% Mizar problem: t47_enumset1,enumset1,242,47 
fof(t47_enumset1,conjecture,(
    ! [A,B,C,D,E] : k3_enumset1(A,B,C,D,E) = k2_xboole_0(k1_tarski(A),k2_enumset1(B,C,D,E)) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_tarski,commutativity_k2_xboole_0,dt_k1_enumset1,dt_k1_tarski,dt_k2_enumset1,dt_k2_tarski,dt_k2_xboole_0,dt_k3_enumset1,idempotence_k2_xboole_0,l51_enumset1,l55_enumset1,t42_enumset1,t4_xboole_1]),
    [file(enumset1,t47_enumset1)]).

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

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

fof(dt_k2_enumset1,axiom,(
    $true ),
    file(enumset1,k2_enumset1),
    []).

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_k3_enumset1,axiom,(
    $true ),
    file(enumset1,k3_enumset1),
    []).

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

fof(l51_enumset1,axiom,(
    ! [A,B,C,D] : k2_enumset1(A,B,C,D) = k2_xboole_0(k2_tarski(A,B),k2_tarski(C,D)) ),
    file(enumset1,l51_enumset1),
    []).

fof(l55_enumset1,axiom,(
    ! [A,B,C,D,E] : k3_enumset1(A,B,C,D,E) = k2_xboole_0(k1_enumset1(A,B,C),k2_tarski(D,E)) ),
    file(enumset1,l55_enumset1),
    []).

fof(t42_enumset1,axiom,(
    ! [A,B,C] : k1_enumset1(A,B,C) = k2_xboole_0(k1_tarski(A),k2_tarski(B,C)) ),
    file(enumset1,t42_enumset1),
    []).

fof(t4_xboole_1,axiom,(
    ! [A,B,C] : k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C)) ),
    file(xboole_1,t4_xboole_1),
    []).