% Mizar problem: t62_mcart_1,mcart_1,1221,45 
fof(t62_mcart_1,conjecture,(
    ! [A,B,C,D] : ~ ( A != k1_xboole_0
      & B != k1_xboole_0
      & C != k1_xboole_0
      & D != k1_xboole_0
      & ~ ! [E] : 
            ( m1_subset_1(E,k4_zfmisc_1(A,B,C,D))
           => ( E != k8_mcart_1(A,B,C,D,E)
              & E != k9_mcart_1(A,B,C,D,E)
              & E != k10_mcart_1(A,B,C,D,E)
              & E != k11_mcart_1(A,B,C,D,E) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,commutativity_k2_tarski,d2_tarski,d3_mcart_1,d4_mcart_1,d5_tarski,dt_k10_mcart_1,dt_k11_mcart_1,dt_k1_mcart_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_mcart_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k3_mcart_1,dt_k3_zfmisc_1,dt_k4_mcart_1,dt_k4_tarski,dt_k4_zfmisc_1,dt_k5_mcart_1,dt_k6_mcart_1,dt_k7_mcart_1,dt_k8_mcart_1,dt_k9_mcart_1,dt_m1_subset_1,existence_m1_subset_1,fc1_xboole_0,fc1_zfmisc_1,rc1_xboole_0,rc2_xboole_0,t113_zfmisc_1,t1_subset,t2_subset,t50_mcart_1,t51_mcart_1,t54_mcart_1,t60_mcart_1,t61_mcart_1,t6_boole,t6_ordinal1,t7_boole,t8_boole]),
    [file(mcart_1,t62_mcart_1)]).

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

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(d2_tarski,axiom,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    []).

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(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

fof(dt_k10_mcart_1,axiom,(
    ! [A,B,C,D,E] : 
      ( m1_subset_1(E,k4_zfmisc_1(A,B,C,D))
     => m1_subset_1(k10_mcart_1(A,B,C,D,E),C) ) ),
    file(mcart_1,k10_mcart_1),
    []).

fof(dt_k11_mcart_1,axiom,(
    ! [A,B,C,D,E] : 
      ( m1_subset_1(E,k4_zfmisc_1(A,B,C,D))
     => m1_subset_1(k11_mcart_1(A,B,C,D,E),D) ) ),
    file(mcart_1,k11_mcart_1),
    []).

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

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

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_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

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_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k3_zfmisc_1),
    []).

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

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_1,axiom,(
    ! [A,B,C,D] : 
      ( m1_subset_1(D,k3_zfmisc_1(A,B,C))
     => m1_subset_1(k5_mcart_1(A,B,C,D),A) ) ),
    file(mcart_1,k5_mcart_1),
    []).

fof(dt_k6_mcart_1,axiom,(
    ! [A,B,C,D] : 
      ( m1_subset_1(D,k3_zfmisc_1(A,B,C))
     => m1_subset_1(k6_mcart_1(A,B,C,D),B) ) ),
    file(mcart_1,k6_mcart_1),
    []).

fof(dt_k7_mcart_1,axiom,(
    ! [A,B,C,D] : 
      ( m1_subset_1(D,k3_zfmisc_1(A,B,C))
     => m1_subset_1(k7_mcart_1(A,B,C,D),C) ) ),
    file(mcart_1,k7_mcart_1),
    []).

fof(dt_k8_mcart_1,axiom,(
    ! [A,B,C,D,E] : 
      ( m1_subset_1(E,k4_zfmisc_1(A,B,C,D))
     => m1_subset_1(k8_mcart_1(A,B,C,D,E),A) ) ),
    file(mcart_1,k8_mcart_1),
    []).

fof(dt_k9_mcart_1,axiom,(
    ! [A,B,C,D,E] : 
      ( m1_subset_1(E,k4_zfmisc_1(A,B,C,D))
     => m1_subset_1(k9_mcart_1(A,B,C,D,E),B) ) ),
    file(mcart_1,k9_mcart_1),
    []).

