% Mizar problem: t27_mcart_5,mcart_5,1569,16 
fof(t27_mcart_5,conjecture,(
    ! [A,B,C,D,E,F,G,H] : 
      ( ~ ( ~ r1_tarski(A,k2_mcart_5(A,B,C,D,E,F,G,H))
          & ~ r1_tarski(A,k2_mcart_5(B,C,D,E,F,G,H,A))
          & ~ r1_tarski(A,k2_mcart_5(C,D,E,F,G,H,A,B))
          & ~ r1_tarski(A,k2_mcart_5(D,E,F,G,H,A,B,C))
          & ~ r1_tarski(A,k2_mcart_5(E,F,G,H,A,B,C,D))
          & ~ r1_tarski(A,k2_mcart_5(F,G,H,A,B,C,D,E))
          & ~ r1_tarski(A,k2_mcart_5(G,H,A,B,C,D,E,F))
          & ~ r1_tarski(A,k2_mcart_5(H,A,B,C,D,E,F,G)) )
     => A = k1_xboole_0 ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,d1_mcart_5,d2_mcart_5,dt_k10_mcart_5,dt_k1_mcart_4,dt_k1_mcart_5,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_mcart_4,dt_k2_mcart_5,dt_k2_zfmisc_1,dt_k3_mcart_5,dt_k4_mcart_5,dt_k4_tarski,dt_k5_mcart_5,dt_k6_mcart_5,dt_k7_mcart_5,dt_k8_mcart_5,dt_k9_mcart_5,dt_m1_subset_1,existence_m1_subset_1,fc1_xboole_0,rc1_xboole_0,rc2_xboole_0,reflexivity_r1_tarski,t11_mcart_5,t18_mcart_5,t19_mcart_5,t1_subset,t25_mcart_4,t25_mcart_5,t2_subset,t3_subset,t3_xboole_1,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(mcart_5,t27_mcart_5)]).

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

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(d2_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H] : k2_mcart_5(A,B,C,D,E,F,G,H) = k2_zfmisc_1(k2_mcart_4(A,B,C,D,E,F,G),H) ),
    file(mcart_5,d2_mcart_5),
    []).

fof(dt_k10_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : 
      ( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
     => m1_subset_1(k10_mcart_5(A,B,C,D,E,F,G,H,I),H) ) ),
    file(mcart_5,k10_mcart_5),
    []).

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_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_4,axiom,(
    $true ),
    file(mcart_4,k2_mcart_4),
    []).

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

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

fof(dt_k3_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : 
      ( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
     => m1_subset_1(k3_mcart_5(A,B,C,D,E,F,G,H,I),A) ) ),
    file(mcart_5,k3_mcart_5),
    []).

fof(dt_k4_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : 
      ( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
     => m1_subset_1(k4_mcart_5(A,B,C,D,E,F,G,H,I),B) ) ),
    file(mcart_5,k4_mcart_5),
    []).

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

fof(dt_k5_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : 
      ( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
     => m1_subset_1(k5_mcart_5(A,B,C,D,E,F,G,H,I),C) ) ),
    file(mcart_5,k5_mcart_5),
    []).

fof(dt_k6_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : 
      ( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
     => m1_subset_1(k6_mcart_5(A,B,C,D,E,F,G,H,I),D) ) ),
    file(mcart_5,k6_mcart_5),
    []).

fof(dt_k7_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : 
      ( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
     => m1_subset_1(k7_mcart_5(A,B,C,D,E,F,G,H,I),E) ) ),
    file(mcart_5,k7_mcart_5),
    []).

fof(dt_k8_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : 
      ( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
     => m1_subset_1(k8_mcart_5(A,B,C,D,E,F,G,H,I),F) ) ),
    file(mcart_5,k8_mcart_5),
    []).

fof(dt_k9_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : 
      ( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
     => m1_subset_1(k9_mcart_5(A,B,C,D,E,F,G,H,I),G) ) ),
    file(mcart_5,k9_mcart_5),
    []).

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(t11_mcart_5,axiom,(
    ! [A] : ~ ( A != k1_xboole_0
      & ! [B] : ~ ( r2_hidden(B,A)
          & ! [C,D,E,F,G,H,I,J] : ~ ( ( r2_hidden(C,A)
                | r2_hidden(D,A) )
              & B = k1_mcart_5(C,D,E,F,G,H,I,J) ) ) ) ),
    file(mcart_5,t11_mcart_5),
    []).

fof(t18_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H] : k2_mcart_5(A,B,C,D,E,F,G,H) = k2_mcart_4(k2_zfmisc_1(A,B),C,D,E,F,G,H) ),
    file(mcart_5,t18_mcart_5),
    []).

fof(t19_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H] : 
      ( ( 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 )
    <=> k2_mcart_5(A,B,C,D,E,F,G,H) != k1_xboole_0 ) ),
    file(mcart_5,t19_mcart_5),
    []).

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

fof(t25_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] : 
      ( ~ ( ~ r1_tarski(A,k2_mcart_4(A,B,C,D,E,F,G))
          & ~ r1_tarski(A,k2_mcart_4(B,C,D,E,F,G,A))
          & ~ r1_tarski(A,k2_mcart_4(C,D,E,F,G,A,B))
          & ~ r1_tarski(A,k2_mcart_4(D,E,F,G,A,B,C))
          & ~ r1_tarski(A,k2_mcart_4(E,F,G,A,B,C,D))
          & ~ r1_tarski(A,k2_mcart_4(F,G,A,B,C,D,E))
          & ~ r1_tarski(A,k2_mcart_4(G,A,B,C,D,E,F)) )
     => A = k1_xboole_0 ) ),
    file(mcart_4,t25_mcart_4),
    []).

fof(t25_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H] : ~ ( 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] : 
            ( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
           => I = k1_mcart_5(k3_mcart_5(A,B,C,D,E,F,G,H,I),k4_mcart_5(A,B,C,D,E,F,G,H,I),k5_mcart_5(A,B,C,D,E,F,G,H,I),k6_mcart_5(A,B,C,D,E,F,G,H,I),k7_mcart_5(A,B,C,D,E,F,G,H,I),k8_mcart_5(A,B,C,D,E,F,G,H,I),k9_mcart_5(A,B,C,D,E,F,G,H,I),k10_mcart_5(A,B,C,D,E,F,G,H,I)) ) ) ),
    file(mcart_5,t25_mcart_5),
    []).

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(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),
    []).