% Mizar problem: t26_mcart_3,mcart_3,1108,12 
fof(t26_mcart_3,conjecture,(
    ! [A,B,C,D,E,F,G] : 
      ( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
     => ~ ( A != k1_xboole_0
          & B != k1_xboole_0
          & C != k1_xboole_0
          & D != k1_xboole_0
          & E != k1_xboole_0
          & F != k1_xboole_0
          & ? [H,I,J,K,L,M] : 
              ( G = k1_mcart_3(H,I,J,K,L,M)
              & ~ ( k3_mcart_3(A,B,C,D,E,F,G) = H
                  & k4_mcart_3(A,B,C,D,E,F,G) = I
                  & k5_mcart_3(A,B,C,D,E,F,G) = J
                  & k6_mcart_3(A,B,C,D,E,F,G) = K
                  & k7_mcart_3(A,B,C,D,E,F,G) = L
                  & k8_mcart_3(A,B,C,D,E,F,G) = M ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,t1_subset,dt_k1_mcart_2,dt_k2_mcart_2,dt_k2_zfmisc_1,dt_k4_tarski,rc1_xboole_0,rc2_xboole_0,t2_subset,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_mcart_3,dt_k1_xboole_0,dt_k2_mcart_3,dt_k3_mcart_3,dt_k4_mcart_3,dt_k5_mcart_3,dt_k6_mcart_3,dt_k7_mcart_3,dt_k8_mcart_3,dt_m1_subset_1,fc1_xboole_0,t6_boole,d1_mcart_3,d2_mcart_3,d3_mcart_3,d4_mcart_3,d5_mcart_3,d6_mcart_3,d7_mcart_3,d8_mcart_3]),
    [file(mcart_3,t26_mcart_3)]).

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_k1_mcart_2,axiom,(
    $true ),
    file(mcart_2,k1_mcart_2),
    []).

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_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

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_3,axiom,(
    $true ),
    file(mcart_3,k1_mcart_3),
    []).

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

fof(dt_k2_mcart_3,axiom,(
    $true ),
    file(mcart_3,k2_mcart_3),
    []).

fof(dt_k3_mcart_3,axiom,(
    ! [A,B,C,D,E,F,G] : 
      ( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
     => m1_subset_1(k3_mcart_3(A,B,C,D,E,F,G),A) ) ),
    file(mcart_3,k3_mcart_3),
    []).

fof(dt_k4_mcart_3,axiom,(
    ! [A,B,C,D,E,F,G] : 
      ( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
     => m1_subset_1(k4_mcart_3(A,B,C,D,E,F,G),B) ) ),
    file(mcart_3,k4_mcart_3),
    []).

fof(dt_k5_mcart_3,axiom,(
    ! [A,B,C,D,E,F,G] : 
      ( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
     => m1_subset_1(k5_mcart_3(A,B,C,D,E,F,G),C) ) ),
    file(mcart_3,k5_mcart_3),
    []).

fof(dt_k6_mcart_3,axiom,(
    ! [A,B,C,D,E,F,G] : 
      ( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
     => m1_subset_1(k6_mcart_3(A,B,C,D,E,F,G),D) ) ),
    file(mcart_3,k6_mcart_3),
    []).

fof(dt_k7_mcart_3,axiom,(
    ! [A,B,C,D,E,F,G] : 
      ( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
     => m1_subset_1(k7_mcart_3(A,B,C,D,E,F,G),E) ) ),
    file(mcart_3,k7_mcart_3),
    []).

fof(dt_k8_mcart_3,axiom,(
    ! [A,B,C,D,E,F,G] : 
      ( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
     => m1_subset_1(k8_mcart_3(A,B,C,D,E,F,G),F) ) ),
    file(mcart_3,k8_mcart_3),
    []).

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_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(d2_mcart_3,axiom,(
    ! [A,B,C,D,E,F] : k2_mcart_3(A,B,C,D,E,F) = k2_zfmisc_1(k2_mcart_2(A,B,C,D,E),F) ),
    file(mcart_3,d2_mcart_3),
    []).

fof(d3_mcart_3,axiom,(
    ! [A,B,C,D,E,F] : ~ ( 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] : 
            ( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
           => ! [H] : 
                ( m1_subset_1(H,A)
               => ( H = k3_mcart_3(A,B,C,D,E,F,G)
                <=> ! [I,J,K,L,M,N] : 
                      ( G = k1_mcart_3(I,J,K,L,M,N)
                     => H = I ) ) ) ) ) ),
    file(mcart_3,d3_mcart_3),
    []).

fof(d4_mcart_3,axiom,(
    ! [A,B,C,D,E,F] : ~ ( 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] : 
            ( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
           => ! [H] : 
                ( m1_subset_1(H,B)
               => ( H = k4_mcart_3(A,B,C,D,E,F,G)
                <=> ! [I,J,K,L,M,N] : 
                      ( G = k1_mcart_3(I,J,K,L,M,N)
                     => H = J ) ) ) ) ) ),
    file(mcart_3,d4_mcart_3),
    []).

fof(d5_mcart_3,axiom,(
    ! [A,B,C,D,E,F] : ~ ( 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] : 
            ( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
           => ! [H] : 
                ( m1_subset_1(H,C)
               => ( H = k5_mcart_3(A,B,C,D,E,F,G)
                <=> ! [I,J,K,L,M,N] : 
                      ( G = k1_mcart_3(I,J,K,L,M,N)
                     => H = K ) ) ) ) ) ),
    file(mcart_3,d5_mcart_3),
    []).

fof(d6_mcart_3,axiom,(
    ! [A,B,C,D,E,F] : ~ ( 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] : 
            ( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
           => ! [H] : 
                ( m1_subset_1(H,D)
               => ( H = k6_mcart_3(A,B,C,D,E,F,G)
                <=> ! [I,J,K,L,M,N] : 
                      ( G = k1_mcart_3(I,J,K,L,M,N)
                     => H = L ) ) ) ) ) ),
    file(mcart_3,d6_mcart_3),
    []).

fof(d7_mcart_3,axiom,(
    ! [A,B,C,D,E,F] : ~ ( 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] : 
            ( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
           => ! [H] : 
                ( m1_subset_1(H,E)
               => ( H = k7_mcart_3(A,B,C,D,E,F,G)
                <=> ! [I,J,K,L,M,N] : 
                      ( G = k1_mcart_3(I,J,K,L,M,N)
                     => H = M ) ) ) ) ) ),
    file(mcart_3,d7_mcart_3),
    []).

fof(d8_mcart_3,axiom,(
    ! [A,B,C,D,E,F] : ~ ( 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] : 
            ( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
           => ! [H] : 
                ( m1_subset_1(H,F)
               => ( H = k8_mcart_3(A,B,C,D,E,F,G)
                <=> ! [I,J,K,L,M,N] : 
                      ( G = k1_mcart_3(I,J,K,L,M,N)
                     => H = N ) ) ) ) ) ),
    file(mcart_3,d8_mcart_3),
    []).