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(fc1_zfmisc_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k4_tarski(A,B)) ),
    file(zfmisc_1,fc1_zfmisc_1),
    []).

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(t113_zfmisc_1,axiom,(
    ! [A,B] : 
      ( k2_zfmisc_1(A,B) = k1_xboole_0
    <=> ( A = k1_xboole_0
        | B = k1_xboole_0 ) ) ),
    file(zfmisc_1,t113_zfmisc_1),
    []).

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(t50_mcart_1,axiom,(
    ! [A,B,C] : ~ ( A != k1_xboole_0
      & B != k1_xboole_0
      & C != k1_xboole_0
      & ~ ! [D] : 
            ( m1_subset_1(D,k3_zfmisc_1(A,B,C))
           => ( k5_mcart_1(A,B,C,D) = k1_mcart_1(k1_mcart_1(D))
              & k6_mcart_1(A,B,C,D) = k2_mcart_1(k1_mcart_1(D))
              & k7_mcart_1(A,B,C,D) = k2_mcart_1(D) ) ) ) ),
    file(mcart_1,t50_mcart_1),
    []).

fof(t51_mcart_1,axiom,(
    ! [A,B,C] : ~ ( A != k1_xboole_0
      & B != k1_xboole_0
      & C != k1_xboole_0
      & ~ ! [D] : 
            ( m1_subset_1(D,k3_zfmisc_1(A,B,C))
           => ( D != k5_mcart_1(A,B,C,D)
              & D != k6_mcart_1(A,B,C,D)
              & D != k7_mcart_1(A,B,C,D) ) ) ) ),
    file(mcart_1,t51_mcart_1),
    []).

fof(t54_mcart_1,axiom,(
    ! [A,B,C,D] : k3_zfmisc_1(k2_zfmisc_1(A,B),C,D) = k4_zfmisc_1(A,B,C,D) ),
    file(mcart_1,t54_mcart_1),
    []).

fof(t60_mcart_1,axiom,(
    ! [A,B,C,D] : ~ ( A != k1_xboole_0
      & B != k1_xboole_0
      & C != k1_xboole_0
      & D != k1_xboole_0
      & ~ ! [E] : 
            ( m1_subset_1(E,k4_zfmisc_1(A,B,C,D))
           => E = k4_mcart_1(k8_mcart_1(A,B,C,D,E),k9_mcart_1(A,B,C,D,E),k10_mcart_1(A,B,C,D,E),k11_mcart_1(A,B,C,D,E)) ) ) ),
    file(mcart_1,t60_mcart_1),
    []).

fof(t61_mcart_1,axiom,(
    ! [A,B,C,D] : ~ ( A != k1_xboole_0
      & B != k1_xboole_0
      & C != k1_xboole_0
      & D != k1_xboole_0
      & ~ ! [E] : 
            ( m1_subset_1(E,k4_zfmisc_1(A,B,C,D))
           => ( k8_mcart_1(A,B,C,D,E) = k1_mcart_1(k1_mcart_1(k1_mcart_1(E)))
              & k9_mcart_1(A,B,C,D,E) = k2_mcart_1(k1_mcart_1(k1_mcart_1(E)))
              & k10_mcart_1(A,B,C,D,E) = k2_mcart_1(k1_mcart_1(E))
              & k11_mcart_1(A,B,C,D,E) = k2_mcart_1(E) ) ) ) ),
    file(mcart_1,t61_mcart_1),
    []).

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

fof(t6_ordinal1,axiom,(
    ! [A,B,C,D,E,F] : ~ ( r2_hidden(A,B)
      & r2_hidden(B,C)
      & r2_hidden(C,D)
      & r2_hidden(D,E)
      & r2_hidden(E,F)
      & r2_hidden(F,A) ) ),
    file(ordinal1,t6_ordinal1),
    []).

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),
    []).