,B,C,D) = k4_tarski(k3_mcart_1(A,B,C),D) ),
    file(mcart_1,d4_mcart_1),
    []).

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) ) ),
    file(mcart_6,k10_mcart_6),
    []).

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) ) ),
    file(mcart_6,k11_mcart_6),
    []).

fof(dt_k1_mcart_1,axiom,(
    $true ),
    file(mcart_1,k1_mcart_1),
    []).

fof(dt_k1_mcart_2,axiom,(
    $true ),
    file(mcart_2,k1_mcart_2),
    []).

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_mcart_5,axiom,(
    $true ),
    file(mcart_5,k1_mcart_5),
    []).

fof(dt_k1_mcart_6,axiom,(
    $true ),
    file(mcart_6,k1_mcart_6),
    []).

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

fof(dt_k2_mcart_1,axiom,(
    $true ),
    file(mcart_1,k2_mcart_1),
    []).

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

fof(dt_k2_mcart_6,axiom,(
    $true ),
    file(mcart_6,k2_mcart_6),
    []).

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

fof(dt_k3_mcart_1,axiom,(
    $true ),
    file(mcart_1,k3_mcart_1),
    []).

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) ) ),
    file(mcart_6,k3_mcart_6),
    []).

fof(dt_k4_mcart_1,axiom,(
    $true ),
    file(mcart_1,k4_mcart_1),
    []).

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) ) ),
    file(mcart_6,k4_mcart_6),
    []).

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

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) ) ),
    file(mcart_6,k5_mcart_6),
    []).

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) ) ),
    file(mcart_6,k6_mcart_6),
    []).

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) ) ),
    file(mcart_6,k7_mcart_6),
    []).

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) ) ),
    file(mcart_6,k8_mcart_6),
    []).

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) ) ),
    file(mcart_6,k9_mcart_6),
    []).

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(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)) ) ) ),
    file(mcart_6,t26_mcart_6),
    []).

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(t7_mcart_1,axiom,(
    ! [A,B] : 
      ( k1_mcart_1(k4_tarski(A,B)) = A
      & k2_mcart_1(k4_tarski(A,B)) = B ) ),
    file(mcart_1,t7_mcart_1),
    []).

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