% Mizar problem: t75_enumset1,enumset1,508,55 
fof(t75_enumset1,conjecture,(
    ! [A,B,C,D,E,F,G] : k6_enumset1(A,A,B,C,D,E,F,G) = k5_enumset1(A,B,C,D,E,F,G) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_tarski,commutativity_k2_xboole_0,dt_k1_tarski,dt_k2_tarski,dt_k2_xboole_0,dt_k4_enumset1,dt_k5_enumset1,dt_k6_enumset1,idempotence_k2_xboole_0,t56_enumset1,t63_enumset1,t69_enumset1]),
    [file(enumset1,t75_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_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

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_k4_enumset1,axiom,(
    $true ),
    file(enumset1,k4_enumset1),
    []).

fof(dt_k5_enumset1,axiom,(
    $true ),
    file(enumset1,k5_enumset1),
    []).

fof(dt_k6_enumset1,axiom,(
    $true ),
    file(enumset1,k6_enumset1),
    []).

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

fof(t56_enumset1,axiom,(
    ! [A,B,C,D,E,F,G] : k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k1_tarski(A),k4_enumset1(B,C,D,E,F,G)) ),
    file(enumset1,t56_enumset1),
    []).

fof(t63_enumset1,axiom,(
    ! [A,B,C,D,E,F,G,H] : k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k2_tarski(A,B),k4_enumset1(C,D,E,F,G,H)) ),
    file(enumset1,t63_enumset1),
    []).

fof(t69_enumset1,axiom,(
    ! [A] : k2_tarski(A,A) = k1_tarski(A) ),
    file(enumset1,t69_enumset1),
    []).