% Mizar problem: t40_mcart_5,mcart_5,1841,32 
fof(t40_mcart_5,conjecture,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P] : 
      ( r2_hidden(k1_mcart_5(A,B,C,D,E,F,G,H),k2_mcart_5(I,J,K,L,M,N,O,P))
    <=> ( r2_hidden(A,I)
        & r2_hidden(B,J)
        & r2_hidden(C,K)
        & r2_hidden(D,L)
        & r2_hidden(E,M)
        & r2_hidden(F,N)
        & r2_hidden(G,O)
        & r2_hidden(H,P) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,d1_mcart_5,d2_mcart_5,dt_k1_mcart_4,dt_k1_mcart_5,dt_k1_xboole_0,dt_k2_mcart_4,dt_k2_mcart_5,dt_k2_zfmisc_1,dt_k4_tarski,dt_m1_subset_1,existence_m1_subset_1,fc1_xboole_0,rc1_xboole_0,rc2_xboole_0,t106_zfmisc_1,t18_mcart_5,t1_subset,t2_subset,t37_mcart_4,t6_boole,t7_boole,t8_boole,t9_mcart_5]),
    [file(mcart_5,t40_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_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_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_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

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(t106_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,D) ) ) ),
    file(zfmisc_1,t106_zfmisc_1),
    []).

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(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(t37_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N] : 
      ( r2_hidden(k1_mcart_4(A,B,C,D,E,F,G),k2_mcart_4(H,I,J,K,L,M,N))
    <=> ( r2_hidden(A,H)
        & r2_hidden(B,I)
        & r2_hidden(C,J)
        & r2_hidden(D,K)
        & r2_hidden(E,L)
        & r2_hidden(F,M)
        & r2_hidden(G,N) ) ) ),
    file(mcart_4,t37_mcart_4),
    []).

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),
    []).

fof(t9_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H] : k1_mcart_5(A,B,C,D,E,F,G,H) = k1_mcart_4(k4_tarski(A,B),C,D,E,F,G,H) ),
    file(mcart_5,t9_mcart_5),
    []).