% Mizar problem: t21_mcart_2,mcart_2,751,16 
fof(t21_mcart_2,conjecture,(
    ! [A,B,C,D,E] : 
      ( ~ ( ~ r1_tarski(A,k2_mcart_2(A,B,C,D,E))
          & ~ r1_tarski(A,k2_mcart_2(B,C,D,E,A))
          & ~ r1_tarski(A,k2_mcart_2(C,D,E,A,B))
          & ~ r1_tarski(A,k2_mcart_2(D,E,A,B,C))
          & ~ r1_tarski(A,k2_mcart_2(E,A,B,C,D)) )
     => A = k1_xboole_0 ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,d1_mcart_2,d2_mcart_2,dt_k1_mcart_2,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_mcart_2,dt_k2_zfmisc_1,dt_k3_mcart_2,dt_k4_mcart_1,dt_k4_mcart_2,dt_k4_tarski,dt_k4_zfmisc_1,dt_k5_mcart_2,dt_k6_mcart_2,dt_k7_mcart_2,dt_m1_subset_1,existence_m1_subset_1,fc1_xboole_0,rc1_xboole_0,rc2_xboole_0,reflexivity_r1_tarski,t12_mcart_2,t13_mcart_2,t19_mcart_2,t1_subset,t2_subset,t3_subset,t3_xboole_1,t4_subset,t5_subset,t63_mcart_1,t6_boole,t7_boole,t8_boole,t8_mcart_2]),
    [file(mcart_2,t21_mcart_2)]).

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(d2_mcart_2,axiom,(
    ! [A,B,C,D,E] : k2_mcart_2(A,B,C,D,E) = k2_zfmisc_1(k4_zfmisc_1(A,B,C,D),E) ),
    file(mcart_2,d2_mcart_2),
    []).

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

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

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_mcart_2,axiom,(
    $true ),
    file(mcart_2,k2_mcart_2),
    []).

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

fof(dt_k3_mcart_2,axiom,(
    ! [A,B,C,D,E,F] : 
      ( m1_subset_1(F,k2_mcart_2(A,B,C,D,E))
     => m1_subset_1(k3_mcart_2(A,B,C,D,E,F),A) ) ),
    file(mcart_2,k3_mcart_2),
    []).

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

fof(dt_k4_mcart_2,axiom,(
    ! [A,B,C,D,E,F] : 
      ( m1_subset_1(F,k2_mcart_2(A,B,C,D,E))
     => m1_subset_1(k4_mcart_2(A,B,C,D,E,F),B) ) ),
    file(mcart_2,k4_mcart_2),
    []).

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

fof(dt_k4_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k4_zfmisc_1),
    []).

fof(dt_k5_mcart_2,axiom,(
    ! [A,B,C,D,E,F] : 
      ( m1_subset_1(F,k2_mcart_2(A,B,C,D,E))
     => m1_subset_1(k5_mcart_2(A,B,C,D,E,F),C) ) ),
    file(mcart_2,k5_mcart_2),
    []).

fof(dt_k6_mcart_2,axiom,(
    ! [A,B,C,D,E,F] : 
      ( m1_subset_1(F,k2_mcart_2(A,B,C,D,E))
     => m1_subset_1(k6_mcart_2(A,B,C,D,E,F),D) ) ),
    file(mcart_2,k6_mcart_2),
    []).

fof(dt_k7_mcart_2,axiom,(
    ! [A,B,C,D,E,F] : 
      ( m1_subset_1(F,k2_mcart_2(A,B,C,D,E))
     => m1_subset_1(k7_mcart_2(A,B,C,D,E,F),E) ) ),
    file(mcart_2,k7_mcart_2),
    []).

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(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(t12_mcart_2,axiom,(
    ! [A,B,C,D,E] : k2_mcart_2(A,B,C,D,E) = k4_zfmisc_1(k2_zfmisc_1(A,B),C,D,E) ),
    file(mcart_2,t12_mcart_2),
    []).

fof(t13_mcart_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( A != k1_xboole_0
        & B != k1_xboole_0
        & C != k1_xboole_0
        & D != k1_xboole_0
        & E != k1_xboole_0 )
    <=> k2_mcart_2(A,B,C,D,E) != k1_xboole_0 ) ),
    file(mcart_2,t13_mcart_2),
    []).

fof(t19_mcart_2,axiom,(
    ! [A,B,C,D,E] : ~ ( A != k1_xboole_0
      & B != k1_xboole_0
      & C != k1_xboole_0
      & D != k1_xboole_0
      & E != k1_xboole_0
      & ~ ! [F] : 
            ( m1_subset_1(F,k2_mcart_2(A,B,C,D,E))
           => F = k1_mcart_2(k3_mcart_2(A,B,C,D,E,F),k4_mcart_2(A,B,C,D,E,F),k5_mcart_2(A,B,C,D,E,F),k6_mcart_2(A,B,C,D,E,F),k7_mcart_2(A,B,C,D,E,F)) ) ) ),
    file(mcart_2,t19_mcart_2),
    []).

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

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

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t3_xboole_1,axiom,(
    ! [A] : 
      ( r1_tarski(A,k1_xboole_0)
     => A = k1_xboole_0 ) ),
    file(xboole_1,t3_xboole_1),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t63_mcart_1,axiom,(
    ! [A,B,C,D] : 
      ( ~ ( ~ r1_tarski(A,k4_zfmisc_1(A,B,C,D))
          & ~ r1_tarski(A,k4_zfmisc_1(B,C,D,A))
          & ~ r1_tarski(A,k4_zfmisc_1(C,D,A,B))
          & ~ r1_tarski(A,k4_zfmisc_1(D,A,B,C)) )
     => A = k1_xboole_0 ) ),
    file(mcart_1,t63_mcart_1),
    []).

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),
    []).

fof(t8_mcart_2,axiom,(
    ! [A] : ~ ( A != k1_xboole_0
      & ! [B] : ~ ( r2_hidden(B,A)
          & ! [C,D,E,F,G] : ~ ( ( r2_hidden(C,A)
                | r2_hidden(D,A) )
              & B = k1_mcart_2(C,D,E,F,G) ) ) ) ),
    file(mcart_2,t8_mcart_2),
    []).