% Mizar problem: t8_recdef_2,recdef_2,267,60 
fof(t8_recdef_2,conjecture,(
    ! [A,B,C,D,E,F] : 
      ( r2_hidden(A,k2_mcart_2(B,C,D,E,F))
     => ( r2_hidden(k8_recdef_2(A),B)
        & r2_hidden(k9_recdef_2(A),C)
        & r2_hidden(k10_recdef_2(A),D)
        & r2_hidden(k11_recdef_2(A),E)
        & r2_hidden(k12_recdef_2(A),F) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,d10_recdef_2,d11_recdef_2,d12_recdef_2,d8_recdef_2,d9_recdef_2,dt_k10_recdef_2,dt_k11_recdef_2,dt_k12_recdef_2,dt_k1_mcart_2,dt_k1_xboole_0,dt_k2_mcart_2,dt_k8_recdef_2,dt_k9_recdef_2,dt_m1_subset_1,existence_m1_subset_1,fc1_xboole_0,rc1_xboole_0,rc2_xboole_0,t13_mcart_2,t17_mcart_2,t1_subset,t2_subset,t6_boole,t7_boole,t8_boole]),
    [file(recdef_2,t8_recdef_2)]).

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

fof(d10_recdef_2,axiom,(
    ! [A] : 
      ( ? [B,C,D,E,F] : A = k1_mcart_2(B,C,D,E,F)
     => ! [B] : 
          ( B = k10_recdef_2(A)
        <=> ! [C,D,E,F,G] : 
              ( A = k1_mcart_2(C,D,E,F,G)
             => B = E ) ) ) ),
    file(recdef_2,d10_recdef_2),
    []).

fof(d11_recdef_2,axiom,(
    ! [A] : 
      ( ? [B,C,D,E,F] : A = k1_mcart_2(B,C,D,E,F)
     => ! [B] : 
          ( B = k11_recdef_2(A)
        <=> ! [C,D,E,F,G] : 
              ( A = k1_mcart_2(C,D,E,F,G)
             => B = F ) ) ) ),
    file(recdef_2,d11_recdef_2),
    []).

fof(d12_recdef_2,axiom,(
    ! [A] : 
      ( ? [B,C,D,E,F] : A = k1_mcart_2(B,C,D,E,F)
     => ! [B] : 
          ( B = k12_recdef_2(A)
        <=> ! [C,D,E,F,G] : 
              ( A = k1_mcart_2(C,D,E,F,G)
             => B = G ) ) ) ),
    file(recdef_2,d12_recdef_2),
    []).

fof(d8_recdef_2,axiom,(
    ! [A] : 
      ( ? [B,C,D,E,F] : A = k1_mcart_2(B,C,D,E,F)
     => ! [B] : 
          ( B = k8_recdef_2(A)
        <=> ! [C,D,E,F,G] : 
              ( A = k1_mcart_2(C,D,E,F,G)
             => B = C ) ) ) ),
    file(recdef_2,d8_recdef_2),
    []).

fof(d9_recdef_2,axiom,(
    ! [A] : 
      ( ? [B,C,D,E,F] : A = k1_mcart_2(B,C,D,E,F)
     => ! [B] : 
          ( B = k9_recdef_2(A)
        <=> ! [C,D,E,F,G] : 
              ( A = k1_mcart_2(C,D,E,F,G)
             => B = D ) ) ) ),
    file(recdef_2,d9_recdef_2),
    []).

fof(dt_k10_recdef_2,axiom,(
    $true ),
    file(recdef_2,k10_recdef_2),
    []).

fof(dt_k11_recdef_2,axiom,(
    $true ),
    file(recdef_2,k11_recdef_2),
    []).

fof(dt_k12_recdef_2,axiom,(
    $true ),
    file(recdef_2,k12_recdef_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_k2_mcart_2,axiom,(
    $true ),
    file(mcart_2,k2_mcart_2),
    []).

fof(dt_k8_recdef_2,axiom,(
    $true ),
    file(recdef_2,k8_recdef_2),
    []).

fof(dt_k9_recdef_2,axiom,(
    $true ),
    file(recdef_2,k9_recdef_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(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(t17_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)
             => ! [H] : 
                  ( m1_subset_1(H,B)
                 => ! [I] : 
                      ( m1_subset_1(I,C)
                     => ! [J] : 
                          ( m1_subset_1(J,D)
                         => ! [K] : 
                              ( m1_subset_1(K,E)
                             => F != k1_mcart_2(G,H,I,J,K) ) ) ) ) ) ) ) ),
    file(mcart_2,t17_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(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),
    []).