% Mizar problem: t28_mod_2,mod_2,621,60 
fof(t28_mod_2,conjecture,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => m1_subset_1(k1_enumset1(B,C,D),A) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k5_classes2,commutativity_k7_classes2,dt_k1_classes2,dt_k1_enumset1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_tarski,dt_k2_xboole_0,dt_k5_classes2,dt_k7_classes2,dt_m1_subset_1,existence_m1_subset_1,fc1_xboole_0,fc2_mod_2,fc2_subset_1,fc2_xboole_0,fc3_subset_1,fc3_xboole_0,idempotence_k2_xboole_0,idempotence_k7_classes2,rc1_xboole_0,rc2_xboole_0,redefinition_k1_classes2,redefinition_k5_classes2,redefinition_k7_classes2,t1_boole,t1_subset,t2_subset,t43_enumset1,t6_boole,t7_boole,t8_boole]),
    [file(mod_2,t28_mod_2)]).

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

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(commutativity_k5_classes2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k5_classes2(A,B,C) = k5_classes2(A,C,B) ) ),
    file(classes2,k5_classes2),
    []).

fof(commutativity_k7_classes2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k7_classes2(A,B,C) = k7_classes2(A,C,B) ) ),
    file(classes2,k7_classes2),
    []).

fof(dt_k1_classes2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m1_subset_1(B,A) )
     => m1_subset_1(k1_classes2(A,B),A) ) ),
    file(classes2,k1_classes2),
    []).

fof(dt_k1_enumset1,axiom,(
    $true ),
    file(enumset1,k1_enumset1),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

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

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

fof(dt_k5_classes2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => m1_subset_1(k5_classes2(A,B,C),A) ) ),
    file(classes2,k5_classes2),
    []).

fof(dt_k7_classes2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => m1_subset_1(k7_classes2(A,B,C),A) ) ),
    file(classes2,k7_classes2),
    []).

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(fc2_mod_2,axiom,(
    ! [A,B,C] : ~ v1_xboole_0(k1_enumset1(A,B,C)) ),
    file(mod_2,fc2_mod_2),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc2_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ),
    file(xboole_0,fc2_xboole_0),
    []).

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    []).

fof(fc3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_xboole_0),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(idempotence_k7_classes2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k7_classes2(A,B,B) = B ) ),
    file(classes2,k7_classes2),
    []).

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(redefinition_k1_classes2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m1_subset_1(B,A) )
     => k1_classes2(A,B) = k1_tarski(B) ) ),
    file(classes2,k1_classes2),
    []).

fof(redefinition_k5_classes2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k5_classes2(A,B,C) = k2_tarski(B,C) ) ),
    file(classes2,k5_classes2),
    []).

fof(redefinition_k7_classes2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k7_classes2(A,B,C) = k2_xboole_0(B,C) ) ),
    file(classes2,k7_classes2),
    []).

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

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(t43_enumset1,axiom,(
    ! [A,B,C] : k1_enumset1(A,B,C) = k2_xboole_0(k2_tarski(A,B),k1_tarski(C)) ),
    file(enumset1,t43_enumset1),
    []).

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),
    []).