% Mizar problem: t22_mcart_3,mcart_3,924,15 
fof(t22_mcart_3,conjecture,(
    ! [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))
           => ( k3_mcart_3(A,B,C,D,E,F,G) = k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(G)))))
              & k4_mcart_3(A,B,C,D,E,F,G) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(G)))))
              & k5_mcart_3(A,B,C,D,E,F,G) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(G))))
              & k6_mcart_3(A,B,C,D,E,F,G) = k2_mcart_1(k1_mcart_1(k1_mcart_1(G)))
              & k7_mcart_3(A,B,C,D,E,F,G) = k2_mcart_1(k1_mcart_1(G))
              & k8_mcart_3(A,B,C,D,E,F,G) = k2_mcart_1(G) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,d1_mcart_2,d1_mcart_3,d2_mcart_3,d3_mcart_1,d4_mcart_1,dt_k1_mcart_1,dt_k1_mcart_2,dt_k1_mcart_3,dt_k1_xboole_0,dt_k2_mcart_1,dt_k2_mcart_2,dt_k2_mcart_3,dt_k2_zfmisc_1,dt_k3_mcart_1,dt_k3_mcart_3,dt_k4_mcart_1,dt_k4_mcart_3,dt_k4_tarski,dt_k5_mcart_3,dt_k6_mcart_3,dt_k7_mcart_3,dt_k8_mcart_3,dt_m1_subset_1,existence_m1_subset_1,fc1_xboole_0,rc1_xboole_0,rc2_xboole_0,t1_subset,t21_mcart_3,t2_subset,t6_boole,t7_boole,t7_mcart_1,t8_boole]),
    [file(mcart_3,t22_mcart_3)]).

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

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(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_1,axiom,(
    ! [A,B,C] : k3_mcart_1(A,B,C) = k4_tarski(k4_tarski(A,B),C) ),
    file(mcart_1,d3_mcart_1),
    []).

fof(d4_mcart_1,axiom,(
    ! [A,B,C,D] : k4_mcart_1(A,B,C,D) = k4_tarski(k3_mcart_1(A,B,C),D) ),
    file(mcart_1,d4_mcart_1),
    []).

fof(dt_k1_mcart_1,axiom,(
    $true ),
    file(mcart_1,k1_mcart_1),
    []).

fof(dt_k1_mcart_2,axiom,(
    $true ),
    file(mcart_2,k1_mcart_2),
    []).

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_1,axiom,(
    $true ),
    file(mcart_1,k2_mcart_1),
    []).

fof(dt_k2_mcart_2,axiom,(
    $true ),
    file(mcart_2,k2_mcart_2),
    []).

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

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

fof(dt_k3_mcart_1,axiom,(
    $true ),
    file(mcart_1,k3_mcart_1),
    []).

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_1,axiom,(
    $true ),
    file(mcart_1,k4_mcart_1),
    []).

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

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

fof(t21_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))
           => G = k1_mcart_3(k3_mcart_3(A,B,C,D,E,F,G),k4_mcart_3(A,B,C,D,E,F,G),k5_mcart_3(A,B,C,D,E,F,G),k6_mcart_3(A,B,C,D,E,F,G),k7_mcart_3(A,B,C,D,E,F,G),k8_mcart_3(A,B,C,D,E,F,G)) ) ) ),
    file(mcart_3,t21_mcart_3),
    []).

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(t7_mcart_1,axiom,(
    ! [A,B] : 
      ( k1_mcart_1(k4_tarski(A,B)) = A
      & k2_mcart_1(k4_tarski(A,B)) = B ) ),
    file(mcart_1,t7_mcart_1),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).