% Mizar problem: t18_mcart_2,mcart_2,681,50 
fof(t18_mcart_2,conjecture,(
    ! [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))
          & ? [G,H,I,J,K] : 
              ( F = k1_mcart_2(G,H,I,J,K)
              & ~ ( k3_mcart_2(A,B,C,D,E,F) = G
                  & k4_mcart_2(A,B,C,D,E,F) = H
                  & k5_mcart_2(A,B,C,D,E,F) = I
                  & k6_mcart_2(A,B,C,D,E,F) = J
                  & k7_mcart_2(A,B,C,D,E,F) = K ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,t1_subset,dt_k2_zfmisc_1,dt_k4_mcart_1,dt_k4_tarski,dt_k4_zfmisc_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_mcart_2,dt_k1_xboole_0,dt_k2_mcart_2,dt_k3_mcart_2,dt_k4_mcart_2,dt_k5_mcart_2,dt_k6_mcart_2,dt_k7_mcart_2,dt_m1_subset_1,fc1_xboole_0,t6_boole,d1_mcart_2,d2_mcart_2,d3_mcart_2,d4_mcart_2,d5_mcart_2,d6_mcart_2,d7_mcart_2]),
    [file(mcart_2,t18_mcart_2)]).

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

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

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_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(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(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

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

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_k2_mcart_2,axiom,(
    $true ),
    file(mcart_2,k2_mcart_2),
    []).

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

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

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(d3_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))
           => ! [G] : 
                ( m1_subset_1(G,A)
               => ( G = k3_mcart_2(A,B,C,D,E,F)
                <=> ! [H,I,J,K,L] : 
                      ( F = k1_mcart_2(H,I,J,K,L)
                     => G = H ) ) ) ) ) ),
    file(mcart_2,d3_mcart_2),
    []).

fof(d4_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))
           => ! [G] : 
                ( m1_subset_1(G,B)
               => ( G = k4_mcart_2(A,B,C,D,E,F)
                <=> ! [H,I,J,K,L] : 
                      ( F = k1_mcart_2(H,I,J,K,L)
                     => G = I ) ) ) ) ) ),
    file(mcart_2,d4_mcart_2),
    []).

fof(d5_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))
           => ! [G] : 
                ( m1_subset_1(G,C)
               => ( G = k5_mcart_2(A,B,C,D,E,F)
                <=> ! [H,I,J,K,L] : 
                      ( F = k1_mcart_2(H,I,J,K,L)
                     => G = J ) ) ) ) ) ),
    file(mcart_2,d5_mcart_2),
    []).

fof(d6_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))
           => ! [G] : 
                ( m1_subset_1(G,D)
               => ( G = k6_mcart_2(A,B,C,D,E,F)
                <=> ! [H,I,J,K,L] : 
                      ( F = k1_mcart_2(H,I,J,K,L)
                     => G = K ) ) ) ) ) ),
    file(mcart_2,d6_mcart_2),
    []).

fof(d7_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))
           => ! [G] : 
                ( m1_subset_1(G,E)
               => ( G = k7_mcart_2(A,B,C,D,E,F)
                <=> ! [H,I,J,K,L] : 
                      ( F = k1_mcart_2(H,I,J,K,L)
                     => G = L ) ) ) ) ) ),
    file(mcart_2,d7_mcart_2),
    []).