% Mizar problem: t68_square_1,square_1,365,19 
fof(t68_square_1,conjecture,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => k5_square_1(k3_xcmplx_0(A,B)) = k3_xcmplx_0(k5_square_1(A),k5_square_1(B)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k3_xcmplx_0,dt_k3_xcmplx_0,dt_k5_square_1,fc1_square_1,rc1_xcmplx_0,fc3_xcmplx_0,d3_square_1]),
    [file(square_1,t68_square_1)]).

fof(commutativity_k3_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k3_xcmplx_0),
    []).

fof(dt_k3_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k3_xcmplx_0),
    []).

fof(dt_k5_square_1,axiom,(
    $true ),
    file(square_1,k5_square_1),
    []).

fof(fc1_square_1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_xcmplx_0(k5_square_1(A)) ) ),
    file(square_1,fc1_square_1),
    []).

fof(rc1_xcmplx_0,axiom,(
    ? [A] : v1_xcmplx_0(A) ),
    file(xcmplx_0,rc1_xcmplx_0),
    []).

fof(fc3_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => v1_xcmplx_0(k3_xcmplx_0(A,B)) ) ),
    file(xcmplx_0,fc3_xcmplx_0),
    []).

fof(d3_square_1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k5_square_1(A) = k3_xcmplx_0(A,A) ) ),
    file(square_1,d3_square_1),
    []).